Knowledge and Information Systems

, Volume 49, Issue 2, pp 749–794 | Cite as

Neighborhood system S-approximation spaces and applications

  • Ali Shakiba
  • Mohammad Reza Hooshmandasl
Regular Paper


In this paper, we will study neighborhood system S-approximation spaces, i.e., combination of S-approximation spaces with identical elements except that they have different knowledge mappings, e.g., the knowledge mappings differ due to different experimental conditions and/or sampling methodology. In such situations, there is a risk of contradictory knowledge sets which can lead to different decisions by the same query. These situations are studied in this paper in detail. Moreover, neighborhood system S-approximation spaces are investigated from a three-way decisions viewpoint with respect to different deciders. In addition, completeness results are shown for optimistic and pessimistic neighborhood system S-approximation spaces, i.e., these constructions can be represented by an ordinary S-approximation space. Also, the concept of knowledge significance is proposed and studied in detail, and we have shown that computing a minimal set of knowledge mappings for a neighborhood system S-approximation space is \({\mathbf {NP}}\)-hard. Finally, the paper is concluded by two illustrative medical examples.


S-approximation spaces Neighborhood systems Three-way decisions Partial monotonicity Two universal approximation Multigranulation rough set theory 



The authors gratefully acknowledge and are in debt of the helpful comments and suggestions of the reviewers, which have improved the presentation and the technicality of this paper.


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Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceYazd UniversityYazdIran
  2. 2.The Laboratory of Quantum Information ProcessingYazd UniversityYazdIran

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