Neural Networks and Fuzzy Systems: Theory and Applications discusses theories DRM-free; Included format: PDF; ebooks can be used on all reading devices. Integration of fuzzy logic and neural networks . In theory, neural networks, and fuzzy systems are equivalent in that they. The choice of describing engineering applications coincides with the Fuzzy Logic and Neural Network research interests of the readers. Modeling and control of.

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Figure 1–1: Soft computing as a composition of fuzzy logic, neural networks and probabilistic reasoning. Intersections include. • neuro-fuzzy. Why expert systems, fuzzy systems, neural networks, and hybrid systems for knowledge engineering and problem solving? Generic and specific AI. 3 1 Fuzzy Systems 8 An introduction to fuzzy logic. Tuning fuzzy control parameters by neural nets Fuzzy rule.

By Nikola Kasabov Overview Neural networks and fuzzy systems are different approaches to introducing human-like reasoning into expert systems. This text is the first to combine the study of these two subjects, their basics and their use, along with symbolic AI methods to build comprehensive artificial intelligence systems. In a clear and accessible style, Kasabov describes rule-based and connectionist techniques and then their combinations, with fuzzy logic included, showing the application of the different techniques to a set of simple prototype problems, which makes comparisons possible. A particularly strong feature of the text is that it is filled with applications in engineering, business, and finance. AI problems that cover most of the application-oriented research in the field pattern recognition, speech and image processing, classification, planning, optimization, prediction, control, decision making, and game simulations are discussed and illustrated with concrete examples. Intended both as a text for advanced undergraduate and postgraduate students as well as a reference for researchers in the field of knowledge engineering, Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering has chapters structured for various levels of teaching and includes original work by the author along with the classic material. Data sets for the examples in the book as well as an integrated software environment that can be used to solve the problems and do the exercises at the end of each chapter are available free through anonymous ftp. Table of Contents.

Neural Networks, 9 9 , References[ edit ] Abraham A. Ang, K.

Neural Computation, 17 1 , Kosko, Bart Lin, C. Bastian, J. Quek, C. In the load forecasting studies, some variables appeared to affect the behavior of the load curve in the case of electrical utilities. These variables include meteorological data like temperature, humidity, lightening, comfort indexes etc, and also information about the consumption profile of the utilities.

It was also noted the distinct behavior of the load series related to the day of the week, the seasonableness and the correlation between the past and present values. A bibliographic research concerning the application of computational intelligence techniques in load forecasting was made.

This research showed that neural network models have been largely employed. The fuzzy logic models have just started to be used recently. Neuro-fuzzy are very recent, and there are almost no references on it. Intersection connectives produce a high output only when all of the inputs have high values. Compensative connectives have the property that a higher degree of satisfaction of one of the criteria can compensate for a lower degree of satisfaction of another criteria to a certain extent.

In the sense, union connectives provide full compensation and intersection connectives provide no compensation. In a decision process the idea of trade-offs corresponds to viewing the global evaluation of an action as lying between the worst and the best local ratings. This occurs in the presence of conflicting goals, when a compensation between the corresponding compabilities is allowed.

Averaging operators realize trade-offs between objectives, by allowing a positive compensation between ratings. Averaging operators represent a wide class of aggregation operators. We prove that whatever is the particular definition of an averaging operator, M, the global evaluation of an action will lie between the worst and the best local ratings: Averaging operators have the following interesting properties: Property 1.

A strictly increasing averaging operator cannot be associative. Property 2. Table 6. One sees aggregation in neural networks, fuzzy logic controllers, vision systems, expert systems and multi-criteria decision aids. In Yager introduced a new aggregation technique based on the ordered weighted averaging OWA operators. An OWA operator of dimension n is mapping F: Furthermore n F a1, a2, A fundamental aspect of this operator is the re-ordering step, in particular an aggregate ai is not associated with a particular weight wi but rather a weight is associated with a particular ordered position of aggregate.

