CHAPTER 1
INTRODUCTION
GENERAL
India is a large subcontinent offering different routes and modes of travel between two given places. Therefore choice of the most appropriate route needs complex analysis of each and every route depending on a number of factors that may influence the efficiency of the route. For the last few years, the route choice problem has been a major research area in the field of transport planning. Due to the complexity and dynamicity of the routes, determining the optimal route is not an easy task. Also, the combination of transport modes available for different routes are large in number, so the decision to select the optimal mode requires huge analysis. Route assignment or route choice concerns the selection of the route (alternatively called paths) between the origin and the destination in transportation networks [20].The route choice problem deals with finding the best route to reach the destination by using single appropriate transport mode or using appropriate combination of modes of transport. Due to the complexity of the modes of transport, research has moved towards soft computing and artificial intelligence. Once solved the solution will have many transport applications. There are several factors that influence choice of route such as travel time, comfort factor, etc. Several models have been developed taking into account all these factors and considering all available modes.
Recent Intelligent Transportation Systems (ITS) applications have highlighted the need for better models of the behavioral processes involved in route choice [19]. In the past several decades a variety of deterministic and/or stochastic models have been developed to solve complex traffic and transportation engineering problems. These mathematical models use objective knowledge to form equations formulating the problems and solve them to arrive at required results. But, while solving real-life transportation problems, subjective factors are ignored because of inability to quantify those using mathematical techniques [21]. The deterministic and stochastic models though theoretically exact are unable to provide satisfactory solutions. On the other hand, a wide range of traffic and transportation engineering parameters are characterized by uncertainty, subjectivity, imprecision and ambiguity. Human operators, dispatchers, drivers and passengers use this subjective knowledge or linguistic information on a daily basis when making decisions [21]. Thus for solving real-life traffic and transportation problems we should not use only objective knowledge (formulae and equations) but also incorporate subjective knowledge (linguistic information). It has been observed that fuzzy logic technique is a popular and powerful tool among researchers for route selection and finding optimum route [56] because it combines the concept of both objective and subjective knowledge. Techniques using fuzzy logic take care of the inherent weaknesses of exact mathematical models.
MOTIVATION
In recent years, economic prosperity has reached a wider section of society. Consequently people are travelling a lot more. They undertake business trips, pleasure trips, pilgrimage and more recently medically tourism in search of affordable health care. Therefore classical route choice problems have to incorporate several factors such as economy combined with comfort and convenience of travel. On account of increased variety of modes of transport routes available between any two given places, choice of most appropriate routs is not an easy task. The challenge posed by route choice problem is thus both intense as well as rewarding.
TRAVELLING ROUTE CHOICE PROBLEM
Route choice along with the choice of mode of transportation plays an important role in deciding about a better transport plan. Selecting parameters of most of the transportation problems is based on subjectivity. Human operators, dispatchers, drivers and passengers use this subjective knowledge or linguistic information on a daily basis while making decisions. The problems dealing with choice of route, mode of transportation, traveler’s perception, his preferences, are all subjective. Therefore models employing binary logic and based on deterministic and stochastic methods are not sufficient on account of their inability to deal with the uncertainty, vagueness and ambiguity of traveler’s decisions. In this context methods based on fuzzy logic are more appropriate to cope with the uncertainties of decisions of individuals.
GOAL
The present work aims at incorporating the subjectivity of decision making in route choice models. The tourism industry has grown exponentially. Therefore classic route choice models have proved insufficient because of increased number of paths. My goal is to employ fuzzy logic in order to arrive at preferred path taking into account various personal preferences of the traveler.
1.5 THESIS OUTLINE
The thesis is organized into six chapters. The first chapter contains the introduction, the problem description and the objectives to be achieved. The second chapter includes literature review of all the routing systems developed in travelling networks, and review of fuzzy logic in detail. It also includes the description of developing fuzzy inference system. The third chapter consists of the mathematical analysis of the route and mode selection system according to the affecting factors. The fourth chapter undertakes the description of the fuzzy rule based system developed for the route and mode selection. The implementation of the routing system based on fuzzy rule base is done on MATLAB and explained in chapter five. Finally, the sixth chapter concludes the thesis and indicates the future research area.
CHAPTER 2
LITERATURE REVIEW
2.1 GENERAL
The shortest distance route system was originated in the year 1954 when G. Dantzig, R. Fulkerson, and S. Johnson proposed the dantzig42 that solved a route that passed through 42 cities [23].The route choice problem has been dealt with employing several techniques using mostly the logit and probit models by Ben-Akiva and Lerman in 1985[9] and Bekhor in 2002[8]. But these models didn’t take into account the uncertainty and subjectivity of perceptions. Also they are not efficient in dealing with the dynamic routing environment. To solve these problems, some researchers worked towards the fuzzy set theory area of soft computing. Teodorovic and Kikuchi, in 1990, first modeled the simple two-route choice problem for selecting the better route [58]. Route choice behavior is also considered by using fuzzy reasoning by Akiyama in 1993[1]. This approach has been improved further by Akiyama and Tsuboi in 1996 by developing a multi ‘ stage fuzzy reasoning approach for solving multi-route choice problem [4]. For decision making, two stages are developed. In the first, travel time, degree of congestion, and risk of accidents are used as factors to determine the feasible route. The second determines the frequency degree for each route based on the difference between shortest path and second shortest path.
Lotan and Koutsopoulos in 1993 developed a framework for route choice which uses the information based on fuzzy logic and reasoning[37].Later, they improved their model in 1998 by dividing their framework in two parts, the first one deals with integration of information and second specifies the decision process[40].
For long distance transport, a single mode of transportation cannot meet the requirements of the user or customer. So, in the process of multimodal transport, selection of transport routes one has to attain thorough knowledge of the relative merits of various modes of transport. For these reasons, multimodal transport has become an important research area. In the multimodal transport network, Southworth F and Peterson BE [55] constructed a model of intermodal and international freight network. To solve the prevalent problem of the low information level and lack of decision support system for multimodal transport in China, Wang Tao and Wang Gang [71] built a combined optimization model. Jiang Jun and Lu Jian [29] established an optimized model taking system optimal performance index of the multimodal transportation network as a goal and used genetic algorithm to solve the problem.
Several researches continued after 2000 incorporating more factors to solve complex multi route problems. In 2000, Henn has improved the fuzzy route choice model considering the account imprecision and uncertainty [26].In 2004, Ridwan considers the spatial knowledge of individual travelers and proposed a model of route choice based on traveler’s preference [51]. Peeta and Yu in 2004 used a hybrid probabilistic model to quantify the alternative routes with respect to qualitative variables [46]. In 2005, Arslan and Khysti propose a hybrid model which combines the concepts from fuzzy logic and analytic hierarchy process AHP [7]. The route selection is given by comparing routes pairwise considering the related factors like travel time, congestion and safety.
The work has been improved by integrating the multiagent systems with artificial intelligence. The interacting agents might be drivers, passengers, etc. For real-time traffic information, Panwai and Dia developed a model in 2006 where drivers act as intelligent agents [44]. The agent’s knowledge specific and relevant to the choice of route is constructed using fuzzy approach.
In 2008, Chu-Hsing Lin and Jui-Ling Yu proposed the genetic algorithm to alleviate the rising computational cost [16]. They used the genetic algorithm to find the shortest time in driving with diverse scenarios of real traffic conditions and varying vehicle speeds. The effectiveness of the algorithm is determined by applying it on a map of modern city with very large number of vertices. They used the Intelligent Transportation System (ITS) which provided route guidance and the map information. It has the sensing technologies and provided the driving information feedback from the users that support the system. They applied both the Dijkstra’s algorithm and the genetic algorithm to compute the shortest driving time. They found that as the number of nodes increases, the memory required by the Dijkstras goes beyond the limited memory of embedded system. They showed that results of genetic algorithm converge relatively faster even with large amount of nodes. Thus the genetic algorithm was found to be more appropriate for handheld devices to find approximately optimal paths.
