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Some properties of equivalence soft set relations. (English) Zbl 1247.03116
Summary: The soft set theory is a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. K. V. Babitha and J. J. Sunil [Comput. Math. Appl. 60, No. 7, 1840–1849 (2010; Zbl 1205.03060)] introduced the notion of soft set relations as a soft subset of the Cartesian product of soft sets and discussed many related concepts such as equivalence soft set relations, partitions and functions. In this paper, we further study the equivalence soft set relations and obtain soft analogues of many results concerning ordinary equivalence relations and partitions. Furthermore, we introduce and discuss the transitive closure of a soft set relation and prove that the poset of the equivalence soft set relations on a given soft set is a complete lattice with the least element and greatest element.
MSC:
03E72Fuzzy set theory
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