When we view the OWA weights as a column vector we shall find it convenient to refer to the weights with the low indices as weights at the top and those with the higher indices with weights at the bottom. It is noted that different OWA operators are distinguished by their weighting function. In Yager pointed out three important special cases of OWA aggregations: We shall now discuss some of these.

Let a1, a2, Then for any OWA operator F a1, a2, Then F a1, a2, Another characteristic associated with these operators is idempotency.

A window type OWA operator takes the average of the m arguments around the center.

Furthermore, note that the nearer W is to an or, the closer its measure is to none; while the nearer it is to an and, the closer is to zero. The following theorem shows that as we move weight up the vector we increase the orness, while moving weight down causes us to decrease orness W. Theorem 6. We can see when using the OWA operator as an averaging operator Disp W measures the degree to which we use all the aggregates equally. Suppose now that the fact of the GMP is given by a fuzzy singleton.

Then the process of computation of the membership function of the consequence becomes very simple. Rule 1: In the on-line control, a non-fuzzy crisp control action is usually required. Consequently, one must defuzzify the fuzzy control action output inferred from the fuzzy reasoning algorithm, namely: Defuzzification is a process to select a representative element from the fuzzy output C inferred from the fuzzy control algorithm.

What is t-norm? What are the properties to be satisfied by a t-norm? What are the various basic t-norms? What is t-conorm? What are the properties to be satisfied by a t-conorm? What are the various basic t-conorms? Prove the following statement: What is t-norm based intersection?

What is t-conorm based union? What are the averaging operators? What are the important properties of averaging operators? Explain order weighted averaging with an example. Explain the Measure of dispersion. What is entropy of an ordered weighted averaging OWA vector? Explain Mamdani rule-based system. Explain Larsen rule-based system. What is defuzzification?

Schwartz and A. Sklar, Associative functions and statistical triangle inequalities, Publication Mathematics, Debrecen, Vol. Czogala and W. Pedrycz, Fuzzy rule generation for fuzzy control, Cybernetics and Systems, Vol. Yagar, Measures of fuzziness based on t-norms, Stochastica, Vol. Yagar, Strong truth and rules of inference in fuzzy logic and approximate reasoning, Cybernetics and Systems, Vol. Novak and W. Lim and T. Filev and R. Nafarich and J. Yagar, A general approach to rule aggregation in fuzzy logic control, Applied Intellignece, Vol.

Wang, and J. Prade, Gradual inference rules in approximate reasoning, Information Sciences, Vol. Fuller and H. Zimmerman, On computation of the compositional rule of inference under triangular norms, Fuzzy Sets and Systems, Vol. Coben and M. Rhee and R. Krishanpuram, Fuzzy rule generation methods for high-level computer vision, Fuzzy Sets and Systems, Vol.

Doherry, P. Driankov and H. Dutta and P. Tian and I. Turksen, Combination of rules or their consequences in fuzzy expert systems, Fuzzy Sets and Systems, Vol. Uchino, T. Yamakawa, T. Miki and S. Nakamura, Fuzzy rule-based simple interpolation algorithm for discrete signal, Fuzzy Sets and Systems, Vol. Arnould and S. Tano, A rule-based method to calculate exactly the widest solutions sets of a max-min fuzzy relations inequality, Fuzzy Sets and Systems, Vol. Cross and T. Pedrycz, Why triangular membership functions?

Fuzzy Sets and Systems, Vol. The inference engine of a fuzzy expert system operates on a series of production rules and makes fuzzy inferences. There exist two approaches to evaluating relevant production rules.

The first is data-driven and is exemplified by the generalized modus ponens. In this case, available data are supplied to the expert system, which then uses them to evaluate relevant production rules and draw all possible conclusions. An alternative method of evaluation is goal-driven; it is exemplified by the generalized modus tollens form of logical inference.

