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Constructive and axiomatic approaches to hesitant fuzzy rough set

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Abstract

Hesitant fuzzy set is a generalization of the classical fuzzy set by returning a family of the membership degrees for each object in the universe. Since how to use the rough set model to solve fuzzy problems plays a crucial role in the development of the rough set theory, the fusion of hesitant fuzzy set and rough set is then firstly explored in this paper. Both constructive and axiomatic approaches are considered for this study. In constructive approach, the model of the hesitant fuzzy rough set is presented to approximate a hesitant fuzzy target through a hesitant fuzzy relation. In axiomatic approach, an operators-oriented characterization of the hesitant fuzzy rough set is presented, that is, hesitant fuzzy rough approximation operators are defined by axioms and then, different axiom sets of lower and upper hesitant fuzzy set-theoretic operators guarantee the existence of different types of hesitant fuzzy relations producing the same operators.

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Acknowledgments

This work is supported by the Natural Science Foundation of China (Nos. 61100116, 61203024), Natural Science Foundation of Jiangsu Province of China (Nos. BK2011492, BK2012700), Natural Science Foundation of Jiangsu Higher Education Institutions of China (Nos. 11KJB520004, 12KJB520003, 13KJB520003), Qing Lan Project of Jiangsu Province of China, Key Laboratory of Intelligent Perception and Systems for High-Dimensional Information (Nanjing University of Science and Technology), Ministry of Education (No. 30920130122005), Opening Foundation of Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, the Chinese Academy of Sciences (No. IIP 2012-3), Foundation of Artificial Intelligence Key Laboratory of Sichuan Province of China.

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Authors and Affiliations

  1. School of Computer Science and Engineering, Jiangsu University of Science and Technology, Zhenjiang, 212003, Jiangsu, People’s Republic of China

    Xibei Yang, Xiaoning Song & Yunsong Qi

  2. School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing, 210094, Jiangsu, People’s Republic of China

    Jingyu Yang

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  1. Xibei Yang
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  2. Xiaoning Song
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  3. Yunsong Qi
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  4. Jingyu Yang
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Correspondence to Xibei Yang.

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Communicated by T.-P. Hong.

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Yang, X., Song, X., Qi, Y. et al. Constructive and axiomatic approaches to hesitant fuzzy rough set. Soft Comput 18, 1067–1077 (2014). https://doi.org/10.1007/s00500-013-1127-2

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