Theory of Hypersoft Sets: Axiomatic Properties, Aggregation Operations, Relations, Functions and Matrices

Abstract

There are several decision-making based situations in which it is necessary to categorize the evaluating parameters into their respective sub-parametric values based non-overlapping sets. The existing soft set model is not compatible with such situations therefore hypersoft set (Hsˆ -set) is developed which manages such situations by utilizing a novel mapping called multi-argument approximate mapping which broadens the domain of soft approximate mapping. This research presents the characterization of several essential axiomatic properties and set-based operations of Hsˆ -set which will help the researchers to implement this emerging theory to other fields of study. The brief discussion on some hybridized structures of Hsˆ -set with fuzzy set-like models
is also provided.