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Neighborhood system S-approximation spaces and applications

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Abstract

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.

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Acknowledgments

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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Authors and Affiliations

  1. Department of Computer Science, Yazd University, Yazd, Iran

    Ali Shakiba & Mohammad Reza Hooshmandasl

  2. The Laboratory of Quantum Information Processing, Yazd University, Yazd, Iran

    Ali Shakiba & Mohammad Reza Hooshmandasl

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  1. Ali Shakiba
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  2. Mohammad Reza Hooshmandasl
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Correspondence to Mohammad Reza Hooshmandasl.

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Shakiba, A., Hooshmandasl, M.R. Neighborhood system S-approximation spaces and applications. Knowl Inf Syst 49, 749–794 (2016). https://doi.org/10.1007/s10115-015-0913-9

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