Here, the expert system searches for data specified in the IF clauses of production rules that will lead to the objective; these data are found either in the knowledge base, in the THEN clauses of other production rules, or by querying the user. Since the data-driven method proceeds from IF clauses to THEN clauses in the chain through the production rules, it is commonly called forward chaining.

Similarly, since the goal-driven method proceeds backward from THEN clauses to the IF clauses, in its search for the required data, it is commonly called backward chaining.

Backward chaining has the advantage of speed, since only the rules leading to the objective need to be evaluated. Example 7. What are the different approaches to evaluating relevant production rules? Explain Mamdani inference mechanism. Explain Tsukamoto inference mechanism. Explain Sugeno inference mechanism. Explain Larsen inference mechanism.

Explain simplified reasoning scheme. Zadeh, Fuzzy logic and approximate reasoning, Synthese, Vol. Zadeh, The concept of a linguistic variable and its application to approximate reasoning I, Information Sciences, Vol.

Zadeh, The concept of a linguistic variable and its application to approximate reasoning II, Information Sciences, Vol. Zadeh, The concept of a linguistic variable and its application to approximate reasoning III, Information sciences, Vol.

Mamdani and B. Pedrycz, Applications of fuzzy relational equations for methods of reasoning in presence of fuzzy data, Fuzzy Sets and Systems, Vol.

Sanchez and L. K, Turksen, Four methods of approximate reasoning with interval-valued fuzzy sets, International Journal of Approximate Reasoning, Vol. Basu and A. Schwecke, Fuzzy reasoning in a multidimensional space of hypotheses, International Journal of Approximate Reasoning, Vol.

Prade, Fuzzy sets in approximate reasoning, Part I: Inference with possibility distributions, Fuzzy Sets and Systems, Vol. Dutta, Approximate spatial reasoning: Pawlak, Rough sets: Theoretical aspects of reasoning about data, Kluwer, Bostan, Chen, A new improved algorithm for inexact reasoning based on extended fuzzy production rules, Cybernetics and Systems, Vol.

Nakanishi, I. Turksen and M. The purpose of the feedback controller is to guarantee a desired response of the output y. The output of the controller which is the input of the system is the control action u. Zadeh was introduced the idea of formulating the control algorithm by logical rules. In a fuzzy logic controller FLC , the dynamic behaviour of a fuzzy system is characterized by a set of linguistic description rules based on expert knowledge.

The expert knowledge is usually of the form IF a set of conditions are satisfied THEN a set of consequences can be inferred. Since the antecedents and the consequents of these IF-THEN rules are associated with fuzzy concepts linguistic terms , they are often called fuzzy conditional statements.

In our terminology, a fuzzy control rule is a fuzzy conditional statement in which the antecedent is a condition in its application domain and the consequent is a control action for the system under control. Basically, fuzzy control rules provide a convenient way for expressing control policy and domain knowledge. Furthermore, several linguistic variables might be involved in the antecedents and the conclusions of these rules.

When this is the case, the system will be referred to as a multi-input-multi- output MIMO fuzzy system.

However, it does not mean that the FLC is a kind of transfer function or difference equation. A prototypical rule-base of a simple FLC realizing the control law above is listed in the following R1: So, our task is the find a crisp control action z0 from the fuzzy rule-base and from the actual crisp inputs x0 and y0: Furthermore, the output of a fuzzy system is always a fuzzy set, and therefore to get crisp value we have to defuzzify it.

A fuzzification operator has the effect of transforming crisp data into fuzzy sets. In most of the cases we use fuzzy singletons as fuzzifiers fuzzifier x0: A fuzzy control rule Ri: Fuzzy control rules are combined by using the sentence connective also. Since each fuzzy control rule is represented by a fuzzy relation, the overall behavior of a fuzzy system is characterized by these fuzzy relations.

