Novel construction methods of interval-valued fuzzy negations and aggregation functions based on admissible orders

Abstract

In this work, we present a review of the existing admissible orders and propose a generalization of all of these orders in the discrete setting. Also, we propose some construction methods of interval-valued fuzzy negations w.r.t. the existing admissible orders on L([0,1]) via arbitrary pairs of fuzzy logic connectives that are defined over the unit interval [0,1] and show that these proposed methods generalize some of the existing construction methods proposed by Asiain et al. Further, we propose also some construction methods of interval-valued aggregation functions w.r.t. the existing admissible orders on L([0,1]) via standard fuzzy logic connectives on [0,1] and also, as a special case, interval-valued t-norms and t-conorms are constructed.