The Ant algorithm is used in several applications of route finding problems in transportation networks. In 2008, Hojjat Salehinejad, Farhad Pouladi and Siamak Talebi developed a dynamic Multiparameter Ant algorithm based route selection system [27]. This system finds the optimal route between any given origin and destination. In the process of finding the optimal route, it considers some of the most important parameters such as distance, traffic, width (number of lines), number of traffic lights, and accident history. The traffic is considered in offline and online mode. This method recognizes routes according to user desired parameters in two traffic information availability (online/offline) modes. The proposed method is simulated on a part of London, UK, and is executed locally for every single car and finds optimum multiparameter direction between Origin/Destination. They found the feasible results by this algorithm.
Wang Qingbin and Hang Zengxia observed that time delay often happens in the transportation and very few articles considered the delay [70]. Therefore trying to arrive at the optimal transport routes and the optimal combination of the transport modes, they constructed a model in 2010 for container multimodal transportation to minimize the total cost that included transportation costs between nodes, transfer costs and average delay costs for model change in the nodes and the overall solution. They also gave an algorithm to solve the model.
In 2011, Zhang Bing-Chuan, Li Bin-Bing, Liu Da-Wei, Zhang Shu-Hui utilized the combined arithmetic based on the Grey Theory and Markov Chain to predict traffic-flow which increased the prediction accuracy[74].They studied that short-term traffic-flow is the theoretical basis for selecting the optimal route, as it utilizes historical and real-time traffic data to predict traffic status within an hour, and then offers the information to travelers which facilitates the choice of optimal route; such a prediction directly affects the routes. They employed the combined arithmetic by taking an example and showed that the combined arithmetic has better prediction accuracy.
Chin-Jung Huang integrated the Hungarian Method and Genetic Algorithm, and constructed the shortest distance route system for traveling in 2012[15]. They studied the d15112 system for a city number up to 15,112 given by D. Applegate, R. Bixby, V.Chvatal, and W. Cook in 2001[17] which was very time-consuming and needed expensive hardware. The system designed by Chin-Jung Huang needs only personal computer to find the shortest distance route and the corresponding distance quickly and effectively. The lower limit of the shortest distance of all routes is determined using the improved Hungarian method of the assignment problems, and is used to check whether the obtained shortest distance or approximately shortest distance meets the requirements. The system is developed using DEV-C ++ based genetic algorithm.
Hitoshi Kanoh and Tomohiro Nakamura studied the route choice problem under a dynamic environment [25]. They used a genetic algorithm which employs the method of viruses as domain specific knowledge. A part of an arterial road is regarded as a virus. They generated a population of viruses in addition to a population of routes. Crossover and infection are used to determine the optimal combination of viruses. When traffic congestion changes during driving, an alternative route can be generated using viruses and other routes in the population in the shortest time. They showed by their experiments that genetic algorithm is superior to Dijkstra’s Algorithm in case of randomly generated road maps and only slightly inferior regarding the length of the route. They also determined that the computational time is meeting deadlines in dynamic route selection problem using actual road maps that are in widespread use for car navigation systems. They also proposed a solution to constraint satisfaction problem.
A paper by Habib M. Kammoun of Tunisia concludes that it is extremely hard to formulate a suitable mathematical model due to uncertainty and dynamicity of several factors [24]. Thus the development of Fuzzy Rule Base System is more appropriate as it has the capability to approximate a real continuous function with a good accuracy. But its application is difficult due to large number of criteria, thus they proposed a route choice model based on hierarchical FRBS. This system evaluates one possible path based on real-time information, driver’s preferences, and other factors. This route choice model is based on organizational multiagent architecture of road network.
The concept of fuzzy logic has been used in many applications of transport. Pappis and Mamdani (1977) [45] solved the practical traffic and transportation problem using fuzzy logic. In the mid- and late-1980s, a group of Japanese authors made a significant contribution to fuzzy set theory applications in traffic and transportation. Nakatsuyama et al. (1983) [43], Sugeno and Nishida (1985) [57] and particularly Sasaki and Akiyama, (1986, 1987, 1988) [52, 53, 54] solved complex traffic and transportation problems by using fuzzy logic techniques. At the end of 1980s and beginning of the 1990s, the fuzzy set theory in traffic and transportation was extensively used at American universities. The pioneering work of the research team of the University of Delaware which include Professor Shinya Kikuchi (Chakroborthy, 1990 [10]; Chakroborthy and Kikuchi, 1990 [11]; Perincherry, 1990 [47];Perincherry and Kikuchi, 1990 [48]; Teodorovic?? and Kikuchi, (1990, 1991) [63, 64]; Kikuchi et al.,(1991, 1993) [35, 34]; Kikuchi, 1992 [33]) deserve special mention for employing fuzzy logic.
Different traffic and transportation problems successfully solved using fuzzy set theory techniques were presented in the works of Chen et al. (1990) [14], Tzeng et al. (1996) [66], Lotan and Koutsopoulos(1993a,b) [38, 39], Xu and Chan, 1993a,b) [72, 73], Teodorovic?? and Babic?? (1993) [59],Akiyama and Shao (1993) [3], Chang and Shyu (1993) [13], Chanas et al. (1993) [12], Akiyamaand Yamanishi (1993) [6], Deb (1993) [18], Perkinson (1994) [49], Hsiao et al. (1994) [28],Vukadinovic?? and Teodorovic?? (1994) [68], Teodorovic?? et al. (1994) [60], Teodorovic??(1994) [61], Teodorovic?? and Kalic?? (1995) [62], Milosavljevic?? et al. (1996) [42], Teodorovicand Pavkovic (1996) [65] and Tzeng et al. (1996) [66].
2.2 FUZZY LOGIC
In the literature sources, we can find different kinds of justification for fuzzy systems theory. Human knowledge nowadays becomes increasingly important ‘ we gain it from experiencing the world within which we live and use our ability to reason to create order in the mass of information (i.e., to formulate human knowledge in a systematic manner). Since we are all limited in our ability to perceive the world and to profound reasoning, we find ourselves everywhere confronted by uncertainty which is a result of lack of information (lexical impression, incompleteness), in particular, inaccuracy of measurements. The other limitation factor in our desire for precision is a natural language used for describing/sharing knowledge, communication, etc. We understand core meanings of word and are able to communicate accurately to an acceptable degree, but generally we cannot precisely agree among ourselves on the single word or terms of common sense meaning. In short, natural languages are vague.
Our perception of the real world is pervaded by concepts which do not have sharply defined boundaries ‘ for example, many, tall, much larger than, young, etc. are true only to some degree and they are false to some degree as well. These concepts (facts) can be called fuzzy or gray (vague) concepts ‘ a human brain works with them, while computers may not do it (they reason with strings of 0s and 1s). Natural languages, which are much higher in level than programming languages, are fuzzy whereas programming languages are not. The door to the development of fuzzy computers was opened in 1985 by the design of the first logic chip by Masaki Togai and Hiroyuki Watanabe at Bell Telephone Laboratories.
The Fuzzy Logic tool was introduced in 1965, also by LotfiZadeh, and is a mathematical tool for dealing with uncertainty. It offers to a soft computing partnership the important concept of computing with words’. It provides a technique to deal with imprecision and information granularity. The fuzzy theory provides a mechanism for representing linguistic constructs such as ‘many,’ ‘low,’ ‘medium,’ ‘often,’ ‘few.’ In general, the fuzzy logic provides an inference structure that enables appropriate human reasoning capabilities.
A fuzzy set is an extension of a classical set. If X is the universe of discourse and its elements are denoted by x, then a fuzzy set A in X is defined as a set of ordered pairs.
A = {x, ??A(x) | x ‘ X}
??A(x) is called the membership function (or MF) of x in A. The membership function maps each element of X to a membership value between 0 and 1. A membership function (MF) is a curve that defines how each point in the input space is mapped to a membership value (or degree of membership) between 0 and 1.
