Rough Sets Model Based On Improved Connection Degree And Its Applications Under Incomplete Information Systems

Research consists of three parts. They are inequality of rough degrees, comparison of rough sets models and rough sets models based on improved connection degrees. Inequality of rough degrees is a supplement for classic rough sets. Comparison of rough sets models can educe rough sets model based on improved connection degree. And the third part is the main body.For inequality of rough degree, there is a question that if there exists another sufficient condition that makes inequality of rough degrees become an equation. So two kinds of sufficient conditions are proposed. Then it shows that they are equivalent and the sufficient condition in the literature is a special one. At last, a new rough degree is defined, and lower approximation has the same inequality and the same sufficient condition as upper approximation with the new definition.There are six models to compare. First it shows that to compare their indiscernibility relation is enough. According to connection degrees in literatures, a new one is produced. Then connection degree of each indiscernibility relation can be worked out, and relations between connection degrees and indiscernibility relation are given. According to connection degrees, it is easy to know connections and differences among six indiscernibility relations, and it is easy to know the way how is the unknown attributes value in each rough set model, and it produces an algorithm that can get six indiscernibility relations of objects in decision table at one time with computers. Without connection degrees, for each indiscernibility relation it needs to make a program to work, then too much work of no use is done.Because indiscernibility relation is the key of rough sets models, and connection degree is very close to indiscernibility relation, to integrate connection degrees and indiscernibility relations is very interesting. Rough sets model based on connection degree is the hotspot at present. In connection degree tolerance relation, numbers of unknown values of attributes are considered in, but essentialities of attributes are neglected. So a new connection degree tolerance relation is produced, and an improved rough sets model based on essentialities of attributes is given. There is a difficulty that how to work out essentialities of attributes. The rough sets model based on tolerance relations can solve the problem. Then the new model is used in incomplete information system, while corresponding attributes reduction and attributes values reductions are produced. At last, it shows that characters of the new model with examples.