The Interpretation Of Some Uncertainty Measures In Rough Set Theory

Based on rough set theory,the relationship between belief function and inner measure belief function and lower probability of a random set are discussed,then we give a interpretation of these uncertainty measure . First we compare rough sets and random sets,and derive the relationship between belief function and lower probability. Furthermore,after analyzing the congregative characteristic of inner measure,we obtain the relationship between belief function and inner measure. In the following part,we define a couple of new approximate operators and a couple of corresponding new approximate measure operators,in this way,inner measure belief function and lower probability all can be considered as the particular cases of this lower approximate measure . Dually we can also obtain the relationship among plausibility function,outer measure and upper probability. Finally we give the interpretation of possibility theory in rough set theory,then present a couple conversion algorithm between rough set and fuzzy set.