Averaging aggregation operators with pythagorean trapezoidal fuzzy numbers and their application to group decision making

Multi-attribute fuzzy pattern decision making based on information systems

This paper introduces an innovative approach aimed at enhancing multi-attribute decision-making through the utilization of fuzzy pattern recognition, with a specific emphasis on engaging decision-makers more effectively. The methodology establishes a multi-attribute fuzzy pattern recognition model within a hybrid information system framework. It categorizes attributes into natural and abstract groups, standardizes them, and employs membership functions to transform them into degrees of membership. This adaptable approach permits the derivation of various decision criteria from the hybrid system. Subsequently, a testing set is generated from this system, and a suitable fuzzy operator is selected. The optimal solution is determined by assessing the similarity between the standard and testing sets. To underscore its effectiveness, a practical example is provided. Crucially, in the realm of multi-attribute decision-making, our method simplifies the process by reducing computational steps in contrast to the conventional TOPSIS model, while maintaining consistent outcomes. This streamlines the decision-making process and reduces complexity. We also demonstrate its applicability in multi-objective decision-making through a case study evaluating exemplary educators, thereby highlighting its adaptability and effectiveness. This method exhibits significant promise for enhancing multi-attribute decision-making and offers practical applications.

A New Ranking Methodology for Pythagorean Trapezoidal Uncertain Linguistic Fuzzy Sets Based on Einstein Operations

In this article, we proposed new Pythagorean trapezoidal uncertain linguistic fuzzy aggregation information—namely, the Pythagorean trapezoidal uncertain linguistic fuzzy Einstein weighted averaging (PTULFEWA) operator, the Pythagorean trapezoidal uncertain linguistic fuzzy Einstein ordered weighted averaging (PTULFEOWA) operator, and the Pythagorean trapezoidal uncertain linguistic fuzzy Einstein hybrid weighted averaging (PTULFEHWA) operator—using the Einstein operational laws. We studied some important properties of the suggested aggregation operators and showed that the PTULFEHWA is more general than the other proposed operators, which simplifies these aggregation operators. Furthermore, we presented a multiple attribute group decision making (MADM) process for the proposed aggregation operators under the Pythagorean trapezoidal uncertain linguistic fuzzy (PTULF) environment. A numerical example was constructed to determine the effectiveness and practicality of the proposed approach. Lastly, a comparative analysis was performed of the presented approach with existing approaches to show that the proposed method is consistent and provides more information that may be useful for complex problems in the decision-making process.