Fuzzy-rough Method Of Measurement

Fuzzy set theory and rough set theory are all mathematical theory to be used to deal with uncertain knowledge. By using these two theories, imprecise, uncertain and other incomplete information can be analyzed and the hidden knowledge can be revealed from information systems.Fuzzy set theory and rough set theory has a strong complementary in dealing with uncertain problem. By combining fuzzy set theory and rough set theory, rough fuzzy set model and fuzzy rough set model were proposed, and the uncertain measurement approaches were established. In this paper, based on the above research works, we further study Rough fuzzy measurement methods. The paper consists of the following three aspects:(1) The fuzzy equivalence relation used in the existing uncertain measurement methods is extended to fuzzy reflexive relation. Some roughness inequalities are obtained by discussing the relationship between the different level approximation operators. In addition, rough entropy which is based on fuzzy reflexive relation is discussed by the cut sets. A new definition of rough entropy is proposed.(2) A kind of fuzzy entropy is presented by using a new entropy function with its fundamental properties being discussed.(3) Two kinds of inclusion degree are proposed based on inclusion degree of fuzzy set. And their basic properties are discussed. Three difference degrees are proposed based on difference degree of fuzzy set by using difference degree of fuzzy rough values.