Entropy-based Granular Computing And Its Application

Granular computing is a new era of information processing and artificial intelligent research field. Its theories and techniques are applied in the processing procedures of fuzzy, inaccuracy, incomplete and mass information’s problem solving. With the fast increasing of the problem complexity, the solution method procedures are also becoming complex. In the practical problem solving procedure, we find that the solution method may not take care of the low level details of problem which is called granular level solution. In fact, the idea of the use of granular concept in problem solving is becoming much more important recently.Both rough set and fuzzy set are mathematics theories which are used to express or solve problems with uncertainty. In the field of information, the concept of entropy is often used to express the uncertainty of information. In this thesis, Shannon entropy, conditional entropy, mutual information, rough entropy of rough set, relative entropy coefficients of fuzzy sets, relative entropy coefficients of rough fuzzy sets have been studied, and the methods to apply them into granular partition of decision table are deeply explored.The main works of this thesis are as following:Firstly, a new definition of conditional rough entropy is put forward after the discussion and comparing with conditional information entropy method. Based on the new definition, several properties are discussed and proved. Secondly, based on the new definition of conditional rough entropy, a new algorithm (KRA-CRRK) about the knowledge reduction is designed.Thirdly, with the concept of mutual information, a new method of inference learning for decision rule is shown.Fourthly, relative entropy coefficient of fuzzy sets and rough fuzzy sets are used in the granularity calculation, and comparing the two applications.