The Genetic Of S-rough Fuzzy Sets And Its Model Of Two Direction Variation

In the real world, there is large amount of imprecise knowledge. At present, it has been known as an important issue to extract useful information from the imprecise knownledge. Both Fuzzy sets and rough sets theory are the studies on inaccuracy knowledge of information system. Both can be used to extract useful features from large amount of data of the complex system, and get the law implied in the data. Based on different bases and by using different methods, the two theorys have their characteristics respectively which can not be replaced by each other. Because the fuzzy and the rough features are the two different aspects of imprecise knowledge, they are complements to each other in dealing with imprecise data. Therefore, the rough fuzzy sets theory that combined by the two are advantageous for the description and manipulation of the imprecise knowledge of information system.Classical Pawlak rough sets are static. S-rough sets are supplements of the Pawlak rough sets. They provid the theoretical basis for the method of dealing with the dynamic problems by the rough sets. The rough fuzzy sets have static characteristic also. The S-rough fuzzy sets theory based on the theory of the S-rough sets, provide a theoretical basis in handling of imprecise knowledge in the dynamic system. The results of these studies are the theoretical foundation of the study of chapter 3 of this article.The rough sets theory is based on the indistinguishability of knowledge. The different elements can not be distinguished in the same equivalence class. When the rough sets model is composed of fuzzy knowledge, the different elements belong to different degrees in the same equivalence class. Then the study of the law of the elements by the use of the equivalence classes, bound to the existence of error. They are the basis of research in reality of the chapter 3 of this article.In the rough sets theory, the domain of elements correspond to the domain of attributes. The elements equivalence classes correspond to the attributes equivalence classes. There exist duality principle between the variation of S-rough sets and the S-rough sets. This theory is applied to the research of data mining. It provide a theoretical basis of finding the data needed in the large database. Therefore, based on these studies, we make a study of the model of the variation of S-rough fuzzy sets in the chapter 4 of this article.In this paper, it composed of the following works mainly:1. Studies focus on the law of the changes of the degrees of elements in the S-rough fuzzy sets. And on this basis, it describes the differences between the degrees of the different elements, that they belong to the same equivalence class in the fuzzy sets, by the definition of the function of different degrees; and studies the law of the changes of the differences between the degrees of different elements in the S-rough fuzzy sets; Through the definition of the grid proximate level of the rough fuzzy sets, it studies the law of changes of the grid proximate level in the S-rough fuzzy sets; Studies focus on the law of the changes of the differences of the degrees of different elements in the f-genetic and (f|-)-genetic of various bands of the equivalence classes in the S-rough fuzzy sets; On the basis of ahead wok, through the research of the law of the changes of the degrees of elements, that they belong to the same equivalence class, in the F -genetic and (F|-)-genetic of various bands in the S-rough fuzzy sets, it gives the definition of the optimal order F -genetic and (F|-)-genetic about the given difference. On the basis of there theories, you can carry out the purpose of controlling the bands of the genetic, and studied the law of changes of the grid proximate level between of the F -genetic and (F|-) -genetic and the original S-rough fuzzy sets.2. On the basis of the studies of the one direction variation of S-rough fuzzy sets, it gives the dual of one direction variation of S-rough fuzzy sets and the two direction variation of S-rough sets, and studies the relationship of the three and the variation of rough fuzzy sets; It defines the equal relations, the inclusion, and the calculation of adding and subtraction of two direction variation of S-rough sets, and studies its features.