A Majority Rule-Based Measure for Atanassov-Type Intuitionistic Membership Grades in MCDM

Orderly Atanassov-type intuitionistic membership grades would be required in decision-making problems, however, sometime they are not completely ordered. To solve this problem, in this article we propose a quantification method for Atanassov-type intuitionistic membership grades, and use it to rank them. According to the majority voting rules, we introduce the measurement function for membership degree. We quantify the uncertainty of information and the preferences of decision-makers conveyed through intuitionistic fuzzy sets. We then use the introduced surrogates to construct the measurement for membership grades. The properties and some logical operations of measurement value are also studied. We recommend using the Takagi–Sugeno model and method to assign values to tuning parameters <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> . Moreover, we present two models for multicriteria decision-making problem, which use the measurement to determine the ranking between sets. Finally, a numerical example of supplier selection is given to show the competitive performance of the proposed method in terms of efficiency and feasibility.