Abstract
This paper studies notions and approaches to attribute reduction in property oriented concept lattices of formal contexts and formal decision contexts based on congruence relations. Firstly, dependence space based on the property oriented concept lattice is researched to obtain the relationship among property oriented concept lattices and the corresponding congruence relations. Then notions of attribute reduction is defined for formal contexts and decision contexts to find minimal attribute subsets which can preserve all congruence classes determined by the original attribute set, and also keep all property oriented extents and their original hierarchy in the property oriented concept lattice. Finally, approaches of discernibility matrix are presented to calculate all attribute reducts.
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