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.

An MCDM approach based on some new Pythagorean cubic fuzzy Frank Muirhead mean operators

“…These proposed operators can afford much adaptability and robustness during the MCDM process due to the occurrence of a parameter vector. Also, the proposed PCFFMM and PCFFGMM operators represent a flexible class of aggregation operators because Frank triangular norms [79] can provide more flexibility than some of the existing operators [74] , [75] , [76] , [77] , [78] based on Algebraic and the Einstein triangular norms due to the presence of an additional parameter. The proposed MCDM method along with the PCFFMM and PCFFGMM operators can provide a more accurate result as compared to some of the existing MCDM methods [74] , [78] for real-life problems with correlated criteria under the Pythagorean cubic fuzzy environment.…”

“…These proposed operators can afford much adaptability and robustness during the MCDM process due to the occurrence of a parameter vector. Also, the proposed PCFFMM and PCFFGMM operators represent a flexible class of aggregation operators because Frank triangular norms [79] can provide more flexibility than some of the existing operators [74] , [75] , [76] , [77] , [78] based on Algebraic and the Einstein triangular norms due to the presence of an additional parameter.…”

“…Hussain et al [78] introduced some new operational laws on PCFS and developed some Pythagorean cubic fuzzy Einstein weighted operators. Wang and Zhao [76] formulated some distance measurements and developed an MCDM approach on the PCFSs. Talukdar and Dutta [77] introduced a class of distance measures on cubic PFSs and studied medical MCDM problems.…”

“…Pythagorean cubic fuzzy sets can take into consideration the confidence levels [75] of each DM during the assessment process. Recently, several MCDM methods [75] , [76] , [77] , [78] have been proposed on the PCFSs. Operators defined on PCFS are more efficient and flexible as compared to the operators based on other extensions of fuzzy sets.…”

Enhanced Combined Techniques for Interval-Valued Intuitionistic Fuzzy Multiple-Attribute Group Decision-Making and Applications to Quality Evaluation of Large-Scale Multi-View 3D Reconstruction

“…Traditional GDM generally only involves a small number of decision-making experts, focusing on solving the problems of a few experts [42][43][44]. However, with the promotion of science and technology and social needs, many decision-making problems in reality require the participation of a large number of decision-making experts, such as commercial projects, electronic democracy, emergency decision-making, etc [45][46][47][48].…”