Research On Fuzzy Roughness Measurement Model Based On Level Effect

Rough set theory and fuzzy set theory are the major tools that have been widely used to deal with uncertain information. While, how to construct available methods to coalesce the two kinds of uncertain information processing in a systematical way has attracted the attention of scholars in both the academic field and the applied field. Rough fuzzy set theory and fuzzy rough set theory as a comprehensive descriptive method with uncertainty by the combination of fuzziness and roughness, however, when dealing with uncertain metric, the classical rough set measurement model by Pawlak is still being followed, though it cannot show the hierarchical structural characteristics of the fuzzy set or give a full play to the role of different fuzzy states in the process of decision making.In this paper, the issue of the uncertainty of the measurement of information will be discussed. And by analyzing the structural features of rough fuzzy sets and fuzzy rough sets, as well as the shortcomings of the existing metric patterns, the concept of level-effect function will be introduced based on the decomposition theorem of rough sets. Moreover, the theory of fuzzy rough measure which is based on the level effect will be put forward and the metric mode of effect roughness degree of rough fuzzy sets and fuzzy rough sets will be developed respectively in the paper. Therewith, decision idea can be put into the metric mode in the form of effect function by the combination of the fuzzy decision case. This will be a further explanation that the fuzzy rough metric mode which is based on the level effect shares the quality of favorable operability and practicability. The reduction method based on the attribute effect roughness degree, which has an extensive application value in many fields such as artificial intelligence, resource management and information security, etc., will be constructed in this paper to solve the attribute reduction problem in a fuzzy environment. Its characteristics and validities will be proved by the combination of some examples. The last part of this paper discusses the limitations of the constructing mechanism of Pawlak’s rough fuzzy metric pattern. Furthermore, on the basis of connection between the target concept itself and the lower and upper approximation, it introduces and constructs a composite quantitative system of roughness, based on the synthesizing effect function. With that system the uncertainty of target sets can be illustrated more precisely. The discussion will not only enrich rough set theory and fuzzy set theory at some degrees, but also hold some significance to construct and perfect the decision theory and method in a complicated environment.