Research Of Rough Sets Model On Double Universes Based On Granular Computing

As a mathematical tool, the rough sets theory plays an important role in treatment of uncertain, incomplete or imprecise information by two precise sets, the lower approximate set and the upper approximate set. Pansystems theory is a theory which focuses on the nature of objects, the connections between these objects, as well as the changes among these connections. Granular computing is tool used for inconsistent and uncertain knowledge. On the basis of classical rough sets theory, granular computing and pansystems theory, this paper discusses the upper and lower approximations, the attributes reduction and the decision rules of model of rough sets on the double universes from three aspects:theory, algorithm and instances.Firstly, this paper introduces the background and significance, the research status at home and abroad, the framework and innovation of the paper, general train of thought, key issues to be resolved,then show the relative theoretical knowledge including the knowledge express system and the knowledge express logic of classical rough set theory, body-shadow relation of pansystems, granule and granular base of granularity in granularity computing and the conception of Pr pair.Secondly, on the basis of the method of using the equivalence class to obtain upper and lower approximations in the meaning of the Cartesian product, we use the equivalence class and the granularity computing to obtain upper and lower approximations in the meaning of both the Cartesian product and unordered-pair. The two methods are the theoretical basis of attribute reduction and decision rule in the paper.Thirdly, we generalize the method of attribute reduction into the rough sets on the double universes and put forward the corresponding approach and steps.Finally, base on the attribute reduction method of the classical rough set theory, we use knowledge express logic to obtain percent of dependent, percent of accuracy, decision rule and the simplification of decision rule from the set of knowledge express systems. Then we use the body-shadow relation and part-entirety relation to express the whole decision algorithm and put forward the concrete steps and method of the decision rule of double universe rough sets.