The choice of describing engineering applications coincides with the Fuzzy Logic and Neural Network research interests of the readers. Modeling and control of. Figure 1–1: Soft computing as a composition of fuzzy logic, neural networks and probabilistic reasoning. Intersections include. • neuro-fuzzy. PDF | Hybrid intelligent systems combining fuzzy logic and neural networks are proving their effectiveness in a wide variety of real-world problems. Fuzzy logic.
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PDF | presentation about introduction to neural and fuzzy logic. Integration of fuzzy logic and neural networks . In theory, neural networks, and fuzzy systems are equivalent in that they. Effectivity of neural networks (in pdf format) Introduction to Neuro-Fuzzy Systems, Advances in Soft Computing Series, Springer-Verlag, Berlin/ Heildelberg.
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Truth Fairly true Very true 1 Fig. Truth Fairly false Very false 1 Fig. Let t be a term of linguistic variable Truth. What are the fuzzy implications? What are the fuzzy modifiers? Explain with an example. What are the linguistic variables? Give examples. Given the set 6 of people in the following age groups: Baldwin and B. Pilsworth, Axiomatic approach to implication for approximate reasoning with fuzzy logic, Fuzzy Sets and Systems, Vol. Bandler, and L. Willmott, Two fuzzier implication operators in the theory of fuzzy power sets, Fuzzy Sets and Systems, Vol.
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Dubois and H. Prade, A theorem on implication functions defined from triangular norms, Stochastica, Vol. Trillas and L. Valverde, On mode and implications in approximate reasoning, In: Gupta, A.
Kandel, W. Bandler and J. Kisska [Eds. Ahlquist, Application of fuzzy implication to probe nonsymmetric relations: Part 1, Fuzzy Sets and Systems, Vol. Oh and W. Smets and P. Cao and A. Da, E. Kerre, G. De Cooman, B. Cappelle and F. Vanmassenhove, Influence of the fuzzy implication operator on the method-of-cases inference rule, International Journal of Approximate Reasoning, Vol.
Ruan and E. Castro, M. Delgado and E. This theory provides a powerful framework for reasoning in the face of imprecise and uncertain information. Central to this theory is the representation of propositions as statements assigning fuzzy sets as values to variables. Let x and y be linguistic variables, e.
If x is An then y is Cn fact: The classical Modus Ponens inference rule says: The fuzzy implication inference is based on the compositional rule of inference for approximate reasoning suggested by Zadeh.
The classical Modus Tollens inference rule says: The Generalized Modus Ponens should satisfy some rational properties. Suppose that A, B and A1 are fuzzy numbers. Example 5.
Total indeterminance: Explain the theory of approximate reasoning. What are the translation rules? Explain them with examples. What are the rational properties? Zadeh, Fuzzy logic and approximate reasoning, Syntheses, Vol. Zadeh, The concept of a linguistic variable and its application to approximate reasoning- Part I, Information Sciences, Vol.
Mizumoto and H. Zadeh, Linguistic variables, approximate reasoning and dispositions, Medical Information, Vol. Zadeh, The role of fuzzy logic in the management of uncertainty in expert systems, Fuzzy Sets and Systems, Vol. Sugeno and T. Yager, Strong truth and rules of inference in fuzzy logic and approximate reasoning, Cybernetics and Systems, Vol.
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Gorzalczany, A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems, Vol. Lee, Y. L Grize and K. Ying, Some notes on multi-dimensional fuzzy reasoning, Cybernetics and Systems, Vol. Cao, A. Kandel and L. Magrez and P. Smets, Fuzzy modus ponens: A new model suitable for applications in knowledge-based systems, International Journal of Intelligent Systems, Vol. Torasso and L.
Console, approximate reasoning and prototypical knowledge, International Journal of Approximate Reasoning, Vol. Kruse and E. Schwecke, Fuzzy reasoning in a multi-dimensional space of hypothesis, International Journal of Approximate Reasoning, Vol. Luo and Z. Keller, D, Subhangkasen, K.
Unklesbay and N. Unklesbay, An approximate reasoning technique for recognition in color images of beef steaks, International Journal of General Systems, Vol. Prade, Fuzzy sets in approximate reasoning, Part 1: Prade, Fuzzy sets in approximate reasoning, Part 2: Logical approaches, Fuzzy Sets and Systems, Vol.
Gupta and J. Dutta, approximate spatial reasoning: Integrating qualitative and quantitative constraints, International Journal of Approximate Reasoning, Vol. Peng, A. Kandel and P. Wang, Concepts, rules and fuzzy reasoning: Ruspini, Approximate reasoning: Hudson, M. Cohen and M. Chen, An improved algorithm for inexact reasoning based on extended fuzzy production rules, Cybernetics and Systems, Vol.
Raha and K. Ray, Analogy between approximate reasoning and the method of interpolation, Fuzzy Sets and Systems, Vol. Reddy and M. Larsen and R. Koczy and K. Hirota, Approximate reasoning by linear rule interpolation and general approximation, International Journal of Approximate Reasoning, Vol.
Zhang, An approximate reasoning system: Design and implementation, International journal of approximate reasoning, Vol. Bien and M. Zhao and B. Functions that qualify as fuzzy intersections and fuzzy unions are usually referred to in the literature as t-norms and t-conorms, respectively.
Furthermore, the standard fuzzy intersection min operator produces for any given fuzzy sets the largest fuzzy set from among those produced by all possible fuzzy intersections t-norms. The standard fuzzy union max operator produces, on the contrary, the smallest fuzzy set among the fuzzy sets produced by all possible fuzzy unions t-conorms.
That is, the standard fuzzy operations occupy specific positions in the whole spectrum of fuzzy operations: In fuzzy sets theory triangular norm are extensively used to model the logical connective and. In other words, any t-norm T satisfies the properties: The basic t-norms are: The minimum t-norm is automatically extended and TP a1, a2, Triangular co-norms are extensively used to model logical connectives or.
In other words, any t-conorm S satisfies the properties: The basic t-conorms are: Let T be a t-norm. Lemma 6. Let S be a t-conorm. The operation union can be defined by the help of triangular conorms. Example 6. These connectives can be categorized into the following three classes union, intersection and compensation connectives.
Union produces a high output whenever any one of the input values representing degrees of satisfaction of different features or criteria is high. 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.
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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.
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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.
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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. Genetic Algorithms: Elements, a simple genetic algorithm, working of genetic algorithms evolving neural networks.
Download Unit 1. Download Unit 2. Download Unit 3. Download Unit 4. Thank you so much sir ,,,these notes are very helpful but please upload data mining and data warehousing notes if you have available… Thank you. Toggle navigation. Software Engineering by Roger S.