An algorithm for group decision making using n-dimensional fuzzy sets, admissible orders and OWA operators

Abstract

In this paper we propose an algorithm to solve group decision making problems using n-dimensional fuzzy sets, namely, sets in which the membership degree of each element to the set is given by an increasing tuple of n elements. The use of these sets has naturally led us to define admissible orders for n-dimensional fuzzy sets, to present a construction method for those orders and to study OWA operators for aggregating the tuples used to represent the membership degrees of the elements. In these conditions, we present an algorithm and apply it to a case study, in which we show that the exploitation phase which appears in many decision making methods can be omitted by just considering linear orders between tuples.

Study on n-Dimensional R-implications

“…An algorithm for MCDM using n-DFS, admissible orders and OWA operators [15] Introduces the concept of admissible order for n-DS presenting a construction method for those orders and studying OWA operators for aggregating tuples.…”

“…According to [15], a linear order on L n (U ) is called admissible if for all x, y ∈ L n (U ) it satisfies: x ≤ y ⇒ x y, meaning that refines ≤.…”

Optimizing Three-Dimensional Constrained Ordered Weighted Averaging Aggregation Problem with Bounded Variables

“…. Therefore, the optimal solution for type B is ( 1−l 3 2 , 1−l 3 2 , l 3 ). Type C is the nonzero components.…”

“…An ordered weighted averaging (OWA) operator [1] is a general class of parametric aggregation operators that appears in many research fields such as decision making [2][3][4][5][6], fuzzy system [7,8], statistics [9][10][11], risk analysis [12] and others [13,14]. For more details, see Carlsson and Fullér [15], Emrouznejad and Marra [16] and Yager et al [17].…”

Orness For Idempotent Aggregation Functions

“…These functions have been widely used in decision making [2,3], where it is necessary to merge the different opinions of several experts, or in image processing tasks [4], where the values of different pixels must be fused in order to obtain a single one.…”