In other words, a fuzzy system can be characterized by a single fuzzy relation which is the combination in question involves the sentence connective also. Symbolically, if we have the collection of rules R1: To infer the output z from the given process states x, y and fuzzy relations Ri, we apply the compositional rule of inference: In the on-line control, a nonfuzzy crisp control action is usually required.

Consequently, one must defuzzify the fuzzy control action output inferred from the fuzzy control algorithm, namely: The most often used defuzzification operators are: Z0 Fig. Example 8. Consider a fuzzy controller steering a car in a way to avoid obstacles. A suitable defuzzification method would have to choose between different control actions choose one of two triangles in the Figure and then transform the fuzzy set into a crisp value.

Namely, he proved the following theorem Theorem 8. What is fuzzy logic controller? Explain two-input-single-output fuzzy system. Explain Mamdani type of fuzzy logic controller.

What are the various parts of fuzzy logic control system? What are the various defuzification methods? What is the effectivity of fuzzy logic control systems? Zadeh, a rationale for fuzzy control, Journal of dynamical systems, Measurement and Control, Vol. Mamdani and S. King and E. Mamdani, The application of fuzzy control systems to industrial process, Automatica, Vol. Kickert and E. Mamdani, Analysis of a fuzzy logic controller, Fuzzy sets and systems, Vol. Brase and D. Ray and D.

Sugeno, An introductory survey of fuzzy control, Infromation Sciences, Vol. Takagi and M. Gupta, J. Kiszks and G. Graham and R. Bladwin and N. Guild, Modeling controllers using fuzzy relations, Kybernets, Vol.

Buckley, Theory of the fuzzy controller: Tanaka and M.

Abdelnour, C. Chang, F. Huang and J. Boullama and A. Kandel , L. Li and Z. Yager, A general approach to rule aggregation in fuzzy logic control, Applied Intelligence, Vol. Wong, C. Chou and D. Ragot and M. Chung and J. Chen and L. Kiupel and P. Yagar, Three models of fuzzy logic controllers, Cybernetics and Systems, Vol. Pedrycz, Fuzzy controllers: Han and V.

Altrock, H. Arend, B. Krause, C. Steffess and E. Yager, and D. Bugarin, S. Barro and R. Here is a list of general observations about fuzzy logic: Fuzzy logic is conceptually easy to understand. The mathematical concepts behind fuzzy reasoning are very simple. Fuzzy logic is flexible. Fuzzy logic is tolerant of imprecise data.

Everything is imprecise if you look closely enough, but more than that, most things are imprecise even on careful inspection. Fuzzy reasoning builds this understanding into the process rather than tacking it onto the end. Fuzzy logic can model nonlinear functions of arbitrary complexity. You can create a fuzzy system to match any set of input-output data. Fuzzy logic can be built on top of the experience of experts. In direct contrast to neural networks, which take training data and generate opaque, impenetrable models, fuzzy logic lets you rely on the experience of people who already understand your system.

Fuzzy logic can be blended with conventional control techniques. In many cases fuzzy systems augment themand simplify their implementation. Fuzzy logic is based on natural language. The basis for fuzzy logic is the basis for human communication. This observation underpins many of the other statements about fuzzy logic. Natural language, that which is used by ordinary people on a daily basis, has been shaped by thousands of years of human history to be convenient and efficient.

Sentences written in ordinary language represent a triumph of efficient communication. We are generally unaware of this because ordinary language is, of course, something we use every day. Since fuzzy logic is built. Why should this be useful? The answer is commercial and practical. Commercially, fuzzy logic has been used with great success to control machines and consumer products. In the right application fuzzy logic systems are simple to design, and can be understood and implemented by non- specialists in control theory.

In most cases someone with a intermediate technical background can design a fuzzy logic controller. The control system will not be optimal but it can be acceptable. Control engineers also use it in applications where the on-board computing is very limited and adequate control is enough.

