Two Extension Models Of Multi-granularity Rough Set

As a method of data processing, multi-granularity method can be used to solve many problem of uncertainties effectively. However, based on the indiscernibility relation, it is hard to apply the classical rough set directly to a variety of complex data, which exist widely in reality. Hence, this paper research two extension models of multi-granularity rough set. The specific work is as follows:(1) Because of multitude of complex data in reality, many scholars extend the equivalence relation between objects to general binary relation, such as tolerance relation, limited tolerance relation, etc. From the viewpoint of reasonableness, limited tolerance relation is more strict and more reasonable than tolerance relation. Then this paper establish the multi-granularity rough set based on limited tolerance relation. What’s more, the requirement of optimistic multi-granularity rough set is loose and that of pessimistic multi-granularity rough set is strict. Based on this, we construct ? multi-granularity rough set based on limited tolerance relation. Variable precision rough set is a extension of Pawlak rough set, which utilize the method of parameter to reduce the requirment of approximate boundary in classical rough set theory and allow some classification errors existing in upper and lower approximation. Hence, we combine the advantages of multi-granularity rough set with that of variable precision rough set and get variable precision ? multi-granulation rough set based on limited tolerance relation. At last, we discuss their approximation accuracies respectively.(2) Intuitionistic fuzzy set is mainly used to describe the fuzziness of object and it is also an effective method in dealing with uncertainty problem. Through a combination of multi-granularity rough set and intuitionistic fuzzy set, we establish the multi-granulation covering rough-intuitionistic fuzzy set model, which enrich multi-granularity rough set theory. Then we discuss the uncertainty of this model from the perspective of rough set and intuitionistic fuzzy set theory and construct rough entropy, roughness and fuzziness of this model. At last, an example is given.