Rough data-deduction based on the upper approximation

This paper describes how to construct a structure called a rough deduction-space. It is an extension of an approximation space, and incorporates a deduction relation related to data connections. In the rough deduction-space, a notion of data deduction is introduced and is referred to as rough data-deduction. Based on integrated information of both the upper approximation and the deduction relation, rough data-deduction accomplishes deductions from data to data, which is different from any logical deduction in mathematical logic. Research on rough data-deduction covers two activities: the rough data-deduction with respect to an equivalence relation and rough data-deductions with respect to different equivalence relations. The activities also concern the relationship between rough data-deduction and rough relations that are rough representations of the deduction relation. This leads to properties involving approximate features implied by rough data-deduction, and reflecting the characteristic that rough data-deduction can describe rough data-connections. In particular, since the research correlates closely to granules, it may offer an avenue of research on granular computing. As an example, a specific problem is modeled by a rough deduction-space. The rough data-connections in the problem are described by use of rough data-deduction.