Abstract
Fuzzy hypersoft set (FHS-set) is an effective and flexible model as it not only minimizes the complexities of fuzzy set for dealing uncertainties, but also fulfills the parameterization requirements of soft set and fuzzy soft set. FHS-set is projected to address the limitations of these models regarding the entitlement of multi-argument approximate function. This kind of function maps the sub-parametric tuples to power set of universe. It emphasizes the partitioning of each attribute into its attribute-valued set that is missing in existing soft set-like structures. These features make it a completely new mathematical tool for solving problems dealing with uncertainties. As convexity has an essential function in optimization and control, pattern classification and recognition, image processing and in different fields of operation research, numerical analysis, etc. In order to tackle the various features of classical convexity (concavity) with uncertain environment of multi-argument approximate function, an articulate cum mathematical technique is utilized to develop a theoretical framework of convexity cum concavity on fuzzy hypersoft set which is more generalized and effective concept to deal with optimization relating problems. Moreover, some generalized properties like strictly convex (concave), strongly convex (concave), \(\delta \)-inclusion and aggregation operations are established. The proposed study is authenticated with the provision of daily-life application based on proposed decision-making algorithm. Lastly, the features of proposed study are compared with the some existing relevant models to show its meritorious impact.
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Authors are thankful to referees for improving the quality of this paper their their valuable suggestions.
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Conceptualization was done by A.U.R. and M.S.; methodology was done by A.U.R. and F.S.; software was done by A.U.R.; validation was done by A.U.R., M.S. and F.S.; formal analysis was carried out by A.U.R. and M.S.; investigation was done by M.S. and F.S.; visualization was done by A.U.R., M.S. and F.S.; supervision was done by M.S. and F.S. All authors have read and agreed to the published version of the manuscript.
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Rahman, A.U., Saeed, M. & Smarandache, F. A theoretical and analytical approach to the conceptual framework of convexity cum concavity on fuzzy hypersoft sets with some generalized properties. Soft Comput 26, 4123–4139 (2022). https://doi.org/10.1007/s00500-022-06857-8
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DOI: https://doi.org/10.1007/s00500-022-06857-8