Fig. 2.1 trimf and trapmf membership functions
Two membership functions are built on the Gaussian distribution curve: a simple Gaussian curve and a two-sided composite of two different Gaussian curves. The two functions are gaussmf and gauss2mf.
The generalized bell membership function is specified by three parameters and has the function name gbellmf. The bell membership function has one more parameter than the Gaussian membership function, so it can approach a non-fuzzy set if the free parameter is tuned. Because of their smoothness and concise notation, Gaussian and bell membership functions are popular methods for specifying fuzzy sets. Both of these curves have the advantage of being smooth and nonzero at all points.
Fig. 2.2 gaussmf, gauss2mf and gbellmf membership functions
Although the Gaussian membership functions and bell membership functions achieve smoothness, they are unable to specify asymmetric membership functions, which are important in certain applications. Next the sigmoidal membership functions defined which is either open left or right. Asymmetric and closed (i.e. not open to the left or right) membership functions can be synthesized using two sigmoidal functions, so in addition to the basic sigmf, also have the difference between two sigmoidal functions, dsigmf, and the product of two sigmoidal functions psigmf.
Fig. 2.3 sigmf, dsigmfand psigmf membership functions
Polynomial based curves account for several of the membership functions in the toolbox. Three related membership functions are the Z, S, and Pi curves, all named because of their shape. The function zmf is the asymmetrical polynomial curve open to the left, smf is the mirror-image function that opens to the right, and pimf is zero on both extremes with a rise in the middle. There’s a very wide selection to choose from when you’re selecting your favorite membership function.
Fig. 2.4 zmf, pimf and smf membership functions
The Fuzzy Logic Toolbox provides GUIs to let you perform classical fuzzy system development and pattern recognition. Using the toolbox, you can:
Develop and analyze fuzzy inference systems
Develop adaptive neurofuzzy inference systems
Perform fuzzy clustering
2.3 FUZZY INFERENCE SYSTEM
The basic elements of every fuzzy logic system are rules, fuzzifier, inference engine and defuz-zifier (Fig. 2.5).
Fig. 2.5 Fuzzy Logic System
Input data are most often crisp values. The task of the fuzzifier is to map crisp numbers into fuzzy sets (cases are also encountered where inputs are fuzzy variables described by fuzzy membership functions). Models based on fuzzy logic consist of `If Then’ rules. Interpreting if-then rules is a three-part process.
Fuzzify inputs: Resolve all fuzzy statements in the antecedent to a degree of membership between 0 and 1. If there is only one part to the antecedent, this is the degree of support for the rule.
Apply fuzzy operator to multiple part antecedents: If there are multiple parts to the antecedent, apply fuzzy logic operators and resolve the antecedent to a single number between 0 and 1. This is the degree of support for the rule.
Apply implication method: Use the degree of support for the entire rule to shape the output fuzzy set. The consequent of a fuzzy rule assigns an entire fuzzy set to the output. This fuzzy set is represented by a membership function that is chosen to indicate the qualities of the consequent. If the antecedent is only partially true, (i.e., is assigned a value less than 1), then the output fuzzy set is truncated according to the implication method.
A typical `If Then’ rule would be:
if distance is less and traffic and road conditions are good, then path preference of road is good.
The fact following `If’ is called a premise or hypothesis or antecedent. Based on this fact it can infer another fact that is called a conclusion or consequent (the fact following `Then’). A set of a large number of rules of the type:
‘If premise then conclusion’ is called a fuzzy rule base.
Fuzzy inference is the process of formulating the mapping from a given input to an output using fuzzy logic. The mapping then provides a basis from which decisions can be made, or patterns discerned. The process of fuzzy inference involves all of the pieces like: membership functions, fuzzy logic operators, and if-then rules. The working of FIS is as follows. The crisp input is converted in to fuzzy by using fuzzification method. After fuzzification the rule base is formed. The rule base and the database are jointly referred to as the knowledge base. Defuzzification is used to convert fuzzy value to the real world value which is the output. The steps of fuzzy reasoning (inference operations upon fuzzy IF’THEN rules) performed by FISs are [56]:
Compare the input variables with the membership functions on the antecedent part to obtain the membership values of each linguistic label. (This step is often called fuzzification.)
Combine (through a specific t-norm operator, usually multiplication or min) the membership values on the premise part to get firing strength (weight) of each rule.
Generate the qualified consequents (either fuzzy or crisp) or each rule depending on the firing strength.
Aggregate the qualified consequents to produce a crisp output. (This step is called defuzzification.)
Mamdani’s Method
The most important type of fuzzy inference method is Mamdani’s fuzzy inference method, which is the most commonly seen inference method. This method was introduced by Mamdani and Assilian (1975). Another well-known inference method is the so-called Sugeno or Takagi’Sugeno’Kang method of fuzzy inference process. This method was introduced by Sugeno (1985). This method is also called as TS method. The main difference between the two methods lies in the consequent of fuzzy rules. Mamdani fuzzy systems use fuzzy sets as rule consequent whereas TS fuzzy systems employ linear functions of input variables as rule consequent. All the existing results on fuzzy systems as universal approximators deal with Mamdani fuzzy systems only and no result is available for TS fuzzy systems with linear rule consequent[56].
An example of a Mamdani inference system is shown in Fig. 2.6. To compute the output of this FIS given the inputs, six steps have to be followed [56]:
Fig. 2.6 A two input, two rule Mamdani FIS with a fuzzy input
Determining a set of fuzzy rules
Fuzzifying the inputs using the input membership functions
Combining the fuzzified inputs according to the fuzzy rules to establish a rule strength
Finding the consequence of the rule by combining the rule strength and the output membership function
Combining the consequences to get an output distribution
Defuzzifying the output distribution (this step is only if a crisp output (class) is needed). There are two common techniques for defuzzifying: Center of mass and Mean of maximum.
In summary, Fig. 2.6 shows a two input Mamdani FIS with two rules. It fuzzifies the two inputs by finding the intersection of the crisp input value with the input membership function. It uses the minimum operator to compute the fuzzy AND for combining the two fuzzified inputs to obtain rule strength. It clips the output membership function at the rule strength. Finally, it uses the maximum operator to compute the fuzzy OR for combining the outputs of the two rules.
Takagi’Sugeno Fuzzy Method (TS Method)
The Sugeno fuzzy model was proposed by Takagi, Sugeno, and Kang in an effort to formalize a system approach to generating fuzzy rules from an input’output data set. Sugeno fuzzy model is also known as Sugeno’Takagi model. A typical fuzzy rule in a Sugeno fuzzy model has the format
IF x is A and y is B THEN z = f(x, y),
where AB are fuzzy sets in the antecedent; Z = f(x, y) is a crisp function in the consequent.
Usually f(x, y) is a polynomial in the input variables x and y, but it can be any other functions that can appropriately describe the output of the output of the system within the fuzzy region specified by the antecedent of the rule. When f(x, y) is a first-order polynomial, we have the first-order Sugeno fuzzy model. When f is a constant, we then have the zero-order Sugeno fuzzy model, which can be viewed either as a special case of the Mamdani FIS where each rule’s consequent is specified by a fuzzy singleton, or a special case of Tsukamoto’s fuzzy model where each rule’s consequent is specified by a membership function of a step function centered at the constant. Moreover, a zero-order Sugeno fuzzy model is functionally equivalent to a radial basis function network under certain minor constraints.
The first two parts of the fuzzy inference process, fuzzifying the inputs and applying the fuzzy operator, are exactly the same. The main difference between Mamdani and Sugeno is that the Sugeno output membership functions are either linear or constant. A typical rule in a Sugeno fuzzy model has the form
IF Input 1 = x AND Input 2 = y, THEN Output is z = ax + by + c.
