Knowledge and Information Systems

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

Neighborhood system S-approximation spaces and applications

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 


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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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