In an uncertain context of T-spherical fuzzy (T-SF) sets, the purpose of this study is to propound an efficacious multiple criteria choice model, named a T-SF REGIME method, predicated on a dominance analysis and a prioritization analysis. The REGIME methodology is a well-founded evaluation technique suitable for multiple criteria choice analysis owing to it has good applicability to the processing of qualitative information and to complex scenarios. Unlike the existing REGIME techniques, this paper takes advantage of a new Minkowski-type distance measure and an evolved Gaussian preference function to propound a ground-breaking T-SF REGIME model. This paper first concentrates on an evolution of the Minkowski-type distance measure and explores special cases with relevant properties for functional use. Next, this paper concerns an ascertainment of the evolved Gaussian preference function as a part of the proposed T-SF REGIME mechanism. This paper focuses on an advancement of the REGIME structure to T-SF uncertain contexts and unfolds an inventive T-SF REGIME methodology by virtue of superiority identifiers/indices, guide identifiers/indices, and joint generalized indices. The usefulness and strength points of the advanced methodology are scrutinized through a realistic application in the field of solar plant to prioritize the options of photovoltaic cells. The application results and comparisons corroborate the high efficiency and strengths of the evolved methodology.

The concept of Pythagorean fuzzy (PF) sets represents a superior tool to model complex uncertainties in an ambiguous and equivocal decision-making framework. In consideration of the significant capacity for exhibiting the uncertainty of subjective appraisals and estimations under the aegis of the PF theory, this paper presents a simple-to-operate decision-making approach that is grounded in some beneficial concepts of original likelihood functions and measurements of dominating and dominated characters. On the strength of beta distributions, this paper seeks to propound new notions of PF likelihood functions and likelihood-oriented dominating/dominated characters and to launch an exploitable multiple criteria evaluation method by means of a dominance ordering model for treating decision analysis within PF environments. This paper initiates an efficient beta distribution-based approach to the construction of novel PF likelihood functions that can quantify the possibility degrees of outranking and outranked relationships between Pythagorean membership grades. The applicable satisfaction and dissatisfaction estimations are established on the likelihood-oriented dominating and dominated characters, respectively. Furthermore, this paper formulates a straightforward dominance ordering model to obtain the ultimate dominance ranking orders of candidate alternatives and accomplish multiple criteria decision-making issues involving complicated uncertainty. A financing decision-making problem concerning working capital requirements is investigated to validate the application results using the advanced methodology. The real-world application is implemented to examine the reasonableness and efficacy of the established techniques. Moreover, comparative studies through the utility of a sensitivity analysis are performed to demonstrate the efficacy and merits of the dominance ordering model. The comparison results manifest that the initiated methodology is an advantageous and reliable decision-making technique that can enhance the methodological development regarding the multiple criteria evaluation model under PF uncertainty. Finally, recommendations for future research directions are also presented in the conclusions.

The aim of this article is to develop a novel multiple criteria decision analysis (MCDA) method using a Pearson-like correlation-based Pythagorean fuzzy (PF) compromise approach under complex uncertainty based on PF sets and interval-valued Pythagorean fuzzy (IVPF) sets. Because of the complexity and ambiguity involved in real-life decision-making situations, this article utilizes the theory of Pythagorean fuzziness, which is characterized by flexible degrees of membership, nonmembership, and indeterminacy to describe uncertain information more comprehensively. PF and IVPF sets possess exceptional abilities to accurately reflect the uncertainty, fuzziness, and vagueness inherent in the decision information. However, manipulating PF and IVPF information is a complicated and difficult task for most decision makers. In this regard, this article extends the well-known and widely used concept of correlation coefficients to develop simple and effective compromise models for solving MCDA problems in PF and IVPF contexts. This article conducts an extended analysis of Pearson-like correlation coefficients for PF and IVPF sets separately and introduces new concepts of PF and IVPF correlation coefficients to furnish a solid basis for the proposed methodology. Furthermore, this article develops useful concepts of PF and IVPF correlation-based closeness coefficients to simultaneously measure the relative closeness to the positive-ideal PF/IVPF solutions and the relative remoteness from the negative-ideal PF/IVPF solutions. On the basis of the developed concepts, this article proposes a novel Pearson-like correlation-based PF/IVPF compromise approach to address uncertain MCDA problems involving PF/IVPF information and determine the ultimate priority orders among competing alternatives. Finally, this article provides an illustrative application about a financing decision of working capital management to verify the developed approach and demonstrate its feasibility and practicality.

The concept of interval-valued Pythagorean fuzzy (IVPF) sets is capable of handling imprecise and ambiguous information and managing complex uncertainty in real-world applications. This paper focuses on multiple criteria decision analysis involving IVPF information and proposes a new outranking decision-making method that uses a closeness-based assignment model. In contrast to the existing assignment-based methodology, the uniqueness of this paper is the consideration of uncertain information represented by IVPF values, the determination of criterion-wise precedence rankings based on a closeness-based approach, and the development of a new measure for scalar representation. First, to underlie anchored judgments in subjective decision-making processes, this paper presents a compromising concept of the closeness index with the positive-ideal and negative-ideal IVPF values to identify criterion-wise precedence ranks among alternatives. Next, this paper defines the concept of matrices of precedence frequency and contribution to provide a basis for the proposed assignment model. To overcome the difficulty of lacking nontrivial scalar representations, a useful measure is also developed to appropriately describe IVPF values. Based on a closeness-based assignment approach, a novel outranking decision-making method is proposed to transform the extended criterion-wise ranks into the ultimate priority orders of the alternatives. The proposed method is first implemented in a practical problem of selecting a bridge construction method to demonstrate its feasibility and applicability. Moreover, its practicality and effectiveness are verified through a comparative analysis with relevant assignment-based approaches. Further comparative analyses with newly developed IVPF decision-making methods are conducted for both a risk evaluation problem and an investment problem to examine the advantages of the proposed method and extend the current technique by considering distinct preference information for adapting to the particularities in practice.