Because of the linear dependence of each rule on the input variables of a system, the Sugeno method is ideal for acting as an interpolating supervisor of multiple linear controllers that are to be applied, respectively, to different operating conditions of a dynamic nonlinear system. For example, the performance of an aircraft may change dramatically with altitude and Mach number. Linear controllers, though easy to compute and well suited to any given flight condition, must be updated regularly and smoothly to keep up with the changing state of the flight vehicle. A Sugeno FIS is extremely well suited to the task of smoothly interpolating the linear gains that would be applied across the input space; it is a natural and efficient gain scheduler. Similarly, a Sugeno system is suited for modeling nonlinear systems by interpolating between multiple linear models.
Because it is a more compact and computationally efficient representation than a Mamdani system, the Sugeno system lends itself to the use of adaptive techniques for constructing fuzzy models. These adaptive techniques can be used to customize the membership functions so that the fuzzy system best models the data.
Fuzzy inference systems have been successfully applied in fields such as automatic control, data classification, decision analysis, expert systems, and computer vision. Because of its multidisciplinary nature, fuzzy inference systems are associated with a number of names, such as fuzzy-rule-based systems, fuzzy expert systems, fuzzy modeling, fuzzy associative memory, fuzzy logic controllers, and simply (and ambiguously) fuzzy systems.
In classical expert systems, rules are derived exclusively from human experts. In fuzzy rule-based systems, the rule base is formed with the assistance of human experts. Drivers, passengers or dispatchers make decisions about route choice, mode of transportation, most suitable departure time or dispatching trucks. In each case the decision-maker is a human. The environment in which a human expert (human controller) makes his decisions is most often very complicated, making it extremely hard to formulate a suitable mathematical model. Thus, the development of fuzzy logic systems seems justified in such situations.
2.4 BUILDING FUZZY INFERENCE SYSTEM USING MATLAB
Fuzzy inference is a method that interprets the values in the input vector and, based on user-defined rules, assigns values to the output vector. Using the GUI editors and viewers in the Fuzzy Logic Toolbox, you can build the rules set, define the membership functions, and analyze the behavior of a fuzzy inference system (FIS). The following editors and viewers are provided [22]:
FIS Editor ‘ Displays general information about a fuzzy inference system
Membership Function Editor ‘ Lets the user display and edit the membership functions associated with the input and output variables of the FIS
Rule Editor ‘ Lets the user view and edit fuzzy rules using one of three formats: full English-like syntax, concise symbolic notation, or an indexed notation
Rule Viewer ‘ Lets the user view detailed behavior of a FIS to help diagnose the behavior of specific rules or study the effect of changing input variables
Surface Viewer ‘ Generates a 3-D surface from two input variables and the output of an FIS
Fig. 2.7 Fuzzy Logic Toolbox Editors
Key features of Fuzzy Inference System ‘
Fuzzy Logic Design application for building fuzzy inference systems and viewing and analyzing results
Membership functions for creating fuzzy inference systems
Support for AND, OR, and NOT logic in user-defined rules
Standard Mamdani and Sugeno-type fuzzy inference systems
Automated membership function shaping through neuroadaptive and fuzzy clustering learning techniques
Ability to embed a fuzzy inference system in a Simulink model
Ability to generate embeddable C code or stand-alone executable fuzzy inference engines
2.5 SOME APPLICATIONS OF FUZZY LOGIC IN TRANSPORT PLANNING
Trip Generation
The fuzzy logic has made inroads into several models for transport planning in recent years. It is proposed to have perspective of these applications of fuzzy logic. Trip generation is one of the steps of transportation forecast process in which travel demands are forecasted. Basically it determines the number of people that want to go on trip and their individual purpose. So as the time progressed, experts have constructed variety of models to estimate the number of generated trips in a better method and to decrease the previous models shortcomings as much as possible.
Trip distribution models are used to determine the number of trips between pairs of zones when the number of trips generated attracted by particular zones is known. Thus, the prediction of trip distribution involves the prediction of flows in a network regardless of a possible transportation mode or travel route. Trip distribution problem using fuzzy logic was also tackled by Kalic and Teodorovic (1996, 1997a, b [30, 31, 32].
Modal split
Wang and Mendel in (1992a) proposed a technique to generate the fuzzy rule base by learning from examples. The results obtained using fuzzy logic and real results were very good. Quadrado and Quadrado (1996) [50] used fuzzy logic to determine the accessibility of different transportation modes in the Lisbon Metropolitan Area. The authors first pointed out that all variables used in the ‘classical’ way of calculating accessibility are characterized by fuzziness.
Route choice
In the past four decades, the route choice problem has been considered by a large number of authors worldwide. Teodorovic and Kikuchi (1990) [63] were first to model the complex route choice problem using fuzzy logic. They used fuzzy inference techniques to study the binary route choice problem. Akiyama et al. (1993) [6] also developed a model for route choice behavior based on the fuzzy reasoning approach. Lotan andKoutsopoulos (1993a, b) [38, 39] developed models for route choice behavior in the presence of information based on concepts from approximate reasoning and fuzzy control. The research of Lotan and Koutsopoulos (1993a, b) [38, 39] is particularly important within the context of ongoing research in Intelligent Vehicle Highway Systems (IVHS). Teodorovic and Kalic (1995) [62] developed an approximate reasoning algorithm to solve the route choice problem in air transportation. Akiyama and Tsuboi (1996) [5] studied route choice behavior by multi-stage fuzzy reasoning.
CHAPTER 3
MATHEMATICAL ANALYSIS
3.1 GENERAL
Our system aims at finding out the most appropriate mode and best route for reaching the destination. Modes of transport that are highly used by the people are road, train and flight. Considering all these three mode of transport, best route will be determined between a pair of places. The choice of the best route has to incorporate several factors such as travel time, comfort level, cost incurred etc. We subdivide these factors into two broad categories:
Convenience Factor
Comfort Factor
Convenience Factor ‘
In determining the best route, the convenience of the traveler plays an important role. It is a commonplace observation that air travel would not be advisable for shorter distances due to the time taken for reaching airports and hassle of security checks. Similarly, in long journeys, travelling by road would not be convenient option. Keeping the comfort and time factor in mind, I have assigned value to the three modes of travel based on the distance.
Table 3.1. Convenience factor depending on Comfort & Travel Time (C), where d is the distance in kms.
d < 200 200 < d < 400 d > 400
By Road (R) 1 0.7 0.5
By Train (T) 0.8 1 0.7
By Air (A) 0.7 0.9 1
Comfort Factor ‘
No matter whatever is the mode of travel, the comfort factor always varies depending on the quality of the travel. The road journey would be comfortable if the quality of road and the traffic conditions are good. The train travel is more comfortable if the train is luxury. And of course business class flights are more comfortable than economy class. Also, weather conditions determine the accessibility of flight. Taking on account all the factors, I have assigned membership values for different modes. Following tables illustrates comfort factor on these bases:
Table 3.2. Train Categorization depending on comfort ( Q )
Type Comfort Factor Value of i
Luxury 1 1
Superfast 0.7 2
Express 0.5 3
Table 3.3. Airways Categorization depending on comfort ( Q ), where Q stands for quality
Type Comfort Factor Value of i
Business 1 1
Economy 0.7 2
Table 3.4. Comfort factor in connecting trains/flights
Type of Journey Comfort
(Regular/Connecting) Factor (b)
Single Train Boarded 1
Multiple Trains Boarded 0.9
3.2 METHODOLOGY
To identify the best route and mode between two places, I will calculate the Best Path Value for each route and mode. The ideal route will have the value 1.
I will start with calculating values of each route for road journey:
(1) For Road:
Fig. 3.1 Road Travel Dependency on Traffic & Quality of roads
Let R1, R2, R3′. Rs be the Array List of number of road routes possible between origin and destination where ‘_(r=1)^n’d_r < 1.25 ?? d0
[‘_(r=1)^n’d_r is the actual distance that would be travelled (distance may vary if there are more than 1 connecting flights), d is the shortest distance possible. So the system will sort only those routes which take from origin to destination not making the distance more than 1.25 times the shortest distance]
To calculate the Path Value, the convenience factor is taken from Table 3.1 based on the total distance. The road route from one place to another can be combination of more than one road and there can be more than one route possible. Now each road patch will have certain level of traffic and road quality. So With each patch, its road quality (qr) and traffic factor (tr) will differ.
