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AIMS Mathematics

2024, Volume 9, Issue 12: 35471-35502. doi: 10.3934/math.20241684
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Research article

The discernibility approach for multi-granulation reduction of generalized neighborhood decision information systems

  • 1.
    School of Computer Science, Minnan Normal University, Zhangzhou, Fujian 363000, China
  • 2.
    Key Laboratory of Data Science and Intelligence Application, Fujian Province University, Zhangzhou, Fujian, 363000, China
  • 3.
    School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian 363000, China
  • Received: 29 September 2024 Revised: 16 November 2024 Accepted: 29 November 2024 Published: 19 December 2024

  • MSC : 68T30, 68T37

  • Attribute reduction of a decision information system (DIS) using multi-granulation rough sets is one of the important applications of granular computing. Constructing discernibility matrices by rough sets to get attribute reducts of a DIS is an important reduction method. By analyzing the commonalities between the multi-granulation reduction structure of decision multi-granulation spaces and that of incomplete DISs based on discernibility tool, this paper explored a general model for the multi-granulation reduction of DISs by the discernibility technique. First, the definition of the generalized neighborhood decision information system (GNDIS) was presented. Second, knowledge reduction of GNDISs by multi-granulation rough sets was discussed, and discernibility matrices and discernibility functions were constructed to characterize multi-granulation reduction structures of GNDISs. Third, the multi-granulation reduction structures of decision multi-granulation spaces and incomplete DISs were characterized by the reduction theory of GNDISs based on discernibility. Then, the multi-granulation reduction of GNDISs by the discernibility tool provided a theoretical foundation for designing algorithms of multi-granulation reduction of DISs.

    Citation: Yanlan Zhang, Changqing Li. The discernibility approach for multi-granulation reduction of generalized neighborhood decision information systems[J]. AIMS Mathematics, 2024, 9(12): 35471-35502. doi: 10.3934/math.20241684

    Related Papers:

  • Attribute reduction of a decision information system (DIS) using multi-granulation rough sets is one of the important applications of granular computing. Constructing discernibility matrices by rough sets to get attribute reducts of a DIS is an important reduction method. By analyzing the commonalities between the multi-granulation reduction structure of decision multi-granulation spaces and that of incomplete DISs based on discernibility tool, this paper explored a general model for the multi-granulation reduction of DISs by the discernibility technique. First, the definition of the generalized neighborhood decision information system (GNDIS) was presented. Second, knowledge reduction of GNDISs by multi-granulation rough sets was discussed, and discernibility matrices and discernibility functions were constructed to characterize multi-granulation reduction structures of GNDISs. Third, the multi-granulation reduction structures of decision multi-granulation spaces and incomplete DISs were characterized by the reduction theory of GNDISs based on discernibility. Then, the multi-granulation reduction of GNDISs by the discernibility tool provided a theoretical foundation for designing algorithms of multi-granulation reduction of DISs.



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