Pessimistic Concept Lattices and Optimistic Concept Lattices Based on Attribute Classification
GAO Le1,2, WANG Zhen1,2, WEI Ling1,2, QI Jianjun3
1. School of Mathematics, Northwest University, Xi′an 710127 2. Institute of Concepts, Cognition and Intelligence, Northwest University, Xi′an 710127 3. School of Computer Science and Technology, Xidian University, Xi′an 710068
Abstract In the formal context with attribute classification, the pessimistic classified formal context and optimistic classified formal context are firstly proposed, the operators and concepts in these contexts are defined, and the relationships between operators and concepts in classified contexts and those in the original contexts are studied. Then, for the pessimistic classified formal context, the mapping between the original concept lattice and the pessimistic classified concept lattice is established, and the generation method of the pessimistic classified concept lattice from the original concept lattice is presented. For the optimistic classified formal context, the relationships between the original concept lattice and the optimistic classified concept lattice are studied by introducing the concept inclusion mapping, and the corresponding generation method of the concept lattice is presented as well. Finally, the practical application and the semantic interpretation of both pessimistic and optimistic classified concept lattices are discussed.
Fund:National Natural Science Foundation of China(No.61772021,11801440,62006190), Natural Science Basic Research Program of Shaanxi Province(No.2021JM-141)
Corresponding Authors:
WEI Ling, Ph.D., professor. Her research interests include formal concept analysis, rough set, three-way decision and granular computing.
About author:: GAO Le, master student. His research interests include formal concept analysis, three-way decision and granular computing.WANG Zhen, Ph.D. candidate. His research interests include formal concept analysis, three-way decision and granular computing.QI Jianjun, Ph.D., associate professor. His research interests include formal concept analysis, three-way decision and intelligent data analysis.
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2021, Vol. 34 
