Prospect‐theory and geometric distance measure‐based Pythagorean cubic fuzzy multicriteria decision‐making

Abstract

The Pythagorean cubic fuzzy set (PCFS) describes a mixture of interval Pythagorean information and Pythagorean fuzzy values. Compared to the Pythagorean and interval Pythagorean fuzzy sets, PCFS contains comprehensive information suitable for solving complex multicriteria decision-making (MCDM) problems. However, the use of existing PCFS comparison tools, including score-function and distance-measurement, is impractical in some cases. To address this concern, this study transforms PCFS into the geometric form, and proposes the use of the PCFS geometric-distance measurements. The proposed method requires the maximum and minimum values of membership and nonmembership degrees to be considered positive and negative reference points, respectively. Moreover, the gain and loss matrices are constructed. The risk-preference coefficient is introduced to improve the original prospect-value expression. The final ranking results of decision-makers considering several risk preferences are presented by balancing the proportion of the positive and negative prospect values, thereby constructing an MCDM model based on the PCFS-geometric-distance measure and prospect theory. The feasibility and practicality of this model are validated via a case study concerning urban human settlements to ensure satisfactory housing conditions and appropriate infrastructure development. As observed, the proposed model can adequately evaluate urban human settlements, thereby demonstrating the potential to solve similar problems. A sensitivity analysis of the risk-preference coefficient and subsequent comparison against existing methods reveal the proposed MCDM model to yield convincing results.