Download Advanced Fuzzy Systems Design and Applications by Yaochu Jin PDF

By Yaochu Jin

Fuzzy rule platforms have discovered a variety of functions in lots of fields of technological know-how and know-how. usually, fuzzy ideas are generated from human specialist wisdom or human heuristics for quite uncomplicated platforms. within the previous few years, data-driven fuzzy rule new release has been very lively. in comparison to heuristic fuzzy ideas, fuzzy principles generated from facts may be able to extract extra profound wisdom for extra advanced platforms. This publication provides a few techniques to the iteration of fuzzy ideas from facts, starting from the direct fuzzy inference established to neural internet­ works and evolutionary algorithms established fuzzy rule new release. along with the approximation accuracy, certain cognizance has been paid to the interpretabil­ ity of the extracted fuzzy ideas. In different phrases, the bushy ideas generated from information are meant to be as understandable to humans as these generated from human heuristics. To this finish, many elements of interpretabil­ ity of fuzzy structures were mentioned, which has to be taken under consideration within the data-driven fuzzy rule new release. during this approach, fuzzy ideas generated from information are intelligible to human clients and consequently, wisdom approximately unknown structures will be extracted.

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2 Knowledge Representation with Fuzzy Preference Models Besides IF-THEN rules, a priori knowledge can also be available that describes the relative importance of different variables or objectives, which are called preferences. Since human judgements, including preferences, are often imprecise, fuzzy logic also plays an important role in decision making and multi-criteria optimization [149). Given n alternatives Ol,02, ... 4 Knowledge Processing with Fuzzy Logic 43 -1 " Fig. 23. Input-output surface of the obtained fuzzy controller.

Membership functions of dn • NL NS ZO PS PL ~------------~~--L-L-~------------ -30 -S -4 0 4 8 __~Vr 30 Fig. 21. Membership functions of V r . The universe of discourse of each variable depends in part on its physical range. However, the proper selection of the universe can improve the performance of the fuzzy system. Trial and error may be necessary in this process. 3. Extraction of fuzzy rules from expert knowledge and common sense. In this example, it is straightforward to get the following rules: R 1: If d n is Very Small and Vr is Negative Small, then a is Negative Big; R 2 : If d n is Very Small and Vr is Zero, then a is Negative Medium; R3: If dn is OK and Vr is Zero, then a is Zero; 42 1.

36 1. 98) where S(Aij , Akj) is the fuzzy similarity between the fuzzy sets Aij and Akj. We can define the fuzzy similarity measure as (159): S(A-. 99) where M(A) is the size of the fuzzy set A. 100) where S(Bi' Bk) is the similarity between the fuzzy sets Bi and Bk. Thus, the consistency of the two fuzzy rules can be defined by: CN(R . 0)2} SRP(Ri,Rk) )2 . 101) This definition for the consistency of fuzzy rules has two fundamental properties. First, the degree of the consistency tends to be high when the SRP and SRC of the two rules are in proportion, provided that the SRP of the two rules is high.

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