Selected Design and Processing Aspects of Fuzzy Sets
Witold Pedrycz, Petr Ekel, Roberta Parreiras · 2010
This chapter presents the discussion on the fundamentals of fuzzy sets by concentrating on three main issues: (1) the design of fuzzy sets (membership functions); (2) logic operations and aggregation of fuzzy sets; and (3) transformations (mappings) of fuzzy sets including the fundamentals of fuzzy arithmetic.These are the essentials which make the framework of fuzzy sets fully operational when supporting a wide range of applications. Fuzzy numbers are convex and normal fuzzy sets defined on the set of real numbers. Operations with fuzzy numbers can be developed with the help of the extension principle. In particular, standard fuzzy arithmetic can be approached choosing the min t-norm. Several other choices are possible, but practice has shown that standard fuzzy arithmetic still is one of the highest applicability. Controlled Vocabulary Terms aggregation; fuzzy set theory