Soft sets and soft rough sets

  • Authors:

  • Feng Feng;Xiaoyan Liu;Violeta Leoreanu-Fotea;Young Bae Jun

  • Affiliations:

  • College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, PR China and Department of Applied Mathematics, Faculty of Science, Xi'an Institute of Posts and Telecommun ...;Department of Applied Mathematics, Faculty of Science, Xi'an Institute of Posts and Telecommunications, Xi'an 710061, PR China;Faculty of Mathematics, "Al.I.Cuza" University, 6600 Iaşi, Romania;Department of Mathematics Education (and RINS), Gyeongsang National University, Chinju 660-701, Republic of Korea

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2011

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Abstract

In this study, we establish an interesting connection between two mathematical approaches to vagueness: rough sets and soft sets. Soft set theory is utilized, for the first time, to generalize Pawlak's rough set model. Based on the novel granulation structures called soft approximation spaces, soft rough approximations and soft rough sets are introduced. Basic properties of soft rough approximations are presented and supported by some illustrative examples. We also define new types of soft sets such as full soft sets, intersection complete soft sets and partition soft sets. The notion of soft rough equal relations is proposed and related properties are examined. We also show that Pawlak's rough set model can be viewed as a special case of the soft rough sets, and these two notions will coincide provided that the underlying soft set in the soft approximation space is a partition soft set. Moreover, an example containing a comparative analysis between rough sets and soft rough sets is given.