| Uncertainty problem is not only the focus of artificial intelligence research,but also the important preface of artificial intelligence.Rough set theory is also an effective tool to deal with uncertainty knowledge.In this paper,we research the uncertainty measurement of generalized rough set model,covering rough set model and incomplete interval-valued information system based on general binary relation.The main content of the paper is stated as follows:We come up with the concept of upper and lower rough entropy based on upper and lower rough equivalence relations.And their properties are studied.Moreover,we prove that the upper rough entropy is equal to the lower rough entropy.In addition,we compare the rough entropy with the entropy proposed by Wang[32],and the results show that the entropy proposed by us has a higher degree of identification.The rough entropy in the classical rough set model is extended to the covering rough set model.A kind of lower rough entropy and its related properties are given based on a lower approximation of the covering,and three kinds of upper rough entropy are given based on the three upper approximations of the covering.Furthermore,we study the concepts of conditional entropy,joint entropy and mutual information in the covering rough set.In addition,we also give the concept of covering reduction.The application of covering rough entropy in the study of duality of approximate operators is discussed.Finally,we study the uncertainty measurement of incomplete interval-valued informa-tion systems.In this paper,we show a method of constructing the ?-similarity relation in information system.And we present the concept of ?-precision,?-coarseness and ?-rough entropy.Based on these definitions,we construct the Aultra-precision.Otherwise,we make a comparative study of our proposed in the automotive data set.The experiment shows that in incomplete interval-valued information system,?-ultra-precision is more efficient than other measures. |
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