Trapezoidal Intuitionistic Fuzzy Power Heronian Aggregation Operator and Its Applications to Multiple-Attribute Group Decision-Making

Decision-making problems involve imprecise and incomplete information that can be modelled well using intuitionistic fuzzy numbers (IFNs). Various IFNs are available in the literature for modelling such problems. However, trapezoidal intuitionistic fuzzy numbers (TrIFNs) are widely used. It is mainly because of the flexibility in capturing the incompleteness that occurs in the data. Aggregation operators play a vital role in real-life decision-making problems (modelled under an intuitionistic fuzzy environment). Different aggregation operators are available in the literature for better decision-making. Various aggregation operators are introduced in the literature as a generalization to the conventional aggregation functions defined on the set of real numbers. Each aggregation operator has a specific purpose in solving the problems effectively. In recent years, the power average (PA) operator has been used to reduce the effect of biased data provided by decision-makers. Similarly, the Heronian mean (HM) operator has a property that considers the inter-relationship among various criteria available in the decision-making problem. In this paper, we have considered both the operators (HM, PA) to introduce a new aggregation operator (on the set of TrIFNs), which takes advantage of both properties of these operators. In this study, firstly, we propose the idea of a trapezoidal intuitionistic fuzzy power Heronian aggregation (TrIFPHA) operator and a trapezoidal intuitionistic fuzzy power weighted Heronian aggregation (TrIFPWHA) operator by combining the idea of the Heronian mean operator and power average operator in real numbers. Secondly, we study different mathematical properties of the proposed aggregation operators by establishing a few essential theorems. Thirdly, we discuss a group decision-making algorithm for solving problems modelled under a trapezoidal intuitionistic fuzzy environment. Finally, we show the applicability of the group decision-making algorithm by solving a numerical case problem, and we compare the proposed method's results with existing methods.

Automated summary

The use of intuitionistic fuzzy numbers and aggregation operators in decision-making problems effectively addresses uncertainty and incompleteness in information, with trapezoidal intuitionistic fuzzy numbers, Heronian mean operator, and power average operator being commonly used methods. The study also suggests that new aggregation operators can combine the properties of different operators to enhance problem-solving efficiency.