Intuitionistic fuzzy multi-attribute group decision-making with an application to plant location selection based on a new extended VIKOR method

• We propose new method for MAGDM problems with trapezoidal intuitionistic fuzzy numbers.
• The weights of the decision-makers and attributes are considered completely unknown.
• The method integrates Shannon entropy and Evidence theory with Bayes approximation.
• A new extended VIKOR method is presented to solve intuitionistic fuzzy MAGDM problems.
• Utility of the method is demonstrated by solving plant location selection problem.

This paper presents a new decision method for multi-attribute group decision-making (MAGDM) problems in general and plant location selection (PLS) problem in particular, with intuitionistic fuzzy information captured through trapezoidal intuitionistic fuzzy numbers (TrIFNs). We assume that the weights of the decision-makers and attributes are completely unknown. The ratings of alternatives with respect to each attribute are considered as linguistic terms, which are mapped to the appropriate TrIFNs. To reduce subjective randomness in the decision-process, we determine attribute weights using the Shannon entropy theory, and weights of the decision-makers by integrating the Evidence theory with Bayes approximation. Furthermore, we extend the classical VIKOR method to solve MAGDM problems under intuitionistic fuzzy environment based on the TrIFNs. Considering that the PLS problem is essentially a MAGDM problem that involves evaluation of the alternatives on several conflicting attributes based on the vague and imprecise assessments of the decision-makers, we demonstrate utility of the proposed decision method by applying it solve the PLS problem. A detailed comparison is presented to demonstrate the advantages of the proposed methodology over the existing methods used for both the intuitionistic fuzzy MAGDM problems and PLS problem.