Supply management and environmental concerns are becoming increasingly relevant to scientific decision analysis around the world. Several companies have implemented the green supply chain management (GSCM) approach for attaining economic advantages while retaining sustainable growth for the environment. Green supplier selection has also been analyzed in many literary works as an important part of GSCM, which is considered an important multi-criteria group decision making (MCGDM) problem. The lack of consideration of the relationships of alternatives to the uncertain environment will be the main reason for weak conclusions in some MCGDM problems. To address these drawbacks, we introduce a new approach for selecting green suppliers with the q-rung orthopair fuzzy information, in which the input assessment is considered by using q-rung orthopair fuzzy numbers (q-ROFNs). A q-ROFN is extremely valuable in representing vague information that occurs in these real-world circumstances. The priority relationship of the alternatives to q-rung orthopair fuzzy information is very helpful to deal with GSCM. Consequently, we develop some prioritized operators with q-ROFNs named the q-rung orthopair fuzzy prioritized weighted average (q-ROFPWA) operator and q-rung orthopair fuzzy prioritized weighted geometric (q-ROFPWG) operator. Several important characteristics of these operators such as idempotents, boundary, and monotonicity are also well proven. Finally, an application of the proposed operators is presented for green supplier selection in GSCM. The scientific nature of the proposed methodology is illustrated by a numerical example to validate its rationality, symmetry, and superiority.

Modeling uncertainties with spherical linear Diophantine fuzzy sets (SLDFSs) is a robust approach towards engineering, information management, medicine, multi-criteria decision-making (MCDM) applications. The existing concepts of neutrosophic sets (NSs), picture fuzzy sets (PFSs), and spherical fuzzy sets (SFSs) are strong models for MCDM. Nevertheless, these models have certain limitations for three indexes, satisfaction (membership), dissatisfaction (non-membership), refusal/abstain (indeterminacy) grades. A SLDFS with the use of reference parameters becomes an advanced approach to deal with uncertainties in MCDM and to remove strict limitations of above grades. In this approach the decision makers (DMs) have the freedom for the selection of above three indexes in $[0,1]$. The addition of reference parameters with three index/grades is a more effective approach to analyze DMs opinion. We discuss the concept of spherical linear Diophantine fuzzy numbers (SLDFNs) and certain properties of SLDFSs and SLDFNs. These concepts are illustrated by examples and graphical representation. Some score functions for comparison of LDFNs are developed. We introduce the novel concepts of spherical linear Diophantine fuzzy soft rough set (SLDFSRS) and spherical linear Diophantine fuzzy soft approximation space. The proposed model of SLDFSRS is a robust hybrid model of SLDFS, soft set, and rough set. We develop new algorithms for MCDM of suitable clean energy technology. We use the concepts of score functions, reduct, and core for the optimal decision. A brief comparative analysis of the proposed approach with some existing techniques is established to indicate the validity, flexibility, and superiority of the suggested MCDM approach.

This manuscript provides an advanced mathematical model for the censuses process to reduce the drawbacks of the existing methods. From the living ideas of m-polar fuzzy set (MPFS) and Pythagorean fuzzy set (PFS), we establish a novel concept of Pythagorean m-polar fuzzy set (PMPFS). We introduce some fundamental operations on Pythagorean m-polar fuzzy sets and explain these concepts with the help of illustrations. With this novel perspective, we build up modified forms of Dombi’s aggregation operators named as Pythagorean m-polar fuzzy Dombi weighted arithmetic average (PMPFDWAA) operator and Pythagorean m-polar fuzzy Dombi weighted geometric average (PMPFDWGA) operator. We discuss certain properties of the proposed operators based on Pythagorean m-polar fuzzy numbers (PMPFNs). Mathematical modeling on real world problems often implicate multi-factors, multi-attributes and multi-polar information. We discuss a case study for the censuses process to elaborate the proposed algorithm for multi-criteria decision-making (MCDM). We also discuss how the drawbacks of existing methods can be handled by applying this novel perspective. Lastly, we present a comparative analysis, validity of proposed algorithm, influence of operational parameter, convergence and sensitivity analysis to indicate the flexibility and advantages of the proposed method.