Experimental analysis of multi-attribute decision-making based on Atanassov intuitionistic fuzzy sets: a discussion of anchor dependency and accuracy functions

Abstract

This article presents a useful method for relating anchor dependency and accuracy functions to multiple attribute decision-making (MADM) problems in the context of Atanassov intuitionistic fuzzy sets (A-IFSs). Considering anchored judgement with displaced ideals and solution precision with minimal hesitation, several auxiliary optimisation models have proposed to obtain the optimal weights of the attributes and to acquire the corresponding TOPSIS (the technique for order preference by similarity to the ideal solution) index for alternative rankings. Aside from the TOPSIS index, as a decision-maker's personal characteristics and own perception of self may also influence the direction in the axiom of choice, the evaluation of alternatives is conducted based on distances of each alternative from the positive and negative ideal alternatives, respectively. This article originates from Li's [Li, D.-F. (2005), ‘Multiattribute Decision Making Models and Methods Using Intuitionistic Fuzzy Sets’, Journal of Computer and System Sciences, 70, 73–85] work, which is a seminal study of intuitionistic fuzzy decision analysis using deduced auxiliary programming models, and deems it a benchmark method for comparative studies on anchor dependency and accuracy functions. The feasibility and effectiveness of the proposed methods are illustrated by a numerical example. Finally, a comparative analysis is illustrated with computational experiments on averaging accuracy functions, TOPSIS indices, separation measures from positive and negative ideal alternatives, consistency rates of ranking orders, contradiction rates of the top alternative and average Spearman correlation coefficients.

Keywords:

• anchor dependency
• accuracy function
• multiple attribute decision-making
• intuitionistic fuzzy set
• displaced ideal