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Recently, some improvement has been made in the dominant notion of fuzzy set that is Yager investigated the generalized concept of fuzzy set, Intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS) and called it q-rung orthopair fuzzy (q-ROF) set (q-ROFS). The aim of this manuscript is to present the concept of q-ROF soft (q-ROFSt) set (q-ROFStS) based on the Dombi operations. Since Dombi operational parameter possess natural flexibility with the resilience of variability. Some new operational laws are defined based on hybrid study of soft sets and q-ROFS. The advantage of Dombi operational parameter is very important to express the experts' attitude in decision making. In this paper, we present q-ROFSt Dombi average (q-ROFSt DA) aggregation operators including q-ROFSt Dombi weighted average (q-ROFSt DWA), q-ROFSt Dombi ordered weighted average (q-ROFSt DOWA) and q-ROFSt Dombi hybrid average (q-ROFSt DHA) operators. Moreover, we investigate q-ROFSt Dombi geometric (q-ROFSt DG) aggregation operators including q-ROFSt Dombi weighted geometric (q-ROFSt DWG), q-ROFSt Dombi ordered weighted geometric (q-ROFSt DOWG), and q-ROFSt Dombi hybrid geometric (q-ROFSt DHG) operators. The basic properties of these operators are presented with detail such us Idempotency, Boundedness, Monotonicity, Shift invariance, and Homogeneity. Thus from the analysis and advantages of proposed model, it is clear that the investigated q-ROFSt DWA operator is the generalized form of IF St DWA, PFSt DWA and q-ROFDWA operators. Similarly, the investigated q-ROFSt DWG operator is the generalized form of IF St DWG, PFSt DWG and q-ROFDWG operators. By applying the develop approach, this manuscript contains the technique and algorithm for multicriteria decision making (MCDM). Further a numerical example is developed to illustrate the flexibility and applicability of the developed operators. [ABSTRACT FROM AUTHOR]

The objective of this manuscript is to investigate the concept of generalized q-rung orthopair fuzzy sets (Gq- R O F Ss) and group generalized q-rung orthopair fuzzy sets (GGq- R O F Ss) by incorporating the concept of generalized parameter and group generalized parameters in q-rung orthopair fuzzy environment. The main advantage of generalized parameter in q-rung orthopair fuzzy environment is to reduce uncertain errors in the original information to ensure the expert's level of trust and improve the accuracy of final decision. On the base of generalized parameter, some aggregation operators are introduced such as generalized q-rung orthopair fuzzy average aggregation operators and group generalized q-rung orthopair fuzzy average aggregation operators and studied their related properties. Furthermore, a multi-criteria decision-making method technique based on proposed approach is presented. Finally, a numerical example is provided to illustrate the feasibility of the proposed methods and deliver the sensitivity analysis and comparative analysis, which show the superiority of developed approached than existing methods. [ABSTRACT FROM AUTHOR]

Molodtsov investigated the pioneer notion of soft set (SfS) which provides a general framework for mathematical problems by affix parameterization tools during the analysis as compared to fuzzy set and q‐rung orthopair fuzzy set (q‐ROFS). The aim of this manuscript is to investigate the notion of q‐rung orthopair fuzzy soft set (q‐ROFSfS), which provide a lay of foundation for those difficulties and complexities which the contemporary theories face during the study of uncertainty. Therefore, our main contribution in this manuscript is to investigate the q‐rung orthopair fuzzy soft weighted averaging, q‐rung orthopair fuzzy soft ordered weighted averaging and q‐rung orthopair fuzzy soft hybrid averaging operators in q‐ROF soft (q‐ROFSf) environment. Further, the fundamental properties of these aggregation operators are studied. On the base of developed approach an algorithm for multicriteria decision making method is being presented. An application of medical diagnosis problems is solved on the proposed algorithm under the q‐ROFSf environment. Finally, comparison between the developed operators with some existing operators are being presented showing the superiority and efficiency of the developed approach than the existing literature. [ABSTRACT FROM AUTHOR]