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Algebraic and topological structures based on novel soft set relations

The algebraic and topological structures based on a new kind of soft set relations, Z-soft set relations, are characterized. Here we introduce the Z-soft set relations and provide further investigations to them. Several new operations of Z-soft set relations are employed to investigate the fundamental properties of Z-soft set relations. In particular, it is shown that the collection of all Z-soft set relations over a soft set gives rise to commutative idempotent hemirings, MV-algebras, Boolean algebras, De Morgan algebras, Kleene algebras and Stone algebras with respect to the new operations defined in this paper. Further, Z-soft set relation topologies are studied by employing Z-anti-reflexive interior operators and Z-reflexive closure operators of Z-soft set relations. It is noteworthy that intrinsic connections between Z-anti-reflexive interior operators and Z-reflexive closure operators have been established.