Uncertainty Measure And Attribute Reduction Based On Interval Intuitionistic Fuzzy Information System

With the wide application of technology of acquiring data, database managementsystems, this is enormous challenges for the capacity of people to process and analyze thedata. In order to solve the problem of "data rich, poor knowledge", how to acquire new,potential, correct and valuable knowledge in very large, messy and noisy databases, hasbecome one of the key research fields in intelligent information processing.Faced with a variety of complicated information systems, when utilizing rough set theoryto deal with these systems, because the system and the set needs to set an approximateexpression are uncertain, therefore the uncertainty of information system becomes one of theessential topics in rough set theory. Currently, the uncertainty of classic information systemand fuzzy information system have had a very good solution, the theory and methods ofattribute reduction in classical information system and fuzzy information system have gaineda fast development and perfection. But with the constant promotion of rough set theory, andalso in order to adapt to practical applications, the decision information system has also beenfurther promoted, one of them is interval intuitionistic fuzzy information system. However,there is little involved in the existing literature for the uncertainty measure of intervalintuitionistic fuzzy information system, and attribute reduction based on the uncertaintymeasure of interval intuitionistic fuzzy information system. Based on these considerations, theuncertainty measure and the attribute reduction on the interval intuitionistic fuzzy informationsystem are studied systematically in this thesis. The main works are as follows:(1)Firstly, a pair of new interval-value intuitionistic fuzzy upper and lowerapproximation operator with symmetry are defined in the interval-value intuitionistic fuzzyapproximation space. Secondly, the corresponding definition of rough membership functionson interval intuitionistic fuzzy are given and the properties are discussed, in the Pawlakapproximation space and interval intuitionistic fuzzy approximation space. Then, twouncertainty measures of rough interval intuitionistic fuzzy set are defined, through thedifferent forms of rough membership functions on interval intuitionistic fuzzy set. Finally, thefuzzy entropy of interval intuitionistic fuzzy rough set is defined by interval intuitionisticfuzzy entropy of the interval intuitionistic fuzzy rough membership functions, the necessaryand sufficient condition of the fuzzy entropy on interval intuitice fuzzy rough set as zero isdiscussed, and the rough measurement of classic set and residual are equal in the intervalintuitionistic fuzzy approximate space, so as to prove the rationality of the definition.(2)The information measurement of interval intuitionistic fuzzy approximation space isstudied in this thesis, and the attribute reduction of decision information systems are given byusing the information measurement. First, on the basis of the relationship between thesimilarity of intuitionistic fuzzy set and entropy, the relationship between the similarity ofinterval intuitionistic fuzzy set and fuzzy entropy is defined, and based on the newly similarity of interval intuitionistic fuzzy sets, the information metrics of interval intuitionistic fuzzyapproximation space is given, which is used the information measure of fuzzy approximationspace. Second, the uncertainty measure and attribute reduction method on intervalintuitionistic fuzzy relations are obtained, and based on divided interval intuitionistic fuzzyinformation particles under interval-value intuitionistic fuzzy relations. Then a newinformation entropy is difined, which combination of particle classification, and consideringthe amount of information functions have complementary nature, and its properties arestudied. In the discussion about the uncertainty measurement, the attribute reductionalgorithm of the system is given. Again, the relative fuzzy entropy that the uncertainknowledge is considered, which is given by the set of attributes divided particles. And theinterval intuitionistic fuzzy approximation space reduction algorithm is proposed. Finally, ininterval intuitionistic fuzzy approximate space, an integrated measure of uncertainty isgiven, both the uncertainty of set and the uncertainty of knowledge are consider in thismethod.