The symbols used are defined as follows ‘
d0 = shortest distance
dr = road patch
d = ‘_(r=1)^n’d_r = total distance
tr =Traffic factor
qr = Road Quality factor
C = convenience,
D = d_0/d (Discomfort factor due to actual distance being more than the shortest distance)
Possible set of values of tr are 0 <tr ‘ 1where smaller value denotes high traffic and idealistic value is 1 which denotes zero traffic.
Possible set of values of qr are 0 <qr ‘ 1where smaller value denotes low quality of road and idealistic value is 1 which denotes best quality possible.
R = (C.D)/(d )??[(‘_(r=1)^n’d_r t_r + ‘_(r=1)^n”d_r q_r ‘)/2]
(2) For Train:
Let T1, T2, T3′. Ts be the Array List of number of train routes possible between origin and destination where ‘_(r=1)^n’d_r < 1.25 ?? d0as in the case of road journey.
To calculate Path Value, the convenience factor is taken from Table 3.1 based on the total distance. The train route from one place to another can be combination of more than one train and there can be more than one route possible. Now each connecting train patch will differ in it’s comfort and might have different quality factor Qr (Taken From Table 3.2).
The symbols used are defined as follows ‘
d0 = shortest distance
d = ‘_(r=1)^n’d_r = total distance
Qr =Train Quality factor
C = convenience,
D = d_0/d (Discomfort factor due to actual distance being more than the shortest distance)
b = discomfort due to change (Taken from Table 3.4)
T = (C.D)/d b^(n-1)??[‘_(r=1)^n’d_r .Q_r ]
(3) For Airways:
Let A1, A2, A3′. As be the Array List of number of air routes possible between origin and destination where ‘_(r=1)^n’d_r < 1.25 ?? d0 as before.
To calculate the Path Value, the convenience factor is taken from Table 3.1 based on the total distance. The Air route from one place to another can be combination of more than one airplane and there can be more than one route possible. Now each connecting airplane patch will differ in its comfort and might have different quality factor Qr (Taken From Table 3.3).
The symbols used are defined as follows ‘
d0 = shortest distance
dr = path travelled by a flight
d = ‘_(r=1)^n’d_r ‘ total distance
Qr = Airplane Quality factor
C = convenience,
D = d_0/d(Discomfort factor due to actual distance being more than the shortest distance)
b = discomfort due to change (Taken from Table 3.4)
fr = discomfort due to check in and check out and approaching the airport
A =(C.D)/d.b^(n-1)??[‘_(r=1)^n’d_r .Q_r.f_r ]
where f1 =.95, f2=1””’.. fr-1=1, fr=.95
3.3 CONCLUSION
In this chapter, all the transport modes are considered and the comfort factor and convenience factor is identified according to general traveller’s perception. For the three common transport modes, the path value is calculated for each.
CHAPTER 4
DESCRIPTION OF THE MULTIMODAL ROUTE SELECTION FUZZY RULE BASED SYSTEM
SOLUTION OF PROBLEM
Since the fuzzy set theory recognizes the vague boundary that exists in some sets, different fuzzy set theory techniques need to be used in order to properly model traffic and transportation problems characterized by ambiguity, subjectivity and uncertainty. Fuzzy logic is an extremely suitable concept with which to combine subjective knowledge and objective knowledge. Fuzzy logic is a convenient way to map an input space to an output space. In terms of transport and routing application, the input space will be the information about all the routes b/w a pair of origin and destination, the output space will be the best possible route.
Input Space (All possible routes) Output Space (Best Route)
Fig. 4.1 Mapping of input space into output space by Fuzzy Systems
PROPOSED WORK
In the proposed system, I have divided the problem of finding the best route and mode. I have assumed that there will be a direct route between source and destination. Also, if there is no direct mode of transport between source and destination then indirect route will be considered by selecting the most appropriate intermediates. Distance is taken as an important factor in all fuzzy rule based system. As travel time and cost of travelling are dependent on the distance, so they are not considered separately. I have assumed that the modes are available at the time of travelling.
4.3 DIRECT ROUTING FUZZY RULE BASED SYSTEM
Considering the three common modes of transport, I have singled out some major factors that affect the effectiveness of the route. The preference of mode is determined by the respective values of the input values.
Basic Assumptions for the Direct Approach
I have not considered cost factor in our analysis of the best route. The whole stress is on comfort and convenience.
If there is no direct train or flight between origin and destination, then I have allowed changing from one flight to other flight; the same holds for train travel. I have not considered cases where a switch over from one mode to other is required.
I have assumed that all modes of travel would be available at time of journey.
I have not taken into account any inconvenience due to odd timings of travel or odd timings of break in journey.
Inconvenience of airport check in and check out and reaching the airport is taken to be same for all airports.
Fig. 4.2 Direct Routing Approach of Route Selection
1] Road Fuzzy rule based system ‘
Inputs
Distance ‘ small, medium, large
Road condition ‘ bad, medium, good
Traffic condition ‘ bad, medium, good
Output: Road Preference ‘ weak, medium, strong
2] Railway Fuzzy rule based system ‘
Inputs
Distance ‘ small, medium, large
Comfort Factor ‘ less comfortable, average comfortable, luxury
Output: Railway Preference ‘ weak, medium, strong’
3] Airway Fuzzy rule based system ‘
Inputs
Distance ‘ small, medium, large
Comfort Factor ‘ less fare, economy class, business class
Output: Airway Preference ‘ weak, medium, strong
The output of roadway, railway and airway FRBS are compared and then the best preference is determined.
4.4 INDIRECT ROUTING FUZZY RULE BASED SYSTEM
When direct modes of transport exist between two places, then two or more than two modes need to be considered. In this process, one more important factor affects the route selection, i.e. number of stoppages. Depending on several factors of direct routing approach and waiting period, the best route and mode is decided. Four FRBS are to be considered.
Basic Assumptions for the Indirect Approach
I have not considered cost factor in our analysis of the best route. The whole stress is on comfort and convenience.
If there is no direct train or flight between origin and destination, then I have considered case where a switch over from one mode to other is required.
I have assumed that all modes of travel would be available at time of journey.
I have not taken any inconvenience due to odd timings of travel or odd timings of break in journey.
Inconvenience of airport check in and check out and reaching the airport is taken to be same for all airports.
Fig. 4.3 Indirect Approach for Route Selection
1] Roadway Railway FRBS ‘ This system considers route involving roadway and railway in no particular order. The inputs will be distance, comfort factor along with waiting period. Comfort factor depends on the road condition, traffic condition and the vehicle. The waiting period will include the time for catching two or more different mode of transport. The values for inputs are as follows-
Distance ‘ small, medium, large
Comfort Factor ‘ less comfortable, average comfortable, luxury
Waiting Period ‘ less than 2 hours, between 2 to 4 hours, more than 4 hours
Output: Roadway Railway Preference ‘ weak, medium, strong
2] Railway Airway FRBS – This system considers route involving railway and airway in no particular order. The inputs will be distance, comfort factor along with waiting period. The values for inputs are as follows ‘
Distance ‘ small, medium, large
Comfort Factor ‘ less comfortable, average comfortable, luxury
Waiting Period ‘ less than 2 hours, between 2 to 4 hours, more than 4 hours
Output: Railway Airway Preference ‘ weak, medium, strong
3] Roadway Airway FRBS ‘ This system considers route involving roadway and airway in no particular order. The inputs will be distance, comfort factor along with waiting period. This waiting period will include the time for catching two or more different mode of transport. The values for inputs are as follows-
Distance ‘ small, medium, large
Comfort Factor ‘ less comfortable, average comfortable, luxury
Waiting period ‘ less than 2 hours, between 2 to 4 hours, more than 4 hours
Output: Roadway Airway Preference ‘ weak, medium, strong
4] Roadway Railway Airway FRBS ‘ This system considers route involving roadway, railway and airway in no particular order. The inputs will be distance, comfort factor and waiting period. This waiting period will include the time for catching two or more different mode of transport. The values for inputs are as follows-
Distance ‘ small, medium, large
Comfort Factor ‘ less comfortable, average comfortable, luxury
Waiting Period ‘ less than 2 hours, between 2 to 4 hours, more than 4 hours
Output: Roadway Railway Airway Preference ‘ weak, medium, strong
I have implemented all these FRBS on MATLAB. Between the given source and destination, the mode of transport and the route is chosen by selecting either the direct or indirect approach. After determining the approach, the path preference is determined by processing all the FRBS.
