A characterization for some type-2 fuzzy strong negations

Abstract

P. Hernandez et al. in 2014 established the axioms that an operation must fulfill in order to be a negation on a bounded poset (partially ordered set). In this work, we focus on the set L of the membership degrees of the type-2 fuzzy sets which are normal and convex functions in [0,1]. This set has a bounded and complete lattice structure, thank to which negations and strong negations have been constructed by the authors applying the Zadeh's Extension Principle. In addition, the authors showed new negations on L that are different from the negations presented in 2014 applying the Zadeh's Extension Principle. In this work, the authors obtain a characterization of the strong negations on L that leave the constant function 1 fixed. (C) 2019 Elsevier B.V. All rights reserved.

P. Hernandez et al. in 2014 established the axioms that an operation must fulfill in order to be a negation on a bounded poset (partially ordered set). In this work, we focus on the set L of the membership degrees of the type-2 fuzzy sets which are normal and convex functions in [0,1]. This set has a bounded and complete lattice structure, thank to which negations and strong negations have been constructed by the authors applying the Zadeh's Extension Principle. In addition, the authors showed new negations on L that are different from the negations presented in 2014 applying the Zadeh's Extension Principle. In this work, the authors obtain a characterization of the strong negations on L that leave the constant function 1 fixed. (C) 2019 Elsevier B.V. All rights reserved.