Abstract：The strictly convex function is introduced into the research of knowledge granularity for the first time. Based on the strictly convex function, a theory framework for constructing knowledge granularity is proposed. A series of knowledge granularity measuring functions is derived under this framework. It is proved that the existing knowledge granularity measuring functions are the special cases or variations of knowledge granularity measures which are derived by strictly convex functions. The definition of the relative knowledge granularity based on strictly convex function is given. Its monotonicity is proved for some special strictly convex functions and the corresponding equality conditions are provided, although it does not hold for general strictly convex functions. It is proved that the existing two conditional information entropies are the special forms of the proposed relative knowledge granularity. Their knowledge granularity essence is revealed. For a consistent decision table, it is proved that the relative knowledge granularity is equivalent to positive region for each other. Therefore, the attribute reduction judgment method of algebraic reduction is presented by the relative granularity in consistent decision table. The correctness of the proposed conclusions is showed by a numerical example.
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2013, Vol. 26 