CHAPTER 5
IMPLEMENTATION OF ROUTE & MODE SELECTION FUZZY RULE BASED SYSTEM ON MATLAB
5.1 GENERAL
Mat lab (Matrix laboratory) is an interactive software system for numerical computations and graphics. MATLAB is a high-level language and interactive environment for numerical computation, visualization, and programming. Using MATLAB, we can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable us to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java’.
Fuzzy Logic Toolbox’ provides functions, apps, and a Simulink?? block for analyzing, designing, and simulating systems based on fuzzy logic. The product guides us through the steps of designing fuzzy inference systems. Functions are provided for many common methods, including fuzzy clustering and adaptive neurofuzzy learning. The toolbox lets us model complex system behaviors using simple logic rules, and then implements these rules in a fuzzy inference system. It can be used as a stand-alone fuzzy inference engine.
For the implementation of the route selection fuzzy rule based system, the following steps need to be done ‘
Defining the number of modes of transport
Defining certain variables for each mode of transport.
Defining the source and destination
Defining the existing routes between source and destination including direct routes. If no direct route exists, then all the indirect routes should be defined.
Defining the rule base that contains all the rules built by considering all the factors of particular mode.
Drawing the inferences from the rule viewer by considering different conditions.
5.2 ROADWAY FUZZY INFERENCE SYSTEM
Fig. 5.1 Road FRBS, FIS editor
Roadway Fuzzy inference system is implemented as Road_FRBS using FIS editor. The input variables also called as FIS variables (Fuzzy Inference System variables) are the distance, road_condition and traffic_condition. The output is determined by using Mamdani method. This output will specify the path preference. The input variables are specified by using Membership Function editor in which the membership functions are chosen and the range of input is specified between [0,10]. Each input variable is defined by some parameters and each parameter has some value associated with it. The input variables are plotted using gaussmf function.
Fig. 5.2 Membership Function Editor of Road FRBS describing ‘road_condition’
Road condition ‘
The input variable ‘road_condition’ can have three values. The condition of road can be bad, medium or good. The range of input variable is specified from 0 to 10. The membership function editor is used to define the curve for the input variable. Gaussmf function is used for the values of ‘road_condition’. Parameters corresponding to each value is defined below ‘
Bad ‘ [1.5 0]
Medium ‘ [1.5 5]
Good ‘ [1.5 10]
Fig. 5.3 Membership Function Editor of Road FRBS describing ‘traffic_condition’
Traffic condition ‘
The input variable ‘traffic_condition’ can have three values. The condition of traffic can be bad, medium or good. The range of input variable is specified from 0 to 10. The membership function editor is used to define the curve for the input variable. Gaussmf function is used for the values of ‘traffic_condition’. Parameters corresponding to each value is defined below ‘
Bad ‘ [1.5 0]
Medium ‘ [1.5 5]
Good ‘ [1.5 10]
Fig. 5.4 Membership Function Editor of Road FRBS describing ‘distance’
Distance ‘
The input variable ‘distance’ can have three values. The distance can be bad, medium or good. The range of input variable is specified from 0 to 10. The membership function editor is used to define the curve for the input variable. Gaussmf function is used for the values of ‘distance’. Parameters corresponding to each value are defined below ‘
Small ‘ [1.5 0]
Medium ‘ [1.5 5]
Large ‘ [1.5 10]
Fig. 5.5 Membership Function Editor of Road FRBS describing ‘pref’
The output variable ‘pref’ is plotted as trimf function taking collection of three points. The values of ‘pref’ are taken as follows-
Weak ‘ [0.0216 1.69 3.35]
Medium ‘ [3.333 5 6.667]
Strong ‘ [6.69 8.36 10]
Fig. 5.6 Rule editor of Road FRBS
After defining all the values for input and output variables, Rules are derived using the variables and their values by using Rule Editor. These rules form the fuzzy rule base. Different conditions are considered by taking the parameter values and accordingly, the ‘pref’ output is defined. The ‘and’ operator is taken between the input parameters as this will serve as maximum occurring condition which effect the resulting output. If all the combinations of the three input variables are considered, it will be 3*3*3 = 27 rules. But few of them are not affecting the result, so I have not considered them. For example if the distance is small and traffic condition is good or medium and road condition is bad, then preference will be weak, as it will make the journey discomfortable. If any of the two conditions is bad, the road will not be preferred.
Fig. 5.7 Rule Viewer of Road FRBS
After the rules are done, the rule viewer will determine the path preference according to different values of the input variables and the defined rules. By changing the values in the rule viewer, the results are got at the same time. The values of input and output variables lie between 0 and 10.
Here when distance is small i.e. 2.35, road condition is 6.81, which means more than medium and traffic condition is 7.77 i.e. more than medium, then road preference will be near to strong i.e. 6.6.
Fig. 5.8 Open Output Surface Viewer of Road FRBS with surface plot style
5.3 RAILWAY FUZZY INFERENCE SYSTEM
Railway Fuzzy inference system is implemented as Train_FRBS using FIS editor. FIS variables (Fuzzy Inference System variables) are the distance and comfort factor. The output is determined by using Mamdani method. This output will specify the path preference. The input variables are specified by using Membership Function editor in which the membership functions are chosen and the range of input is specified between [0,10]. Each input variable is defined by some parameters and each parameter has some value associated with it. The input variables are plotted using gaussmf function. The values for the input parameters for the corresponding FIS variables are as follows ‘
Fig. 5.9 FIS editor of Railway FRBS
Fig. 5.10 Membership Function Editor of Railway FRBS describing ‘distance
Distance
The input variable ‘distance’ can have three values. The distance can be bad, medium or good. The range of input variable is specified from 0 to 10. The membership function editor is used to define the curve for the input variable. Gaussmf function is used for the values of distance. Parameters corresponding to each value are defined below ‘
Small ‘ [1.5 0]
Medium ‘ [1.5 5]
Large ‘ [1.5 10]
Fig. 5.11 Membership Function Editor of Railway FRBS describing ‘comfort_factor’
Comfort Factor
The input variable ‘comfort_factor’ can have three values. The level of comfort can be less, average or luxury. The range of input variable is specified from 0 to 10. The membership function editor is used to define the curve for the input variable. Gaussmf function is used for the values of ‘comfort_factor’. Parameters corresponding to each value are defined below ‘
Less comfortable ‘ [1.5 0]
Average comfortable ‘ [1.5 5]
Luxury ‘ [1.5 10]
Fig. 5.12 Membership Function Editor of Railway FRBS describing ‘rail_pref’
The output variable ‘rail_pref’ is plotted as trimf function taking collection of three points. The values of ‘rail_pref’ are taken as follows-
Weak ‘ [0.0216 1.689 3.355]
Medium ‘ [3.333 5 6.667]
Strong ‘ [6.667 8.333 10]
Fig. 5.13 Rule editor of Railway FRBS
After defining all the values for input and output variables, Rules are derived using the variables and their values by employing Rule Editor. Different conditions are considered by taking the parameter values and accordingly, the ‘rail_pref’ output is defined. The ‘and’ operator is taken between the input parameters as this will serve as maximum occurring condition which effect the resulting output. If all the combinations of the three input variables are considered, it will be 3*3= 9 rules. All the nine rules are specified.
