By Yaochu Jin
Fuzzy rule platforms have stumbled on quite a lot of functions in lots of fields of technology and know-how. generally, fuzzy ideas are generated from human professional wisdom or human heuristics for quite basic structures. within the previous few years, data-driven fuzzy rule new release has been very lively. in comparison to heuristic fuzzy ideas, fuzzy ideas generated from information may be able to extract extra profound wisdom for extra complicated platforms. This publication provides a couple of techniques to the new release of fuzzy ideas from facts, starting from the direct fuzzy inference dependent to neural internet works and evolutionary algorithms established fuzzy rule iteration. along with the approximation accuracy, distinct consciousness has been paid to the interpretabil ity of the extracted fuzzy principles. In different phrases, the bushy ideas generated from information are meant to be as understandable to people as these generated from human heuristics. To this finish, many points of interpretabil ity of fuzzy platforms were mentioned, which has to be taken into consideration within the data-driven fuzzy rule iteration. during this method, fuzzy principles generated from facts are intelligible to human clients and as a result, wisdom approximately unknown platforms should be extracted.
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Extra resources for Advanced Fuzzy Systems Design and Applications
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.
B. 3 Interpretability of Fuzzy Rule System 29 where /3i, i = 1,2, ... , h are the coefficients of the polynomial that can approximate the given function g(x), h is the order of the polynomial, t2 is the accuracy that the fuzzy system can approximate the polynomial. For example, the given function is g(x) = eX defined on [-1,1]. 1, how many fuzzy rules are needed? 0038. 0962. 7. Consequently, the minimal needed rule number N = 2n* = 117. 01, then the minimal number of rules will be 1793. 87) is very likely conservative.
N) are fuzzy subsets for the system state Xi. It has been shown that a fuzzy system consisting of the above fuzzy linear sub-systems are capable of describing a highly nonlinear system. 5 Fuzzy Systems are Universal Approximators When a fuzzy system is designed for modeling and control, the most important thing is that the designed fuzzy system is theoretically able to realize the desired functional mapping. Therefore, the approximation capability of fuzzy systems is of great concern. It has been shown that both the Mamdani-type and the TSK-type fuzzy rule systems are universal approximators.