Fuzzy logic is not the answer to all technical problems, but for control problems where simplicity and speed of implementation is important then fuzzy logic is a strong candidate. A cross section of applications that have successfully used fuzzy control includes: Fuzzy logic is not a cure-all. When should you not use fuzzy logic? If you find it is not convenient, try something else. If a simpler solution already exists, use it. Fuzzy logic is the codification of common sense-use common sense when you implement it and you will probably make the right decision.

Many controllers, for example, do a fine job without using fuzzy logic. However, if you take the time to become familiar with fuzzy logic, you will see it can be a very powerful tool for dealing quickly and efficiently with imprecision and non- linearity. However, many people died or injured because of traffic accidents all over the world.

When statistics are investigated India is the most dangerous country in terms of number of traffic accidents among Asian countries. Many reasons can contribute these results, which are mainly driver fault, lack of infrastructure, environment, literacy, weather conditions etc. However, agree that this rate is higher in India since many traffic accidents are not recorded, for example single vehicle accidents or some accidents without injury or fatality.

In this study, using fuzzy logic method, which has increasing usage area in Intelligent Transportation Systems ITS , a model was developed which would obtain to prevent the vehicle pursuit distance automatically. Using velocity of vehicle and pursuit distance that can be measured with a sensor on vehicle a model has been established to brake pedal slowing down by fuzzy logic.

This goal forms the background for the present traffic safety program. The program is partly based on the assumption that high speed contributes to accidents. Many researchers support the idea of a positive correlation between speed and traffic accidents. One way to reduce the number of accidents is to reduce average speeds. Speed reduction can be accomplished by police surveillance, but also through physical obstacles on the roads.

Obstacles such as flower pots, road humps, small circulation points and elevated pedestrian crossings are frequently found in many residential areas around India. However, physical measures are not always appreciated by drivers.

These obstacles can cause damages to cars, they can cause difficulties for emergency vehicles, and in winter these obstacles can reduce access for snow clearing vehicles. The major objectives with ITS are to achieve traffic efficiency, by for instance redirecting traffic, and to increase safety for drivers, pedestrians, cyclists and other traffic groups.

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. A set of a large number of rules of the type: If premise Then conclusion is called a fuzzy rule base. In fuzzy rule-based systems, the rule base is formed with the assistance of human experts; recently, numerical data has been used as well as through a combination of numerical data-human experts.

An interesting case appears when a combination of numerical information obtained from measurements and linguistic information obtained from human experts is used to form the fuzzy rule base. In this case, rules are extracted from numerical data in the first step. In the next step this fuzzy rule base can but need not be supplemented with the rules collected from human experts. The inference engine of the fuzzy logic maps fuzzy sets onto fuzzy sets.

A large number of different inferential procedures are found in the literature. In most papers and practical engineering applications, minimum inference or product inference is used. During defuzzification, one value is chosen for the output variable. The literature also contains a large number of different defuzzification procedures. The final value chosen is most often either the value corresponding to the highest grade of membership or the coordinate of the center of gravity.

The general structure of the model is shown in Fig. Membership functions are given in Figures 9. Because of the fact that current distance sensors perceive approximately m distance, distance membership function is used m scale. Brake rate membership function is used scale for expressing percent type.

Low Medium High 1 0. Fuzzy Allocation Map rules of the model was constituted for membership functions whose figures are given on Table It is important that the rules were not completely written for all probability. Figure 6 shows that the relationship between inputs, speed and distance, and brake rate.

Table 9. For this model, various alternatives are able to cross- examine using the developed model. Many reasons can contribute these results for example mainly driver fault, lack of infrastructure, environment, weather conditions etc.

In this study, a model was established for estimation of brake rate using fuzzy logic approach. Car brake rate is estimated using the developed model from speed and distance data. So, it can be said that this fuzzy logic approach can be effectively used for reduce to traffic accident rate.

This model can be adapted to vehicles. These decisions could be the determination of a flow rate for a chemical process or a drug dosage in medical practice.

