Defuzzification of Intuitionistic Z-Numbers for Fuzzy Multi Criteria Decision Making

Abstract

Z-numbers and intuitionistic fuzzy numbers are both important as they consider the reliability of the judgement, membership and non-membership functions of the numbers. The combination of these two numbers produce intuitionistic Z-numbers which need to be defuzzified before aggregation of multiple experts' opinions could be done in the decision making problems. This paper presents the generalised intuitionistic Z-numbers and proposes a centroid-based defuzzification of such numbers, namely intuitive multiple centroid. The proposed defuzzification is used in the decision making model and applied to the supplier selection problem. The ranking of supplier alternatives is evaluated using the ranking function based on centroid. In the present paper, the ranking is improved since the intuitionistic fuzzy numbers (IFN) are integrated within the evaluations which were initially in form of Z-numbers, considering their membership and non-membership grades. The ranking of the proposed model gives almost similar ranking to the existing model, with simplified but detailed defuzzification method.

An integrated Z-number and intuitionistic fuzzy sets for considering uncertainty in the risk assessment using the SHIPP methodology

“…2022) addressed the problem of supplier selection by combining Z-numbers with an intuitionistic fuzzy method. The outcome demonstrates IZN's critical role in characterizing uncertainty in decision-maker assessments when resolving decision-making issues 20 . Another research conducted by Yuxuan Xing (2022) introduced the all-Process Hydrogen Accident Risk Assessment (PHARA) model.…”

“…The membership and non-membership values quantify the extent to which an element belongs or does not belong to the fuzzy set. Compared to the classical fuzzy set, the IFS offers enhanced flexibility in dealing with uncertainty 20 .…”