Generation of interval-valued fuzzy and atanassov's intuitionistic fuzzy connectives from fuzzy connectives and from Kalpha operators: Laws for conjunctions and disjunctions, amplitude

In this paper, we study in-depth certain properties of interval-valued fuzzy sets and Atanassov’s intuitionistic fuzzy sets (A-IFSs). In particular, we study the manner in which to construct different interval-valued fuzzy connectives (or Atanassov’s intuitionistic fuzzy connectives) starting from an operator. We further study the law of contradiction and the law of excluded middle for these sets. Furthermore, we analyze the following properties: idempotency, absorption, and distributiveness. We conclude relating idempotency with the capacity that some of the connectives studied have for maintaining, in certain conditions, the amplitude (or Atanassov’s intuitionistic index) of the intervals on which they act. C © 2008 Wiley Periodicals, Inc.