Granular reduction in formal fuzzy contexts: graph representation, graph approach and its algorithm

Attribute reduction is one of the significant research issues in the formal fuzzy context (FFC). However, the extant method of computing the minimal granular reducts by Boolean reasoning is an NP problem. To this end, a graph-theoretic-based heuristic algorithm is proposed to compute the granular re...

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Published in:	The Artificial intelligence review Vol. 56; no. 12; pp. 15101 - 15127
Main Authors:	Gong, Zengtai, Zhang, Jing
Format:	Journal Article
Language:	English
Published:	Dordrecht Springer Netherlands 01.12.2023 Springer Springer Nature B.V
Subjects:	Algorithms Analysis Artificial Intelligence Attributes Computer Science Experiments Graph representations Graph theory Graphical representations Heuristic Heuristic methods Reduction Run time (computers) Transformation Formal fuzzy decision contexts Vertex covers Formal fuzzy contexts Granular reduction
ISSN:	0269-2821, 1573-7462
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Abstract	Attribute reduction is one of the significant research issues in the formal fuzzy context (FFC). However, the extant method of computing the minimal granular reducts by Boolean reasoning is an NP problem. To this end, a graph-theoretic-based heuristic algorithm is proposed to compute the granular reducts in an FFC. We introduce the induced graph of the granular discernibility matrix and show that the minimal vertex cover of this induced graph is equivalent to the reduction of the FFC, thus transforming the problem of reduction the FFC into the problem of finding the minimal vertex cover of the graph. The manuscript also sets forth algorithms for finding minimal granular reducts based on graph theory. Further, data experiments are designed, and we formulate a transformation model from an information system with multi-valued attributes to an FFC, considering the characteristics of the continuous type of numerical attributes used in the experiments. Experimental results show that our proposed method performs well in terms of time complexity and running time.
AbstractList	Attribute reduction is one of the significant research issues in the formal fuzzy context (FFC). However, the extant method of computing the minimal granular reducts by Boolean reasoning is an NP problem. To this end, a graph-theoretic-based heuristic algorithm is proposed to compute the granular reducts in an FFC. We introduce the induced graph of the granular discernibility matrix and show that the minimal vertex cover of this induced graph is equivalent to the reduction of the FFC, thus transforming the problem of reduction the FFC into the problem of finding the minimal vertex cover of the graph. The manuscript also sets forth algorithms for finding minimal granular reducts based on graph theory. Further, data experiments are designed, and we formulate a transformation model from an information system with multi-valued attributes to an FFC, considering the characteristics of the continuous type of numerical attributes used in the experiments. Experimental results show that our proposed method performs well in terms of time complexity and running time.
Audience	Academic
Author	Zhang, Jing Gong, Zengtai
Author_xml	– sequence: 1 givenname: Zengtai surname: Gong fullname: Gong, Zengtai email: zt-gong@163.com, gongzt@nwnu.edu.cn organization: College of Mathematics and Statistics, Northwest Normal University – sequence: 2 givenname: Jing surname: Zhang fullname: Zhang, Jing organization: College of Mathematics and Statistics, Northwest Normal University
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Snippet	Attribute reduction is one of the significant research issues in the formal fuzzy context (FFC). However, the extant method of computing the minimal granular...
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SubjectTerms	Algorithms Analysis Artificial Intelligence Attributes Computer Science Experiments Graph representations Graph theory Graphical representations Heuristic Heuristic methods Reduction Run time (computers) Transformation
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Title	Granular reduction in formal fuzzy contexts: graph representation, graph approach and its algorithm
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