Parametric distance measure for trapezoidal intuitionistic fuzzy numbers and application in Multi-criteria group decision-making

It is important to have an intuitionistic fuzzy set that allows each set element to have a membership value, a non-membership value, and a hesitancy value. This is because each element of the set can possess all three values. We will focus on one type of continuous intuitionistic fuzzy number, called trapezoidal intuitionistic fuzzy numbers, because they are more flexible in representing information about membership and non-membership functions and are continuous. This research aims to introduce a parametric ranking and distance measure to compare and obtain the distinction value between intuitionistic trapezoidal fuzzy numbers. Parametric measures offer more flexibility than deterministic measurement tools in modeling real-world problems by considering a suitable variety of responses based on different levels of parameters. After presenting the structure and effective indicators of the proposed tool, we have detailed its features and basic principles. Moreover, based on this measure, a hybrid process is designed for multi-criteria group decision-making (MCGDM) problems with trapezoidal intuitionistic fuzzy data. A numerical example is also examined to elucidate the implementation process of this integrated methodology. Additionally, comparative analysis with some related methods confirms the adequate performance of the new parametric measure in combined methods with similar subjects.