A theoretical context for (θ,β)-convexity and (θ,β)-concavity with hypersoft settings

Sub-attribute-valued sets are occasionally viewed as more significant in real-life circumstances than a single set of attributes. The current models that deal with ambiguity and uncertainty, or soft sets, are insufficient to address such situations. To adequately fit the current models for multi-attributive sets, the hypersoft set, an extension of the soft set, has been developed. The multi-argument approximate function takes the place of the soft sets' approximate function. Many academics have recently focused on convexity in uncertain environments or soft and fuzzy structures. This paper examines the traditional concepts of -convex and -concave sets in a hypersoft set context, discussing their fundamental inclusive features and set-theoretic operations. Furthermore, traditional notions of first and second senses for convexity are applied to suggested convex structures to provide more broadly applicable outcomes for ambiguous situations.