Ali, M. Irfan; Feng, Feng; Liu, Xiaoyan; Min, Won Keun; Shabir, M. On some new operations in soft set theory. (English) Zbl 1186.03068 Comput. Math. Appl. 57, No. 9, 1547-1553 (2009). 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 P.K. Maji, R. Biswas and 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. Cited in 3 ReviewsCited in 282 Documents MSC: 03E72 Theory of fuzzy sets, etc. 68T37 Reasoning under uncertainty in the context of artificial intelligence Keywords:soft sets; union; intersection; complement; difference Citations:Zbl 1032.03525 PDFBibTeX XMLCite \textit{M. I. Ali} et al., Comput. Math. Appl. 57, No. 9, 1547--1553 (2009; Zbl 1186.03068) Full Text: DOI References: [1] Molodtsov, D., Soft set theory-First results, Comput. Math. Appl., 37, 19-31 (1999) · Zbl 0936.03049 [2] Maji, P. K.; Biswas, R.; Roy, A. R., Soft set theory, Comput. Math. Appl., 45, 555-562 (2003) · Zbl 1032.03525 [3] Aktaş, H.; Çağman, N., Soft sets and soft groups, Inform. Sci., 177, 2726-2735 (2007) · Zbl 1119.03050 [4] Yang, C. F., A note on soft set theory, Comput. Math. Appl., 56, 1899-1900 (2008), [Comput. Math. Appl. 45 (4-5) (2003) 555-562] · Zbl 1152.68647 [5] Feng, F.; Jun, Y. B.; Zhao, X. Z., Soft semirings, Comput. Math. Appl., 56, 2621-2628 (2008) · Zbl 1165.16307 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.