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Zbl 1186.03068
Ali, M.Irfan; Feng, Feng; Liu, Xiaoyan; Min, Won Keun; Shabir, M.
On some new operations in soft set theory. (English)
[J] Comput. Math. Appl. 57, No. 9, 1547-1553 (2009). ISSN 0898-1221

Summary: Molodtsov introduced the theory of soft sets, which can be seen as a new mathematical approach to vagueness. In this paper, we first point out that several assertions (Proposition 2.3 (iv)-$(vi)$, Proposition 2.4 and Proposition 2.6 (iii), (iv)) in a previous paper by {\it P.K. Maji, R. Biswas} and {\it A.R. Roy} [Comput. Math. Appl. 45, No. 4--5, 555--562 (2003; Zbl 1032.03525)] are not true in general, by counterexamples. Furthermore, based on the analysis of several operations on soft sets introduced in the same paper, we give some new notions such as the restricted intersection, the restricted union, the restricted difference and the extended intersection of two soft sets. Moreover, we improve the notion of complement of a soft set, and prove that certain De Morgan's laws hold in soft set theory with respect to these new definitions.

MSC 2000:: *03E72 Fuzzy sets (logic)
68T37 Reasoning under uncertainty

Keywords: soft sets; union; intersection; complement; difference

Citations: Zbl 1032.03525

Cited in: Zbl 1217.03037

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