Fig. 5.14 Rule Viewer of Railway FRBS
After the rules are done, the rule viewer will determine the path preference according to different values of the input variables and the defined rules. By changing the values in the rule viewer, the results are got at the same time. The values of input and output variables lie between 0 and 10.
Here when distance is 8.3 i.e. large, and traffic condition is 7.77 i.e. more than medium, then rail preference will be close to strong i.e. 6.35.
Fig. 5.15 Open Output Surface Viewer of Railway FRBS with surface plot style
5.4 AIRWAY FUZZY INFERENCE SYSTEM
Airway Fuzzy inference system is implemented as Airway_FRBS using FIS editor. FIS variables (Fuzzy Inference System variables) are the distance and comfort factor. The output is determined by using Mamdani method. This output will specify the path preference. The input variables are specified by using Membership Function editor in which the membership functions are chosen and the range of input is specified between [0,10]. Each input variable is defined by some parameters and each parameter has some value associated with it. The input variables are plotted using gaussmf function. The values for the input parameters for the corresponding FIS variables are as follows ‘
Fig. 5.16 FIS editor of Airway FRBS
Fig. 5.17 Membership Function Editor of Airway FRBS describing ‘distance’
Distance
The input variable ‘distance’ can have three values. The ‘distance’ can be small, medium or large. The range of input variable is specified from 0 to 10. The membership function editor is used to define the curve for the input variable. Gaussmf function is used for the values of distance. Parameters corresponding to each value are defined below ‘
Small ‘ [1.5 0]
Medium ‘ [1.5 5]
Large ‘ [1.5 10]
Fig. 5.18 Membership Function Editor of Airway FRBS describing ‘comfort_factor’
Comfort Factor
The input variable ‘comfort_factor’ can have three values. The level of comfort is according to the fare, which is categorized into less fare, economy class or business class. The range of input variable is specified from 0 to 10. The membership function editor is used to define the curve for the input variable. Gaussmf function is used for the values of ‘comfort_factor’. Parameters corresponding to each value are defined below ‘
Less Fare ‘ [1.5 0]
Economy ‘ [1.5 5]
Business ‘ [1.5 10]
Fig. 5.19 Membership Function Editor of Airway FRBS describing ‘pref’
The output variable ‘pref’ is plotted as trimf function taking collection of three points. The values of ‘pref’ are taken as follows-
Weak ‘ [0.0216 1.689 3.355]
Medium ‘ [3.333 5 6.667]
Strong ‘ [6.667 8.333 10]
Fig. 5.20 Rule Editor of Airway FRBS
After defining all the values for input and output variables, Rules are derived using the variables and their values by using Rule Editor. Different conditions are considered by taking the parameter values and accordingly, the ‘pref’ output is defined. The ‘and’ operator is taken between the input parameters as this will serve as maximum occurring condition which effect the resulting output. If all the combinations of the three input variables are considered, it will be 3*3= 9 rules. All the nine rules are specified.
Fig. 5.21 Rule Viewer of Airway FRBS
After the rules are done, the rule viewer will determine the path preference according to different values of the input variables and the defined rules. By changing the values in the rule viewer, the results are got at the same time. The values of input and output variables lie between 0 and 10.
Here when distance is 8.3 i.e. large, and traffic condition is 7.77 i.e. more than medium, then air preference will be near to strong i.e. 6.35.
Fig. 5.22 Open Output Surface Viewer of Airway FRBS with surface plot style
5.5 ROADWAY RAILWAY FUZZY INFERENCE SYSTEM
Roadway Railway Fuzzy inference system is implemented as Road_train__FRBS using FIS editor. FIS variables (Fuzzy Inference System variables) are the distance, comfort factor and waiting period. The output is determined by using Mamdani method. This output will specify the path preference. The input variables are specified by using Membership Function editor in which the membership functions are chosen and the range of input is specified between [0,10]. Each input variable is defined by some parameters and each parameter has some value associated with it. The input variables are plotted using gaussmf function. The values for the input parameters for the corresponding FIS variables are as follows ‘
Fig. 5.23 FIS editor of Road Train FRBS
Fig. 5.24 Membership Function Editor of Road Train FRBS describing ‘distance
Distance ‘
The input variable ‘distance’ can have three values. The distance can be small, medium or large. The range of input variable is specified from 0 to 10. The membership function editor is used to define the curve for the input variable. Gaussmf function is used for the values of ‘distance’. Parameters corresponding to each value are defined below ‘
Small ‘ [1.5 0]
Medium ‘ [1.5 5]
Large ‘ [1.5 10]
Fig. 5.25 Membership Function Editor of Road Train FRBS describing ‘comfort factor’
Comfort Factor
The input variable ‘comfort_factor’ can have three values. The level of comfort can be less comfortable, average or luxury. The range of input variable is specified from 0 to 10. The membership function editor is used to define the curve for the input variable. Gaussmf function is used for the values of ‘comfort_factor’. Parameters corresponding to each value are defined below ‘
Less ‘ [1.5 0]
Average ‘ [1.5 5]
Luxury ‘ [1.5 10]
Fig. 5.26 Membership Function Editor of Road Train FRBS describing ‘waiting period’
Waiting Period-
The input variable ‘waiting_period’ can have three values. The range of waiting period can be less than 2 hours, between 2 to 4 hours or more than 4 hours. The range of input variable is specified from 0 to 10. The membership function editor is used to define the curve for the input variable. Gaussmf function is used for the values of ‘waiting_period’. Parameters corresponding to each value are defined below ‘
Less than 2 hours’ [1.5 0]
Between 2 to 4 hours ‘ [1.5 5]
More than 4 hours ‘ [1.5 10]
Fig. 5.27 Membership Function Editor of Road Train FRBS describing ‘pref’
The output variable ‘pref’ is plotted as trimf function taking collection of three points. The values of ‘pref’ are taken as follows-
Weak ‘ [0.0216 1.689 3.355]
Medium ‘ [3.333 5 6.667]
Strong ‘ [6.667 8.333 10]
Fig. 5.28 Rule Editor of Road Train FRBS
After defining all the values for input and output variables, Rules are derived using the variables and their values by using Rule Editor. Different conditions are considered by taking the parameter values and accordingly, the ‘pref’ output is defined. The ‘and’ operator is taken between the input parameters as this will serve as maximum occurring condition which effect the resulting output. If all the combinations of the three input variables are considered, it will be 3*3*3 = 27 rules. But I have considered 15 rules in which the path preference varies.
For example if distance is small and comfort factor is less comfortable, then whatever be the value of waiting period, the path preference will be weak. Thus, defining rules for more than 4 hours are not required.
Fig. 5.29 Rule Viewer of Road Train FRBS
After the rules are done, the rule viewer will determine the path preference according to different values of the input variables and the defined rules. By changing the values in the rule viewer, the results are got at the same time. The values of input and output variables lie between 0 and 10.
Here when distance is 7.05 i.e. large, comfort_factor is 7.05, i.e. more than average comfortable and waiting period is 2.23 i.e. less than 2 hours, then preference of travelling by road and train will be near to medium i.e. 4.86.
Fig. 5.30 Open Output Surface Viewer of Road Train FRBS with surface plot style
5.6 RAILWAY AIRWAY FUZZY INFERENCE SYSTEM
Railway Airway Fuzzy inference system is implemented as Train_air__FRBS using FIS editor. FIS variables (Fuzzy Inference System variables) are the distance, comfort factor and waiting period. The output is determined by using Mamdani method. This output will specify the path preference. The input variables are specified by using Membership Function editor in which the membership functions are chosen and the range of input is specified between [0,10]. Each input variable is defined by some parameters and each parameter has some value associated with it. The input variables are plotted using gaussmf function. The values for the input parameters for the corresponding FIS variables are as follows ‘
Fig. 5.31 FIS editor of Train Air FRBS
Distance
Small ‘ [1.5 0]
Medium ‘ [1.5 5]
Large ‘ [1.5 10]
Comfort Factor
Less ‘ [1.5 0]
Average ‘ [1.5 5]
Luxury ‘ [1.5 10]
Waiting Period
Less than 2 hours’ [1.5 0]
Between 2 to 4 hours ‘ [1.5 5]
More than 4 hours ‘ [1.5 10]
The membership functions are the same as for Roadway Railway FRBS. After defining all the values for input and output variables, Rules are derived using the variables and their values by using Rule Editor. Different conditions are considered by taking the parameter values and accordingly, the ‘pref’ output is defined. The ‘and’ operator is taken between the input parameters as this will serve as maximum occurring condition which effect the resulting output. If all the combinations of the three input variables are considered, it will be 3*3*3 = 27 rules. But I have considered 22 rules in which the path preference varies.
