Decision Making with Intuitionistic Fuzzy Best-Worst Method

Abstract

Best-worst method (BWM) is an efficient multi-attribute decision-making (MADM) method. This paper puts forward two decision-making methods with intuitionistic fuzzy (IF) BWM (IF-BWM). Firstly, a new consistency definition of IF-BWM is presented. To comprehensive reflect the consistency level of original IF preference comparisons, an acceptable input-and-output-based consistency ratio (CR) of IF-BWM preference comparisons is defined to measure the consistency level of IF-BWM preference comparisons. A goal linear programming model is built to improve the consistency level of input-based CR from the original IF-BWM preference comparisons. To induce an optimal multiplicative normalized IF weight vector (IFWV), a programming model is set up. Accordingly, a novel individual IF-BWM is proposed. Using the deviation between IF values, an analytic expression of determining experts' weights is formulated. By minimizing the weighted deviation between individual multiplicative normalized IFWVs and group multiplicative normalized IFWV, a programming model is built to determine the optimal group multiplicative normalized IFWV. Subsequently, a novel group IF-BWM is put forward. Two real-life examples are furnished to reveal the validity of proposed individual IF-BWM and group IF-BWM in practice. In view of theoretical aspect, this paper fosters the theory of IF-BWM by firstly proposing an input-based CR, output-based CR, an acceptable input-and-output-based CR and group IF-BWM. The model of improving CR of IF-BWM preference comparisons is initially discussed. This paper has a certain guiding significance for the following research on IF-BWM and provides a novel perspective for an MADM problem with positive and negative preference information.