Aggregation operators on type-2 fuzzy sets

Abstract

Cubillo et al. in 2015 established the axioms that an operation must fulfill to be an aggregation operator on a bounded poset (partially ordered set), in particular onM (set of fuzzy membership degrees of T2FSs, which are the functions from [0,1] to [0,1]). Previously, Takáˇc in 2014 had applied Zadeh's extension principle to obtain a set of operators on M which are, under some conditions, aggregation operators on L*, the set of strongly normal and convex functions of M. In this paper, we introduce a more general set of operators on M than were given by Takáˇc, and we study, among other properties, the conditions required to satisfy the axioms of the aggregation operator on L (set of normal and convex functions on M), which includes the set L*.