Design of fuzzy logic controllers based on generalized T-operators

Gupta, Manjari; Qi, J.

doi:10.1016/0165-0114(91)90173-n

Cited by 131 publications

(25 citation statements)

References 5 publications

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“…In the literature there are many possibilities for the selection of the fuzzy operators that determine how to evaluate each individual rule and how to obtain a final conclusion from all the rules. There are also conflicting opinions about the best selection of these fuzzy primitives [32]- [34]. In this paper, the fuzzy inference method uses the product as T-norm and the centroid method with sum-product operator as the defuzzification strategy.…”

Section: Statement Of the Problemmentioning

confidence: 99%

A systematic approach to a self-generating fuzzy rule-table for function approximation

Pomares

Rojas

Ortega

et al. 2000

IEEE Trans. Syst., Man, Cybern. B

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Abstract-In this paper, a systematic design is proposed to determine fuzzy system structure and learning its parameters, from a set of given training examples. In particular, two fundamental problems concerning fuzzy system modeling are addressed: 1) fuzzy rule parameter optimization and 2) the identification of system structure (i.e., the number of membership functions and fuzzy rules). A four-step approach to build a fuzzy system automatically is presented:Step 1 directly obtains the optimum fuzzy rules for a given membership function configuration.Step 2 optimizes the allocation of the membership functions and the conclusion of the rules, in order to achieve a better approximation.Step 3 determines a new and more suitable topology with the information derived from the approximation error distribution; it decides which variables should increase the number of membership functions. Finally, Step 4 determines which structure should be selected to approximate the function, from the possible configurations provided by the algorithm in the three previous steps. The results of applying this method to the problem of function approximation are presented and then compared with other methodologies proposed in the bibliography.

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Section: Statement Of the Problemmentioning

confidence: 99%

A systematic approach to a self-generating fuzzy rule-table for function approximation

Pomares

Rojas

Ortega

et al. 2000

IEEE Trans. Syst., Man, Cybern. B

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“…These two types are used far more often than any other types. As a matter of fact, the remaining types [3] have hardly been used. As for reasoning used in the rules, any fuzzy inference methods may be used.…”

Section: Configuration Of General Mamdani Fuzzy Controllersmentioning

confidence: 98%

Conditions for analytically determining general fuzzy controllers of Mamdani type to be nonlinear, piecewise linear or linear

Ying

2004

Soft Comput

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A fuzzy controller has many degrees of freedom in terms of its component selection (e.g., different types of fuzzy sets, and different kinds of fuzzy rules). Consequently, linear or piecewise linear controllers can be unconsciously resulted, which is undesirable, as it is irrational to use fuzzy control that way. Fuzzy controllers should be used, and taken advantage of, as nonlinear controllers only, not as linear or piecewise linear controllers. Currently, there exist no rigorous methods, analytical or otherwise, to precisely determine whether a fuzzy controller designed is nonlinear or not. In the present paper, we establish conditions under which linearity, piecewise linearity or nonlinearity of a general class of Mamdani fuzzy controllers can be determined. These fuzzy controllers can use input fuzzy sets of any types, arbitrary fuzzy rules, arbitrary singleton output fuzzy sets, arbitrary inference methods, either Zadeh or the product fuzzy logic AND operator, and the centroid defuzzifier. We prove that the fuzzy controllers using Zadeh AND operator are always nonlinear, regardless of choice of the other components. The general fuzzy controllers using the product AND operator are also always nonlinear except when all input fuzzy sets are triangular or trapezoidal and a couple of other conditions are satisfied. The exceptions lead to piecewise linear or linear controllers. A concrete example is provided to illustrate the results. Our new findings provide muchneeded insight to connections between the components and nonlinearity of the fuzzy controllers. They enable fuzzy control developers to correctly choose appropriate types and configurations of the components (e.g., triangular fuzzy sets instead of Gaussian ones) at the beginning of design stage, saving design time and effort. Soft Comput (2005) 9: 606-616

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“…Moreover, Bellman and Zadeh (1977) stated that the appropriate composite operator strongly depends on the application context and has no universal definition in the situations where the intersection connector acts interactively. Gupta and Qi (1991) studied the performance of the fuzzy logic controllers with various combinations of t-norms and t-conorms implemented and concluded that the performance very much depends on the choice of the composite operators. Van de Walle et al (1998) andDe Baets et al (1998) discussed the requirements of choosing a suitable t-norm for modeling a fuzzy preference structure.…”

Section: Resolution Of Sup-t Equationsmentioning

confidence: 99%

On the resolution and optimization of a system of fuzzy relational equations with sup-T composition

Fang

2008

Fuzzy Optim Decis Making

123

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This paper provides a thorough investigation on the resolution of a finite system of fuzzy relational equations with sup-T composition, where T is a continuous triangular norm. When such a system is consistent, although we know that the solution set can be characterized by a maximum solution and finitely many minimal solutions, it is still a challenging task to find all minimal solutions in an efficient manner. Using the representation theorem of continuous triangular norms, we show that the systems of sup-T equations can be divided into two categories depending on the involved triangular norm. When the triangular norm is Archimedean, the minimal solutions correspond one-to-one to the irredundant coverings of a set covering problem. When it is non-Archimedean, they only correspond to a subset of constrained irredundant coverings of a set covering problem. We then show that the problem of minimizing a linear objective function subject to a system of sup-T equations can be reduced into a 0-1 integer programming problem in polynomial time. This work generalizes most, if not all, known results and provides a unified framework to deal with the problem of resolution and optimization of a system of sup-T equations. Further generalizations and related issues are also included for discussion.

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Design of fuzzy logic controllers based on generalized T-operators

Cited by 131 publications

References 5 publications

A systematic approach to a self-generating fuzzy rule-table for function approximation

A systematic approach to a self-generating fuzzy rule-table for function approximation

Conditions for analytically determining general fuzzy controllers of Mamdani type to be nonlinear, piecewise linear or linear

On the resolution and optimization of a system of fuzzy relational equations with sup-T composition

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