Fuzzy Operations and Relations

In the previous Chapter we got familiar with the basic concepts of a fuzzy variable and a fuzzy set which relate to the fuzzy value, fuzzy number or term. This brings us to the interesting issue of the connectivity or the interaction between the named variables and values. In this Chapter we will focus our attention on the various connections and relations between fuzzy sets; two given fuzzy sets A and B are somehow connected to produce a new fuzzy set C = A ◊ B. Such operations ◊ that create a new fuzzy set out of two are called fuzzy. The nature of fuzzy operations calls for a bit lengthy explanation — even though we are comfortable with the operations in classical algebra, crisp set theory and classical logic.