Power Geometric Operations of Trapezoidal Atanassov's Intuitionistic Fuzzy Numbers Based on Strict t-Norms and t-Conorms and Its Application to Multiple Attribute Group Decision Making

Trapezoidal Atanassov's intuitionistic fuzzy numbers (TrAIFNs) is one of the useful tools to manage the fuzziness and vagueness in expressing decision data and solving decision making problems. In this paper, based on the operation laws defined by strict t-norms and t-conorms, four kinds of power geometric operators, i.e., triangular (co)norms-based (T-based) power geometric operator of TrAIFNs, T-based weighted power geometric operator of TrAIFNs, T-based power ordered weighted geometric operator of TrAIFNs, and T-based power hybrid geometric operator of TrAIFNs, are developed. To minimize loss of information in process, a new ranking method of TrAIFNs are presented based on the newly proposed possibility differences of TrAIFNs; Moreover, utilizing strict t-conorms, a new similarity measurement of TrAIFNs is innovated. Thereby, in combination with all the referred elements, two approaches to multiple attributes group decision making using TrAIFNs are developed. In the end, the feasibility of those methods and the superiority over the existing methods are demonstrated by a numerical example.

Automated summary

This paper introduces trapezoidal Atanassov's intuitionistic fuzzy numbers (TrAIFNs) and its applications. Based on the operation laws defined by strict t-norms and t-conorms, four kinds of power geometric operators are developed, and new ranking and similarity measurement methods for TrAIFNs are proposed. The feasibility and superiority of these methods are demonstrated through a numerical example.