The Approximate Representation Of An Uncertain Concept In Pawlak’s Space

Klein has pointed out that uncertainty exists in mathematics. With the development of cognitive technology, researchers pay more attentions to how to represent and process uncertain problems. Rough set has become a major tool for dealing with uncertain problems. From another point of view, researchers try to take advantage of knowledge base induced by condition attributes to obtain the approximation set of target concept X which has a better similar degree than that of R(X) or R(X). The core idea is that transforming a rough set into a fuzzy set and using a cut-set to get different degree of membership which can be used to obtain approximation set of the target concept X. And then, approximation set can be applied to rule acquisition and so on. In addition, researchers have discussed how the similar degree changes with different knowledge granularity.If the target set, an uncertain concept, is an Interval set (Z) or a Vague set (A), how to describe the uncertain concept in the existing knowledge base? In this paper, we will firstly show some definitions, such as similar degree, upper approximation set R(Z), lower approximation set R(Z), and so on. And then, in order to overcome the shortcomings of R(Z) and R(Z) in approximately describing Z, a better approximation set, R0.5(Z), is provided. Next, how the similar degree between Z and R0.5(Z) changes with the varied knowledge granularity is discussed. For a Vague set A, some basic knowledge is reviewed, and some new definitions are given. Such as step-average-Vague set and so on. And then, some characters of the new sets including0.5-crisp set are shown. How the similar degree changes with the varied knowledge granularity is also discussed carefully. Finally, we use one of the characters to propose an improved algorithm about image segmentation.The approximate representations of Interval set and Vague set in Pawlak’s space are discussed in this thesis. Many new definitions have been proposed, such as approximation set of Interval set, step-average-Vague set. The relational theorems have been proposed and proved. At last, the experiments are completed. We hope these results can promote the development of the uncertain artificial intelligence.