By Yaochu Jin

Fuzzy rule structures have came upon quite a lot of purposes in lots of fields of technology and expertise. often, fuzzy principles are generated from human specialist wisdom or human heuristics for fairly basic structures. within the previous few years, data-driven fuzzy rule iteration has been very lively. in comparison to heuristic fuzzy ideas, fuzzy principles generated from information may be able to extract extra profound wisdom for extra complicated structures. This e-book provides a few ways to the iteration of fuzzy principles from info, starting from the direct fuzzy inference dependent to neural internet­ works and evolutionary algorithms dependent fuzzy rule new release. along with the approximation accuracy, exact recognition has been paid to the interpretabil­ ity of the extracted fuzzy ideas. In different phrases, the bushy principles generated from information are meant to be as understandable to people as these generated from human heuristics. To this finish, many facets of interpretabil­ ity of fuzzy platforms were mentioned, which has to be taken into consideration within the data-driven fuzzy rule new release. during this manner, fuzzy principles generated from information are intelligible to human clients and for this reason, wisdom approximately unknown platforms will be extracted.

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Extra resources for Advanced Fuzzy Systems Design and Applications

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In this section, several aspects that are believed to be essential for the interpretability offuzzy systems will be discussed [125, 229, 35, 114]. They include the properties of fuzzy membership functions, of the fuzzy partitions of the linguistic variable, of the consistency of the rule base, and of the structure of the rule base. For the fuzzy partition of the linguistic variables, both the completeness and distinguishability are considered. Furthermore, the number of fuzzy subsets in a partition should be limited (empirically not larger than ten).

One additional remark on the consistency definition is that it is mainly suitable for the Mamdani-type fuzzy rules. For the Takagi-Sugeno-Kang (TSK) fuzzy rules, the consistency is harder to evaluate, when the rule consequent is a function of the input variables. However, the interpretability of the TSK fuzzy rules may be investigated in terms of the physical meaning of each local model that the rule consequent carries [251]. Consistency evaluation of fuzzy rules is sometimes difficult. This happens when a fuzzy system has more than one output variable and the relationship between these variables is unclear.

The number of strategy parameters for each object parameter is different in various evolution strategy algorithms. It is seen that genetic algorithms have more flexible representations than evolution strategies, which may be one reason why genetic algorithms have found applications in a much wider range of fields. On the other hand, different representations exhibit different causality properties between the genotype and phenotype of an evolutionary algorithm. By causality, it is meant that the degree of variations in the genotype space should be properly reflected by the degree of variation in the phenotype space.

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