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General type-2 fuzzy rough sets based on \(\alpha \)-plane Representation theory

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Abstract

Rough sets theory and fuzzy sets theory are mathematical tools to deal with uncertainty, imprecision in data analysis. Traditional rough set theory is restricted to crisp environments. Since theories of fuzzy sets and rough sets are distinct and complementary on dealing with uncertainty, the concept of fuzzy rough sets has been proposed. Type-2 fuzzy set provides additional degree of freedom, which makes it possible to directly handle highly uncertainties. Some researchers proposed interval type-2 fuzzy rough sets by combining interval type-2 fuzzy sets and rough sets. However, there are no reports about combining general type-2 fuzzy sets and rough sets. In addition, the \(\alpha \)-plane representation method of general type-2 fuzzy sets has been extensively studied, and can reduce the computational workload. Motivated by the aforementioned accomplishments, in this paper, from the viewpoint of constructive approach, we first present definitions of upper and lower approximation operators of general type-2 fuzzy sets by using \(\alpha \)-plane representation theory and study some basic properties of them. Furthermore, the connections between special general type-2 fuzzy relations and general type-2 fuzzy rough upper and lower approximation operators are also examined. Finally, in axiomatic approach, various classes of general type-2 fuzzy rough approximation operators are characterized by different sets of axioms.

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Acknowledgments

The authors would like to thank reviewers for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (51177137, 61134001) and the Fundamental Research Funds for the Central Universities (SWJTU11CX034).

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Authors and Affiliations

  1. School of Transportation and Logistics, Southwest Jiaotong University, Chengdu, 610031, China

    Tao Zhao

  2. School of Electrical Engineering, Southwest Jiaotong University, Chengdu, 610031, China

    Jian Xiao

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  1. Tao Zhao
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  2. Jian Xiao
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Correspondence to Tao Zhao.

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Communicated by L. Spada.

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Zhao, T., Xiao, J. General type-2 fuzzy rough sets based on \(\alpha \)-plane Representation theory. Soft Comput 18, 227–237 (2014). https://doi.org/10.1007/s00500-013-1082-y

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