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The relationship among soft sets, soft rough sets and topologies

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Abstract

Molodtsov’s soft set theory is a newly emerging tool to deal with uncertain problems. Based on the novel granulation structures called soft approximation spaces, Feng et al. initiated soft rough approximations and soft rough sets. Feng’s soft rough sets can be seen as a generalized rough set model based on soft sets, which could provide better approximations than Pawlak’s rough sets in some cases. This paper is devoted to establishing the relationship among soft sets, soft rough sets and topologies. We introduce the concept of topological soft sets by combining soft sets with topologies and give their properties. New types of soft sets such as keeping intersection soft sets and keeping union soft sets are defined and supported by some illustrative examples. We describe the relationship between rough sets and soft rough sets. We obtain the structure of soft rough sets and the topological structure of soft sets, and reveal that every topological space on the initial universe is a soft approximating space.

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Authors and Affiliations

  1. College of Science, Guangxi University for Nationalities, Nanning, Guangxi, 530006, People’s Republic of China

    Zhaowen Li

  2. College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, People’s Republic of China

    Tusheng Xie

Authors
  1. Zhaowen Li
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  2. Tusheng Xie
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Corresponding author

Correspondence to Zhaowen Li.

Additional information

Communicated by L. G. Lacasa.

This work is supported by the National Natural Science Foundation of China (No. 11061004, 71140004), the Natural Science Foundation of Guangxi (No. 2013GXNSFBA019016) and Guangxi University Science and Technology Research Project (No. 2013ZD020, 2013ZD061).

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Li, Z., Xie, T. The relationship among soft sets, soft rough sets and topologies. Soft Comput 18, 717–728 (2014). https://doi.org/10.1007/s00500-013-1108-5

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