Defuzzification Index for Ranking of Fuzzy Numbers on the Basis of Geometric Mean

Abstract

The importance of fuzzy numbers to express uncertainty in certain applications, concerned with decision making, is observed in a large number of problems of different kinds. In Decision making problems, the best of available alternatives is chosen to the possible extent. In the process of ordering the alternatives, ranking of fuzzy numbers plays a key role. A large volume of ranking methods, based on different features, have been available in this domain. Owing to the complicated nature of fuzzy numbers, the so far introduced methods suffered setbacks or posed difficulties or showed drawbacks in one context or other. In addition, some methods are lengthy and complicated to apply on concerned problems. In this article, a new ranking procedure based on defuzzification, stemmed from the concepts of geometric mean and height of a fuzzy number, is proposed. Finally, numerical comparisons are made with other existing procedures for testing and validation of proposed method with the support of some standard numerical examples.

3D Printer Selection for Aircraft Component Manufacturing Using a Nonlinear FGM and Dependency-Considered Fuzzy VIKOR Approach

“…FGM-fuzzy weighted average (FWA) [52][53][54], the ordered weighted average (OWA) [55][56][57], FGM-FTOPSIS [58][59][60][61][62][63], and FGM-fuzzy VIKOR [64][65][66][67]. Clearly, the same 3D printer, Stratasys Fortus 900mc, was chosen by all methods, showing the trustability of the experimental result using the proposed methodology.…”

“…As a resul distance between a 3D printer and its reference point was closer than that w considering the dependency, as shown in Figure 3. (7) The application results of four contrasting MCDM methods are reported in Tab FGM-fuzzy weighted average (FWA) [52][53][54], the ordered weighted average (O [55][56][57], FGM-FTOPSIS [58][59][60][61][62][63], and FGM-fuzzy VIKOR [64][65][66][67]. Clearly, the 3D printer, Stratasys Fortus 900mc, was chosen by all methods, showin trustability of the experimental result using the proposed methodology.…”

Untitled

“…Definition (1) [13] Let be a universe of discourse. A fuzzy set ̃ is defined to be a set of ordered pairs ̃ {( ̃( ))| + where ̃( ) ,and ̃( ) is called the membership function.…”