On some new operations in soft set theory

被引：1034

作者：

Ali, M. Irfan ^{[1
]}

Feng, Feng ^{[2
]}

Liu, Xiaoyan ^{[2
]}

Min, Won Keun ^{[3
]}

Shabir, M. ^{[1
]}

机构：

[1] Quaid I Azam Univ, Dept Math, Islamabad, Pakistan

[2] Xian Inst Posts & Telecommun, Dept Appl Math & Appl Phys, Xian 710061, Peoples R China

[3] Kangwon Natl Univ, Dept Math, Chunchon 200701, South Korea

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2009年 / 57卷 / 09期

关键词：

Soft sets; Union; Intersection; Complement; Difference;

D O I：

10.1016/j.camwa.2008.11.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 [应用数学];

摘要：

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 Maji et al. [P.K. Maji, R. Biswas, A.R. Roy, Soft set theory, Comput. Math. Appl. 45 (2003) 555-562] 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. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：1547 / 1553

页数：7

共 6 条

[1]

Soft sets and soft groups [J].