Search

WOS: 000288580700018 Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, first we prove that certain De Morgan's law hold in soft set theory with respect to different operations on soft sets. Then, we discuss the basic properties of operations on soft sets such as intersection, extended intersection, restricted union and restricted difference. Moreover, we illustrate their interconnections between each other. Also we define the notion of restricted symmetric difference of soft sets and investigate its properties. The main purpose of this paper is to extend the theoretical aspect of operations on soft sets. Crown Copyright (C) 2011 Published by Elsevier Ltd. All rights reserved.

WOS: 000287553200010 tool to deal with uncertainties. In this paper, we introduce and study soft subrings and soft ideals of a ring by using Molodtsov's definition of the soft sets. Moreover, we introduce soft Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical subfields of a field and soft submodule of a left R-module. Some related properties about soft substructures of rings, fields and modules are investigated and illustrated by many examples. (C) 2010 Elsevier Ltd. All rights reserved.

WOS: 000293718900016 Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, first we correct some of the problematic cases in a previous paper by Aktas and Cagman [H. Aktas, N. Cagman, Soft sets and soft groups, Inf. Sci. 177 (2007) 2726-2735]. Moreover, we introduce the concepts of normalistic soft group and normalistic soft group homomorphism, study their several related properties, and investigate some structures that are preserved under normalistic soft group homomorphisms. (C) 2011 Elsevier Ltd. All rights reserved.