An integrated group FWA-ELECTRE III approach based on interval type-2 fuzzy sets for solving the MCDM problems using limit distance mean

Abstract

The material handling equipment (MHE) has a close connection with layout of machinery and plays the important role in productivity of servicing or manufacturing systems. Since each of MHE has distinct characteristics than the others with respect to conflicting criteria and design experts may state the different subjective judgments with respect to qualitative criteria, the material handling equipment selection problem (MHESP) can be taken into account as a group multi-criteria decision-making (GMCDM) problem. In this paper, a version of type-2 fuzzy sets (T2FSs), named Gaussian interval type-2 fuzzy sets (GIT2FSs), is first used as an alternative to the traditional triangular membership functions (MFs) to weight criteria and sub-criteria and also evaluate of alternatives with respect to sub-criteria. The synthetic value method of GIT2FSs is then carried out to convert the assessments stated as GIT2FSs for each alternative with respect to each sub-criterion and also weights of criteria (sub-criteria) into the single fuzzy rating and weight, respectively. Then, the fuzzy weighted average (FWA) approach is adopted to integrate the single fuzzy ratings of each alternative with respect to sub-criteria and the single fuzzy weights of sub-criteria under each criterion with the aggregated weighted ratings. In next stage, ELECTRE III (ELimination Et Choix Traduisant la Realite´—elimination and choice translation reality) is generalized with GIT2FSs to select the optimal MHE through a new ranking approach. Moreover, some arithmetic operations and properties are extended to GIT2FSs. In addition, to demonstrate its potential applications, the proposed methodology is implemented in a real case study and an illustrative example, and then, the ranking results are compared with those of the others in the literature. Finally, the sensitivity analysis is carried out to show robustness and stability of the obtained results.