Multiple attribute decision making using Beta distribution of intervals, expected values of intervals, and new score function of interval-valued intuitionistic fuzzy values

Abstract

In this paper, we propose a new multiple attribute decision making (MADM) method using the Beta distribution of intervals, the expected values of intervals, and the proposed new score function of interval-valued intuitionistic fuzzy values (IVIFVs). Firstly, it transformed each IVIFV in the decision matrix (DM) into three intervals to get the transformed matrix (TM). Then, it calculates the expected values of the obtained three intervals for each triplet in the TM, respectively, and then uses the proposed new score function to calculate the score value of each IVIFV in the DM to obtain the score matrix. Then, it transforms the interval-valued intuitionistic fuzzy (IVIF) weight of each attribute into three intervals and calculates the expected values of the obtained three intervals, respectively. Then, it uses the proposed new score function to calculate the score value of the IVIF weight of each attribute to obtain the normalized optimal weight of each attribute. Finally, based on the obtained score matrix and the obtained optimal weight of each attribute, it computes the weighted score of each alternative to get the preference order of alternatives. The proposed MADM method can overcome the drawbacks of the existing MADM methods in IVIF environments.