Ranking of interval type 2 fuzzy numbers using correlation coefficient and Mellin transform

Abstract

Ranking of fuzzy numbers exhibits a significant role to solve the multiple attributes group decision making (MAGDM) problems. One of the commonly used indices for MAGDM problems is the correlation coefficient. Type-2 fuzzy numbers (T2FNs) are considered to be more effective than type-1 fuzzy numbers (T1FNs) to handle uncertainties in MAGDM problems. Moreover, T2FNs allow additional freedom to reflect uncertainty. In this paper, we propose a new approach to rank the interval type-2 fuzzy numbers (IT2FNs) using the correlation coefficient, where the correlation coefficient is obtained using the Mellin transform. Initially, we define the correlation coefficient for interval type-2 trapezoidal fuzzy numbers (IT2TrFNs) using Mellin transform and prove some of its major features. Then a new group decision-making method has been recommended using the proposed ranking concept. Eventually, three examples are given to demonstrate the usefulness of the suggested method. Finally, a comparative study is conducted to depict the feasibility of the developed ranking technique.