A Direct Proof of Every Rough Set is a Soft Set

The purpose of this paper is devoted to revealing interconnection between rough sets and soft sets. We use the constructive and descriptive approaches of rough set theory and present a direct proof that Pawlak’s and Iwinski’s rough sets can be considered as soft sets.

[1]  Andrzej Skowron,et al.  Rudiments of rough sets , 2007, Inf. Sci..

[2]  Yiyu Yao,et al.  Constructive and Algebraic Methods of the Theory of Rough Sets , 1998, Inf. Sci..

[3]  D. Molodtsov.  Soft set theory—First results , 1999 .

[4]  Vilém Novák,et al.  Fuzzy Set , 2009, Encyclopedia of Database Systems.

[5]  Gian Luigi Ferrari,et al.  Parameterized Structured Operational Semantics , 1998, Fundam. Informaticae.

[6]  A. R. Roy,et al.  Soft set theory , 2003 .

[7]  Victor W. Marek,et al.  Contributions to the Theory of Rough Sets , 1999, Fundam. Informaticae.

[8]  T. Iwiński.  Algebraic approach to rough sets , 1987 .