A novel aggregation method for generating Pythagorean fuzzy numbers in multiple criteria group decision making: An application to materials selection

Pythagorean Fuzzy Numbers are more capable of modeling uncertainties in real-life decision-making situations than Intuitionistic Fuzzy Numbers. Majority of research in Pythagorean Fuzzy Numbers, used in Multiple Criteria Decision-Making problems, has focused on developing operators and decision-making frameworks rather than the methodologies of generating the Pythagorean Fuzzy Numbers. Hence, this study aims at developing a novel aggregation method to generate Pythagorean Fuzzy Numbers from decision makers’ crisp data for Multiple Criteria Decision-Making problems. The aggregation method differs from other methods, used in generating Intuitionistic Fuzzy Numbers, by its ability to measure the uncertainty degrees in decision makers’ information and using them to generate Pythagorean Fuzzy Numbers. Initially, decision makers evaluate alternatives based on preset criteria using crisp decisions (i.e., crisp numbers) which are assigned by decision makers. A normalization method is used to normalize the given numbers from zero to one. Linear transformation is then used to identify the satisfactory and dissatisfactory elements of all normalized values. In the aggregation stage, the Sugeno fuzzy measure and Shapley value are used to fairly distribute the decision makers’ weights into the Pythagorean fuzzy numbers. Additionally, new functions to calculate uncertainty from decision-makers evaluations are developed using Takagai-Sugeno approach. An illustrative example in engineering materials selection application is presented to demonstrate the efficiency and applicability of the proposed methodology in real-life scenarios. Comparative analysis is performed to compare the results and performance of the introduced approach to other aggregation techniques.