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The judgment method of valid objects and its application

There is little room for doubt about Formal Concept Analysis (FCA) as a strong tool to be used in many domains, such as cognitive science, etc. Concept lattice is the basic data structure in FCA, and it is induced by contexts. A context is an incidence matrix that shows the relationship between objects and attributes. Attributes often share hierarchical relations which decide the form of objects. Based on attribute hierarchy, valid/invalid object were defined, the judgment method of valid/invalid object was developed on the relation between reachability matrix and valid objects, and valid object was explained from the perspective of graph theory. The judgment algorithm of valid object was proposed. The analysis of the algorithms also showed linear growth with respect to the number of valid objects. Mathematical models with 10 attributes were built for the algorithms by linear regression analysis.