Bipolar soft neighborhoods with application in decision-making

Résumé

This paper introduces bipolar soft (BS) neighborhood structures within the framework of soft set theory. First, several properties associated with lower and upper approximations based on a binary BS relation are examined, and the proposed approximation operators are shown to satisfy several fundamental properties. Next, an additional structure formulated through BS neighborhoods is explored. The concept of bipolar soft NjBS-neighborhood spaces is investigated, and their main characteristics are analyzed. Two types of topologies, overline{T}_zeta and underline{T}_zeta, induced by bipolar soft reflexive relations are then characterized. These topological structures are used to approximate rough sets, and a direct method is proposed to generate such topologies from the underlying relations. Finally, a numerical example is provided to illustrate the applicability of the proposed approach to decision-making.

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