Abstract
As science and technology continue to advance at a rapid pace, people are facing increasingly complex data, and research on uncertain information technology has become a hot field. Compared to intuitionistic fuzzy sets, Pythagorean fuzzy sets are more tolerant and flexible in representing uncertain information. Therefore, this article mainly focuses on the study of three-way decisions based on Pythagorean fuzzy β covering. First, considering the disadvantages of other methods in comparing the magnitudes of Pythagorean fuzzy numbers, we propose the concept of the ideal positive degree in a Pythagorean fuzzy environment and determine a method for calculating conditional probabilities based on this newly defined ideal positive degree. Second, regret theory and prospect theory are combined to obtain a relative utility function. Then, based on the aforementioned conditional probabilities and relative utility function, a three-way multi-attribute decision-making method based on the Pythagorean fuzzy environment is established. Finally, the three-way multi-attribute decision-making method is utilized to solve the problem of selecting the optimal choice for rural revitalization industrial projects. Through experimental comparison and analysis, the effectiveness and reliability of this method are verified.
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