Fuzzy best-worst method based on triangular fuzzy numbers for multi-criteria decision-making

In this paper, we propose a new fuzzy best-worst method (BWM) based on triangular fuzzy numbers for multi-criteria decision-making (MCDM). Aimed at the Best-to-Others vector and the Others-to-Worst vector in the form of triangular fuzzy numbers, this paper regards consistency equations as fuzzy equations. The derivation of optimal fuzzy weights of criteria is formulated as a fuzzy decision-making problem, where a mathematical programming model is constructed to derive optimal fuzzy weights of criteria to build a normalized triangular fuzzy weight vector. Then, we propose four linear programming models based on the obtained mathematical programming model for the optimistic decision maker, the pessimistic decision maker and the neutral decision maker, respectively. Through a proper selection of the values of tolerance parameters, each of the linear programming models certainly has a unique global optimal solution. Moreover, this paper proposes the concept of fuzzy consistency index and the concept of fuzzy consistency ratio. Several application examples are used to validate the proposed fuzzy BWM. The proposed fuzzy BWM provides us with a very useful way for MCDM in fuzzy environments. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

This paper introduces a new fuzzy best-worst method based on triangular fuzzy numbers for multi-criteria decision-making. Mathematical programming models are constructed to derive optimal fuzzy weights of criteria and four linear programming models are proposed for different types of decision makers. The concept of fuzzy consistency index and ratio are also proposed and validated through application examples.