Neighborhood-Based Soft hg-Hypergroupoids and Reduced Small Structures

다국어 초록 (Multilingual Abstract)

In this study, hg-hypergroupoid and partial hg-hypergroupoid structures defined via neighborhood intersections are investigated within a parameter-dependent framework. Structural parameters and soft set parameters are treated separately, and the relationship between these two parameter sets is modeled through an appropriate mapping. This approach allows neighborhood-based hyperoperations to be examined as flexible structures that vary with respect to different parameter values. The partial nature arising from the possible existence of empty hyperproducts is analyzed in detail, and the conditions under which the structure becomes a total hg-hypergroupoid are explicitly characterized. Moreover, by means of examples defined on $\mathbf{Z_6}$ equipped with the modular distance, it is shown that the proposed theoretical framework can be reduced to a concrete and discrete special case.