Multi-Criteria Group Decision-Making Models in a Multi-Choice Environment

Abstract

The best–worst method (BWM) has recently demonstrated its applicability in addressing various decision-making problems in a practical setting. The traditional BWM method is based on deterministic information gathered from experts as pairwise comparisons of several criteria. The advantage of BWM is that it uses fewer calculations and analyses while maintaining good, acceptable consistency ratio values. A multi-choice best–worst method (MCBWM), which considers several options for pairwise comparison of preferences between the criteria, has recently been developed. The experts are given the option to select values from several comparison scales. The MCBWM technique has been shown to be better. Presenting the options for which an optimal solution has been found simplifies the calculation and establishes the ideal weight values. This study proposes two different mathematical programming models for solving multi-criteria decision-making problems having multiple decision-makers. The two methods are proposed considering the multi-choice uncertainty assumption in pairwise criteria comparisons. Additionally, it considers the best–worst method as the base model. The multi-choice uncertainty is applied to determine the best choice out of multiple choices. It gives a real-life scenario to the decision-making problems. Although there are many other forms of uncertainty, such as fuzzy, intuitionistic fuzzy, neutrosophic, probabilistic, etc., it focuses on choices instead of ambiguity in terms of the probabilistic or fuzzy nature of parameters. The parameter considered as multi-choice is the pairwise comparison. These parameters are handled by applying the Lagrange interpolating polynomial method. The proposed models are novel in terms of their mathematical structure and group decision-making approach. The models are formulated and further validated by solving numerical examples. It provides a framework for solving mcdm problems where the weightage to the decision-makers is also incorporated. The CR values for all the models of example 1 and 2, and the case study has been found acceptable.

Keywords

• best–worst method
• multi-choice best–worst method
• multi-criteria decision-making
• group decision-making
• mathematical programming