Generation of interval-valued fuzzy negations from trillas’ theorem. the case of interval type-2 fuzzy sets

Abstract

In this work we introduce amethod for building interval-valued negations using the characterization theorem for strong negations which was proposed by Trillas in 1979. We also show that interval type-2 fuzzy sets are a three dimensional representation of interval-valued fuzzy sets and we analyze the problems to build complementation for such interval type-2 fuzzy sets. We finally propose a method to construct this complementation.