Concept Lattice Generation Based On Attributes Classification

Formal concept analysis,proposed by Wille in 1982,is a mathematical tool for data analysis and knowledge discovery.Because of the concise of knowledge expression and the visibility of knowledge presentation in formal concept analysis,extensive researches about this theory were proposed by many scholars.Formal context and concept lattice are two basic notions in formal concept analysis where the former one gives the data foundation,and the latter one presents a hierarchical structure of the knowledge in formal contexts.However,the complex structure of concept lattice may also occur some inconvenience in its practical applications,thus the simplification of concept lattice has become one of the most important research topics in formal concept analysis.For example,some researchers introduced the clustering methods from machine learning into formal concept analysis,achieve the simplification of knowledge by summarizing and abstracting the original concept lattice through the clusters of objects,attributes or concepts.However,most researches only focus on the selection of clustering methods,but ignore the subsequent new knowledge structures.Therefore,this paper presents three kinds of models based on different situations of attributes classification in real life,and focuses on the binary relation between objects and attribute classes,also the corresponding classified formal contexts and their concept lattices.After then,the analysis is carried out through examples.The details are as follows:1.The formal context with attribute classification is formally described,and the pessimistic classified context and corresponding pessimistic classified concept lattice are proposed.The relationships between operators and concepts in pessimistic classified context and those in the original context are studied,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 is presented.2.The optimistic classified context and its concept lattice are defined,the relationships between operators and concepts in optimistic classified context and those in the original context are studied,and the connection of the original concept lattice and the optimistic classified concept lattice is explored by using concept inclusion mapping,then the generation method of optimistic classified concept lattice is presented.3.Combined with the theory of fuzzy formal concept analysis,the fuzzy classified context and fuzzy classified concept lattice are defined,the connections of the original concept lattice and the fuzzy classified concept lattice is studied,the relationships between fuzzy classified concept lattices under different thresholds are also explored.