Advanced Fuzzy Systems Design and Applications by Yaochu Jin

By Yaochu Jin

Fuzzy rule structures have came upon quite a lot of purposes in lots of fields of technology and expertise. ordinarily, fuzzy ideas are generated from human specialist wisdom or human heuristics for rather basic platforms. within the previous couple of years, data-driven fuzzy rule new release has been very energetic. in comparison to heuristic fuzzy ideas, fuzzy principles generated from information may be able to extract extra profound wisdom for extra complicated structures. This booklet offers a couple of techniques to the iteration of fuzzy principles from information, starting from the direct fuzzy inference established to neural internet­ works and evolutionary algorithms established fuzzy rule new release. along with the approximation accuracy, unique realization has been paid to the interpretabil­ ity of the extracted fuzzy ideas. In different phrases, the bushy principles generated from info are meant to be as understandable to humans as these generated from human heuristics. To this finish, many elements of interpretabil­ ity of fuzzy platforms were mentioned, which has to be taken under consideration within the data-driven fuzzy rule iteration. during this means, fuzzy principles generated from info are intelligible to human clients and for that reason, wisdom approximately unknown platforms may be extracted.

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Fuzzy partitions: (a) Distinguishable; (b) Indistinguishable. 5 Consistency of Fuzzy Rules Consistency of the rules in a fuzzy rule base concerns with the consistency of the validness of the knowledge represented by the rule base. Roughly speaking, fuzzy rules are conflicting to each other in the following situations: 1. The condition parts are the same, but the consequent parts are com- pletely different. For example, Rl: If Xl is Al and X2 is A 2 , then y is positive Large; R2: If Xl is Al and X2 is A 2 , then y is negative Large.

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.

Each alternative has a linguistic utility such as very important, important, don't care, not important and so on. • Linguistic fuzzy preference relations. 8, one can also express his judgement as "Objective Xi is more important than xl". Among the three preference models, fuzzy preference relations are the most widely used model. Several issues in fuzzy preference relations worth further discussion. Transitivity is one of the most important albeit disputing issue. Although there are examples in real world in which intransitivity of preferences occurs, it is still very helpful in applications to require the transitivity of preferences.

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