Abstract
Recently, Yager presented the new concept of q-rung orthopair fuzzy (q-ROF) set (q-ROFS) which emerged as the most significant generalization of Pythagorean fuzzy set (PFS). From the analysis of q-ROFS, it is clear that the rung q is the most significant feature of this notion. When the rung q increases, the orthopair adjusts in the boundary range which is needed. Thus, the input range of q-ROFS is more flexible, resilient, and suitable than the intuitionistic fuzzy set (IFS) and PFS. The aim of this manuscript is to investigate the hybrid concept of soft set ( S t S) and rough set with the notion of q-ROFS to obtain the new notion of q-ROF soft rough (q-ROF S t R) set (q-ROF S t RS). In addition, some averaging aggregation operators such as q-ROF S t R weighted averaging (q-ROF S t RWA), q-ROF S t R ordered weighted averaging (q-ROF S t ROWA), and q-ROF S t R hybrid averaging (q-ROF S t RHA) operators are presented. Then, the basic desirable properties of these investigated averaging operators are discussed in detail. Moreover, we investigated the geometric aggregation operators, such as q-ROF S t R weighted geometric (q-ROF S t RWG), q-ROF S t R ordered weighted geometric (q-ROF S t ROWG), and q-ROF S t R hybrid geometric (q-ROF S t RHG) operators, and proposed the basic desirable characteristics of the investigated geometric operators. The technique for multicriteria decision-making (MCDM) and the stepwise algorithm for decision-making by utilizing the proposed approaches are demonstrated clearly. Finally, a numerical example for the developed approach is presented and a comparative study of the investigated models with some existing methods is brought to light in detail which shows that the initiated models are more effective and useful than the existing methodologies.
Highlights
Decision-making has always been a hot topic under consideration by the researchers
From the analysis of Definitions 11 and 12, it is clear that the q-ROFStRWA operator weights only the q-ROFVs, while q-ROFStROWA operator weights the ordered position of the q-ROFVs instead of weighting the values themselves. To overcome this limitation and motivated by the idea of combining weighted averaging and the ordered weighted averaging by using the combined notion of soft rough set, we present q-ROFStRHA operator, which weights both the given q-ROFV and its ordered position. e basic desirable properties of the developed operator are presented in detail
To present the applicability and efficiency of the developed approach with some other existing methods based on intuitionistic fuzzy set (IFS), Pythagorean fuzzy set (PFS), and q-ROFS methods by using the same illustrative example
Summary
Multicriteria decision-making (MCDM) has a high prospective and discipline manner to improve and evaluate multiple conflicting criteria in all areas of decision-making. In this competitive environment, an enterprise needs the most accurate and rapid response to change the customer needs. For an intelligent and successful decision, the experts require careful preparation and analysis of each and every character for an alternative and they can take a good decision if they are armed with all the data and information that they need To handle this complexity, Zadeh [1] originated the dominant and pioneer concept of the fuzzy set. Xu [4] investigated the series of aggregation operators such as IF weighted averaging (IFWA), IF ordered weighted averaging (IFOWA), and IF hybrid averaging (IFHA) operators under IF environment
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