On the algebraic structures of the space of interval-valued intuitionistic fuzzy numbers

TL;DR

This paper explores the algebraic structure of the space of interval-valued intuitionistic fuzzy numbers, proving it forms a complete chain under certain comparison relations and entropy-based orderings.

Contribution

It establishes that the space of IVIFNs forms a complete chain under specific comparison relations, extending the understanding of their algebraic and order properties.

Findings

The space of IVIFNs is a complete chain under the proposed relations.

The comparison relation based on score and entropy functions is an admissible order.

IVIFNs form a complete chain with respect to multiple comparison indices.

Abstract

This study is inspired by those of Huang et al. (Soft Comput. 25, 2513--2520, 2021) and Wang et al. (Inf. Sci. 179, 3026--3040, 2009) in which some ranking techniques for interval-valued intuitionistic fuzzy numbers (IVIFNs) were introduced. In this study, we prove that the space of all IVIFNs with the relation in the method for comparing any two IVIFNs based on a score function and three types of entropy functions is a complete chain and obtain that this relation is an admissible order. Moreover, we demonstrate that IVIFNs are complete chains to the relation in the comparison method for IVIFNs on the basis of score, accuracy, membership uncertainty index, and hesitation uncertainty index functions.