Dombi weighted geometric aggregation operators on the class of trapezoidal-valued intuitionistic fuzzy numbers and their applications to multi-attribute group decision-making

Abstract

The trapezoidal-valued intuitionistic fuzzy numbers (TrVIFNs) are vital in dealing with real-life decision-making problems (containing uncertainty and vagueness) in engineering and management. The study of aggregation operators on the set of trapezoidal-valued intuitionistic fuzzy numbers is essential for solving decision-making problems modelled under a trapezoidal-valued intuitionistic fuzzy (TrVIF) environment. Since TrVIFNs are the generalization class of different types of intuitionistic fuzzy numbers. The main contribution of this paper is to introduce the idea of Dombi t-norm and Dombi t-conorm based aggregation operators on the class of TrVIFNs. In this paper, firstly, we develop a Trapezoidal-Valued Intuitionistic Fuzzy Dombi Weighted Geometric operator, Trapezoidal-Valued Intuitionistic Fuzzy Dombi Order Weighted Geometric operator, Trapezoidal-Valued Intuitionistic Fuzzy Dombi Hybrid Geometric operator, and we establish mathematical properties through various theorems. Secondly, we propose a multiattribute group decision-making algorithm, such as a trapezoidal-valued multiattribute group decision-making algorithm that uses the proposed aggregation operators. Thirdly, we show the applicability of the proposed decision-making method in solving a multiattribute group decision-making problem involving the photovoltaic site selection. Further, we discuss the sensitivity analysis of the proposed algorithms to demonstrate their stability and reliability. Finally, we show the efficacy of the proposed decision-making approach by comparing it with a few familiar group decision-making methods.