Power Average of Trapezoidal Intuitionistic Fuzzy Numbers Using Strict t-Norms and t-Conorms

Abstract

As an extension of intuitionistic fuzzy number (IFN), trapezoidal intuitionistic fuzzy number (TrIFN) is one of the useful tools to deal with ill-known quantities in decision data and decision making problems. In this paper, based on the strict t-norms and t-conorms, new operation laws for the normalized TrIFNs are defined. Specially, the operation laws of TrIFNs take the speculative and radical principle and have the property of closeness in the set of normalized TrIFNs. Then, the power average operator for real numbers is extended to four power average operators for TrIFNs, i.e., the triangular (co)norms-based (t-based) power average for TrIFNs, t-based weighted power average operator for TrIFNs, t-based power ordered weighted average operator for TrIFNs, and t-based power hybrid average operator for TrIFNs. To show the feasibility and reasonability in the applications of multiple attributes group decision making using the developed operations for TrIFNs, a numerical example is provided. It is shown that there is more flexibility in the choice of the parameters associated with the degree of the risk one can bear.