| Rough sets theory is a kind of mathematical tool which deals with fuzzy and uncertainty of knowledge. The principal method of its research is by using attribute reduction, preserved the same classification ability, to obtain the classification rules. There are a variety of generalizations of rough sets, such as continuous rough sets, incomplete rough sets, fuzzy rough sets, neighborhood rough sets, and decision making rough sets. Among them, continuous rough sets, incomplete rough sets and fuzzy rough sets are based on the similar relationship.So a natural question arises:whether we can investigate these three rough sets in a unified way. For all we know, there are no relevant results for this question in the literatures so far.The main contribution of the thesis is to combine continuous rough sets, incomplete rough sets and fuzzy rough sets into a unified rough sets model which based on the similar relationship, and study the properties of the similar relationship, the attribute reduction, and the extracting rules as a whole. Firstly, by studying the properties of the traditional rough sets, we extend these properties to the similar relationship, and then obtain the general properties of the similar relationship. Secondly, we choose an appropriate similar function and an appropriate regulate function to make all the similar relationship normalized, and hence unify the different forms of similar relationship and get a unified reduction method. Finally, we put forward a new method of classification based on the similarity. What’s more, the feasibility of all kinds of the reduction and the new classification are demonstrated.In addition, get the rough set which contains similar relationship into unification can reduce the repetitive work of attribute reduction and rule extraction based on the same properties. As a result, the research of any branch can be used for reference other branches which also contain the similar relationship. |
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