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Generalized Interval-Valued Fuzzy Rough Set and its Application in Decision Making

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Abstract

This paper presents a general study of generalized interval-valued fuzzy rough sets integrating the rough set theory with the interval-valued fuzzy set theory by constructive and axiomatic approaches. In the constructive approach, by employing an interval-valued fuzzy residual implicator and its dual operator, generalized upper and lower interval-valued fuzzy rough approximation operators with respect to an arbitrary interval-valued fuzzy approximation space are first defined. Then properties of generalized interval-valued fuzzy rough approximation operators are discussed. Furthermore, connections between special types of interval-valued fuzzy relations and properties of generalized interval-valued fuzzy approximation operator are also established. In the axiomatic approach, generalized interval-valued fuzzy rough approximation operators are defined by axioms. We prove that different axiom sets can characterize the essential properties of generalized interval-valued fuzzy rough approximation operators. Also the composition of two approximation spaces is explored. Finally, a practical application is provided to illustrate the efficiency of the generalized interval-valued fuzzy rough set model.

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Acknowledgments

The authors would like to thank the anonymous referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 610054, People’s Republic of China

    Haidong Zhang & Lan Shu

  2. School of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou, 730030, Gansu, People’s Republic of China

    Haidong Zhang

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  1. Haidong Zhang
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  2. Lan Shu
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Correspondence to Haidong Zhang.

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Zhang, H., Shu, L. Generalized Interval-Valued Fuzzy Rough Set and its Application in Decision Making. Int. J. Fuzzy Syst. 17, 279–291 (2015). https://doi.org/10.1007/s40815-015-0012-9

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  • DOI: https://doi.org/10.1007/s40815-015-0012-9

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