For example if distance is small and comfort factor is less comfortable, then whatever be the value of waiting period, the path preference will be weak. Thus, defining rules for more than 4 hours are not required.
Fig. 5.32 Rule Editor of Train Air FRBS
Fig. 5.33 Rule Viewer of Train Air FRBS
After the rules are done, the rule viewer will determine the path preference according to different values of the input variables and the defined rules. By changing the values in the rule viewer, the results are got at the same time. The values of input and output variables lie between 0 and 10.
Here when distance is 7.65 i.e. large, comfort_factor is 0.81, i.e. more than average comfortable and waiting period is 4.76 i.e. less than 2 hours, then preference of travelling by train and air will be near to medium i.e. 4.02.
Fig. 5.34 Open Output Surface Viewer of Train Air FRBS with surface plot style
5.7 ROADWAY AIRWAY FUZZY INFERENCE SYSTEM
Roadway Airway Fuzzy inference system is implemented as Road_air__FRBS using FIS editor. FIS variables (Fuzzy Inference System variables) are the distance, comfort factor and waiting period. The output is determined by using Mamdani method. This output will specify the path preference. The input variables are specified by using Membership Function editor in which the membership functions are chosen and the range of input is specified between [0,10]. Each input variable is defined by some parameters and each parameter has some value associated with it. The input variables are plotted using gaussmf function. The values for the input parameters for the corresponding FIS variables are as follows ‘
Fig. 5.35 FIS Editor of Road Air FRBS
Distance
Small ‘ [1.5 0]
Medium ‘ [1.5 5]
Large ‘ [1.5 10]
Comfort Factor
Less ‘ [1.5 0]
Average ‘ [1.5 5]
Luxury ‘ [1.5 10]
Waiting Period
Less than 2 hours’ [1.5 0]
Between 2 to 4 hours ‘ [1.5 5]
More than 4 hours ‘ [1.5 10]
The membership functions are the same as for Roadway Railway FRBS. After defining all the values for input and output variables, Rules are derived using the variables and their values by using Rule Editor. Different conditions are considered by taking the parameter values and accordingly, the ‘pref’ output is defined. The ‘and’ operator is taken between the input parameters as this will serve as maximum occurring condition which effect the resulting output. If all the combinations of the three input variables are considered, it will be 3*3*3 = 27 rules. But I have considered 20 rules in which the path preference varies.
For example if distance is small and comfort factor is less comfortable, then whatever be the value of waiting period, the path preference will be weak. Thus, defining rules for more than 4 hours are not required.
Fig. 5.36 Rule Editor of Road Air FRBS
Fig. 5.37 Rule Viewer of Road Air FRBS
After the rules are done, the rule viewer will determine the path preference according to different values of the input variables and the defined rules. By changing the values in the rule viewer, the results are got at the same time. The values of input and output variables lie between 0 and 10.
Here when distance is 5 i.e. medium, comfort_factor is 5, i.e. average comfortable and waiting period is 5.84 i.e. between 2-4 hours, then preference of travelling by road and air will be near to medium i.e. 4.78.
Fig. 5.38 Open Output Surface Viewer of Road Air FRBS with surface plot style
5.8 ROADWAY RAILWAY AIRWAY FUZZY INFERENCE SYSTEM
Roadway Railway Airway Fuzzy inference system is implemented as Road_train_air__FRBS using FIS editor. FIS variables (Fuzzy Inference System variables) are the distance, comfort factor and waiting period. The output is determined by using Mamdani method. This output will specify the path preference. The input variables are specified by using Membership Function editor in which the membership functions are chosen and the range of input is specified between [0,10]. Each input variable is defined by some parameters and each parameter has some value associated with it. The input variables are plotted using gaussmf function. The values for the input parameters for the corresponding FIS variables are as follows ‘
Fig. 5.39 FIS Editor of Road Train Air FRBS
Distance
Small ‘ [1.5 0]
Medium ‘ [1.5 5]
Large ‘ [1.5 10]
Comfort Factor
Less ‘ [1.5 0]
Average ‘ [1.5 5]
Luxury ‘ [1.5 10]
Waiting Period
Less than 4 hours’ [1.5 0]
Between 4 to 8 hours ‘ [1.5 5]
More than 8 hours ‘ [1.5 10]
The membership functions are the same as for Roadway Railway FRBS. After defining all the values for input and output variables, Rules are derived using the variables and their values by using Rule Editor. Different conditions are considered by taking the parameter values and accordingly, the pref output is defined. The ‘and’ operator is taken between the input parameters as this will serve as maximum occurring condition which effect the resulting output. If all the combinations of the three input variables are considered, it will be 3*3*3 = 27 rules. But I have considered 20 rules in which the path preference varies.
For example if distance is small and comfort factor is less comfortable, then whatever be the value of waiting period, the path preference will be weak. Thus, defining rules for more than 4 hours are not required.
Fig. 5.40 Rule Editor of Road Train Air FRBS
Fig. 5.41 Rule Viewer of Road Train Air FRBS
After the rules are done, the rule viewer will determine the path preference according to different values of the input variables and the defined rules. By changing the values in the rule viewer, the results are got at the same time. The values of input and output variables lie between 0 and 10.
Here when distance is 7.65 i.e. more than medium, comfort_factor is 7.16, i.e. more than average comfortable and waiting period is 2.71 i.e. less than 2 hours, then preference of travelling by road, train and air will be more than medium i.e. 6.37.
Fig. 5.42 Open Output Surface Viewer of Road Train Air FRBS with surface plot style
CHAPTER 6
CONCLUSION & FUTURE DIRECTIONS OF RESEARCH
6.1 CONCLUSION
Fuzzy logic could be used successfully to model situations in which people have to make choice amongst multiples of decision depending on underlying conditions. It makes use of subjective as well as objective knowledge. In my work I have developed a Route selection fuzzy rule based system which considers all the perspectives related to the selection of optimal route and mode of transport. The approach that is used is based on the availability of the routes between origin and the destination. The system identifies all the variables affecting the preference of route and mode. Rules are made according to the preference of the decision maker. Fuzzy inference system that is built from the determined rules compute the path preferences in all the modes of transport considering all the existing routes.
I have implemented the FRBS on MATLAB which will work with a user interface that will supply input of origin, destination, and other necessary details. Also, a database including all the existing modes and routes works in the background. The proposed FRBS identifies all the routes in different modes and compute the path preference.
By observing the developed FRBS, it has been possible to design rules according to the perception of the people. The number of inputs, the number of fuzzy sets used to describe fuzzy variables, and the number of rules very much influence the quality of the solution generated by a fuzzy logic system. With fuzzy rule based systems, the subjectivity and uncertainty of the decision can be easily handled.
6.2 FUTURE RESEARCH
The implemented fuzzy rule based system can be used in various transport applications. Trip generation, Route choice, etc. has various points where this system can be used. The principle of fuzzy logic has been employed with great success in designing several commercial products e.g. vacuum cleaners, washing machines, microwave ovens, cameras etc. With increasing traffic in tourist and business activities the fuzzy logic applications are bound to be used for solving practical problems of mode and route selection.
Future research involves the development of the application that will develop the database of routes and corresponding modes of transport and integrate it with the fuzzy rule based system to arrive at the best path.