Construction of admissible linear orders for interval-valued Atanassov intuitionistic fuzzy sets with an application to decision making

Abstract

In this work we introduce a method for constructing linear orders between pairs of intervals by using aggregation functions. We adapt this method to the case of interval-valued Atanassov intuitionistic fuzzy sets and we apply these sets and the considered orders to a decision making problem.

Additively Consistent Interval-Valued Intuitionistic Fuzzy Preference Relations and Their Application to Group Decision Making

“…Nevertheless, one cannot ensure that the models in Equations (13) and (14) will always have nonempty feasible solutions. If there are empty feasible solutions of Equations (13) and (14), no consistent IVFPRs can be obtained from the initial IVIFPR. To fix this limitation, some relaxed variables p − ij , p + ij , q − ij , and q + ij are introduced into the IVIFV, then each IVIFV…”

“…In this paper, according to the conditions of the additively consistent IVFPR, two special IVFPRs (the absolute risk-taking-consistent IVFPR and the absolute risk-averse-consistent IVFPR) can be extracted from the original IVIFPR using Equations (14) and (15). In particular, if there are empty feasible solutions of Equations (14) and (15), two adjusted programming models, Equations (16) and (17) are constructed.…”

“…Later, Atanassov and Gargov [5] used the IFS to propose an interval-valued intuitionistic fuzzy set (IVIFS). Consequently, the interval-valued fuzzy preference relation (IVFPR) [6][7][8][9] and the interval-valued intuitionistic fuzzy (IVIF) preference relations (IVIFPR) [10][11][12][13][14] appeared in succession.…”

Information fusion for intuitionistic fuzzy decision making: An overview

“…Additionally, Bustince et al [47] and Miguel et al [48] investigated the methods of constructing admissible orders in terms of two aggregation functions. The important roles of admissible orders in different aspects, such as in the construction of the ordered weighted aggregation operators [49,50] and in the selection of alternatives in decision making [50,51], were also investigated.…”

Foundation of Interval-Valued Intuitionistic Fuzzy Limit and Differential Theory and an Application to Continuous Data

“…To some extent, interval values can better reveal the characteristics of things: vagueness and uncertainties. Due to the advantages of the IVIFS, it has been investigated widely and has been successfully applied to many elds, such as aggregation operators [8,9], decision-making [10,11], preference relations [12,13], entropy [14,15], and so on.…”