IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, zyxwvutsrqpon VOL. 24, NO. zyxwvutsrqpo I, JULY 1994 zyxwvuts 1035 Analysis of Flexible Structured Fuzzy Logic Controllers Ronald R. Yager, Dimitar P. Filev, and Tom Sadeghi, Senior Member, ZEEE Abstract- We suggest a new approach to the construction of fuzzy logic controllers based upon the selection of systems parameters. We first show that the standard fuzzy logic con- trollers have four basic operations which determine the nature of their functioning, the aggregation process used to combine individual antecedent firing levels to give a rule firing level, the determination of rule output based on antecedent firing level, the aggregation of individual rule outputs to find combined output, and the defuzzification process. We next show how we can parameterize these operationsusing S-OWA operators. These parameterized models give zyxwvutsr us a new class of Flexible Structured Fuuy Logic Controllers (FS-FLC). We look at the structure and performance of these controllers. We then suggest that one can improve the structure of fuzzy logic controllers by learning the values of the parameters introduced. 1. INTRODUCTION HE extensive development of fuzzy control is associated T with the Fuzzy Logic Controller (FLC) suggested by Mamdani and his associates zyxwvutsrq [1]-[4] as a knowledge-based system consisting of a family of logical rules that relate the error between the set point and the system output, its first derivative 'and the value of control variable generated by the fuzzy controller. In the most of the theoretical works and practical applications of fuzzy logic control the FLC is identified with the Mamdani model of FLC, and the structure of FLC is postulated on the basis of this model. The problem of tuning the controller is solved by appropriate modification of the membership functions of antecedent and consequent fuzzy sets. In this work we provide for a significant generalization of the Mamdani fuzzy logic control structure. We call these sys- tems Flexible Structured Fuuy Logic Controllers (FS-FLC). With these new types of controllers we provide for a param- eterization of the basic operations used in the Mamdani type controller. More specifically the operators used to implement the aggregation of antecedents in rules, the firing of rules, the aggregation of the rule outputs, and the defuzzification process are allowed to be variable. By parameterizing the aggregation operators we enable a higher degree of modeling for the system. As we shall see the classic Mamdani model Manuscript received September 5, 1992; revised August 16, 1993. R. R. Yager and D. P. Filev are with the Machine Intelligence Institute, T. Sadeghi is with the Department of Electrical Engieering, State University IEEE Log Number 9402089. Iona College, New Rochelle, NY 10801 USA. of New York, Binghamton, NY 13902-6000 USA. as well as the Takagi-Sugeno zyxw [5] become special cases of this very general class of models. With the introduction of these FS-FLC we have two com- plementary modes for tuning, the first are the membership membership functions of the linguistic variables, Le., the parameters of FLC, the second are connectives used in the fuzzy reasoning mechanism of the controller. As we shall see the use of FS-FLC essentially provides a medium in which we are, in a continuous manner, changing the structure of the controller. We note that considerable use is made of the S-OWA operators [8] in implementing these Flexible Structured Fuzzy Logic Controllers. 11. SOFTENING THE PARADIGM OF THE MMDANI MODEL OF FLc Lets consider a multiple input-single output FLC. The knowledge base of the FLC is defined by the set of linguistic rules of the type: IF zyxwvu U1 = B;l AND . . . AND U, = B;, THEN V = Di, i = (1, zyx m). In the above& are reference antecedent fuzzy sets of the T in- put variables Ul, U2, . . . , U, and zyxw D;, are reference consequent fuzzy sets of the output variable V. The Bij are defined on the discrete universes of discourse Xj , j = (1, T-) and V has as its universe the finite set Y. We shall assume Card(Xj) = pj, Card(Y) = q. At times we shall find it useful to represent the meGbership functions &(E), D;(y) of the fuzzy sets B;j and D;, by column vectors [B;j] and [D;]([B;j]* and [oilT will be considered row vectors). We shall also let [Xj] and [Y] be column vectors whose elements are all ones. Note that the vectors [&j] and [Xj] are pj-dimensional and the vectors [D;] and [Y] are q -dimensional. Under the Mamdani model of FLC the output fuzzy set F;, inferred by the ith rule is zyxw F;(Y) = 7; A D;(Y) where T; is the firing strength of the ith rule, defined for given crisp inputs u1, . . . , UT by T; = B;l(ul) A.*-AB;,('LL,). The output fuzzy sets F;, inferred by the individual rules are aggregated by an OR aggregating operator, thus the overall 0018-9472/94$04.00 0 1994 IEEE