By Michael Smithson
Fuzzy Set research for Behavioral and Social Sciences (Recent examine in Psychology) ASIN: 0387964312
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Extra resources for Fuzzy Set Analysis for Behavioral and Social Sciences
Example text
Kickert's chapter on "Fuzzy linguistic models" also is clear and concise. For those interested in decision theory and its offshoots, this book remains one of the most balanced appraisals of the advantages and drawbacks of fuzzy set theory for that field. Much of what Kickert has to say applies to the human sciences as well. The volume by Zadeh et. al. would be an appropriate jumping-off point for those who feel reasonably at home with basic fuzzy set concepts, language, and notation after reading this book (or even this chapter).
But others have applauded this outcome since they never approved of the Excluded Middle, which may well account for the relative popularity of fuzzy sets and fuzzy logic in China. Of the alternative operators for "and" and "or", the bounded sum pair actually preserves the Excluded Middle because t p+ t p '= 1. Fuzzy logic becomes interesting once we move onto the topic of implication. Zadeh's original proposal for implication begins with the claim that "if P then Q else R" is defined as (P and Q) or (P' and R).
Weak equality for sets A and B exists if A weakly includes Band B weakly includes A. Likewise, for any index of inclusion, a similarity index may be defined as the minimum degree to which A includes B or B includes A. The concept of overlap is looser than similarity, since one set may overlap another if it includes that set or is equal to it. Thus, weak overlap between sets A and B exists if A weakly includes B or B weakly includes A, ~nd correspondingly an overlap index may be defined as the maximum degree to which A includes B or B includes A.