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Concept granular computing systems and their approximation operators

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Abstract

In this paper, three kinds of adjoint extent-intent and intent-extent operators between two complete lattices are constructed. Three new types of concept granular computing systems are then formulated via a quadruple including two complete lattices and the corresponding adjoint operators. It is showed that all the concepts in any of the concept granular computing systems form a complete lattice. Furthermore, based on the four types of concept granular computing systems, we present four types of rough set approximation operators in a formal context which can characterize different aspect of knowledge. Some important properties of the proposed approximation operators are also proved.

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Acknowledgments

The authors are very indebted to the anonymous referees for their critical comments and suggestions for the improvement of this paper. This work was supported by the grants from the National Natural Science Foundation of China (Nos. 61173181, 61272021, 61363056,6157332), the National Social Science Foundation of China (No. 14XXW004), the Humanities and Social Science funds Project of Ministry of Education of China (Nos. 11XJJAZH001, 12YJA630019), the Fundamental Research Funds for the Central Universities, the Zhejiang Provincial Nature Science Foundation of China (No. LZ12F03002), and Key Laboratory of Oceanographic Big Data Mining & Application of Zhejiang Province (No. OBDMA201504).

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Authors and Affiliations

  1. College of Computer and Communication Engineering, China University of Petroleum, Qingdao, Shandong, 266580, People’s Republic of China

    Faming Gong & Ming-Wen Shao

  2. Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhejiang, 316022, People’s Republic of China

    Ming-Wen Shao

  3. School of Management, Xi’an University of Architecture and Technology, Xi’an, Shanxi, 710055, People’s Republic of China

    Guofang Qiu

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  1. Faming Gong
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  2. Ming-Wen Shao
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Correspondence to Ming-Wen Shao.

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Gong, F., Shao, MW. & Qiu, G. Concept granular computing systems and their approximation operators. Int. J. Mach. Learn. & Cyber. 8, 627–640 (2017). https://doi.org/10.1007/s13042-015-0457-z

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  • DOI: https://doi.org/10.1007/s13042-015-0457-z

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