The form of the control model also determines the appropriate level of precision in the result obtained.

Numerical models provide high precision, but the complexity or non-linearity of a process may make a numerical model unfeasible.

In these cases, linguistic models provide an alternative. Here the process is described in common language. The linguistic model is built from a set of if-then rules, which describe the control model. Although Zadeh was attempting to model human activities, Mamdani showed that fuzzy logic could be used to develop operational automatic control systems.

Much of the fuzzy literature uses set theory notation, which obscures the ease of the formulation of a fuzzy controller. Although the controllers are simple to construct, the proof of stability and other validations remain important topics. The outline of fuzzy operations will be shown here through the design of a familiar room thermostat.

A fuzzy variable is one of the parameters of a fuzzy model, which can take one or more fuzzy values, each represented by a fuzzy set and a word descriptor. The room temperature is the variable shown in Fig. Three fuzzy sets: The power of a fuzzy model is the overlap between the fuzzy values.

A single temperature value at an instant in time can be a member of both of the overlapping sets. In conventional set theory, an object in this case a temperature value is either a member of a set or it is not a member. In fuzzy logic, the boundaries between sets are blurred. In the overlap region, an object can be a partial member of each of the overlapping sets.

The blurred set boundaries give fuzzy logic its name.

By admitting multiple possibilities in the model, the linguistic imprecision is taken into account. The membership functions defining the three fuzzy sets shown in Fig.

There are no constraints on the specification of the form of the membership distribution. The Gaussian form from statistics has been used, but the triangular form is commonly chosen, as its computation is simple. The number of values and the range of actual values covered by each one are also arbitrary. Finer resolution is possible with additional sets, but the computation cost increases. As the complexity of a system increases, our ability to make precise and yet significant statements about its behaviour diminishes until a threshold is reached beyond which precision and significance or relevance become almost mutually exclusive characteristics.

The operation of a fuzzy controller proceeds in three steps. The first is fuzzification, where measurements are converted into memberships in the fuzzy sets. The second step is the application of the linguistic model, usually in the form of if-then rules. Finally the resulting fuzzy output is converted back into physical values through a defuzzfication process.

The membership functions are used to calculate the memberships in all of the fuzzy sets. The fuzzy inference is extended to include the uncertainty due to measurement error as well as the vagueness in the linguistic descriptions. In Fig. The minimum operation yields the overlap region of the two sets and the maximum operation gives the highest membership in the overlap.

It is interesting to note that there is no requirement that the sum of all memberships be 1. These use the measured state of the process, the rule antecedents, to estimate the extent of control action, the rule consequents. Although each rule is simple, there must be a rule to cover every possible combination of fuzzy input values. Thus, the simplicity of the rules trades off against the number of rules.

For complex systems the number of rules required may be very large. The rules needed to describe a process are often obtained through consultation with workers who have expert knowledge of the process operation.

The rules can include both the normal operation of the process as well as the experience obtained through upsets and other abnormal conditions. Exception handling is a particular strength of fuzzy control systems. For very complex systems, the experts may not be able to identify their thought processes in sufficient detail for rule creation. Rules may also be generated from operating data by searching for clusters in the input data space.

A simple temperature control model can be constructed from the example of Fig. Rule 1 transfers the 0. Similar values from rules 2 and 3 are 0. When several rules give membership values for the same output set, Mamdani used the maximum of the membership values. The result for the three rules is then 0. The rules presented in the above example are simple yet effective. To extend these to more complex control models, compound rules may be formulated. For example, if humidity was to be included in the room temperature control example, rules of the form: These can be used directly where the membership values are viewed as the strength of the recommendations provided by the rules.

It is possible that several outputs are recommended and some may be contradictory e. In automatic control, one physical value of a controller output must be chosen from multiple recommendations. In decision support systems, there must be a consistent method to resolve conflict and define an appropriate compromise.