Knowledge Acquisition And Uncertainty In Intuitionstic Fuzzy Environment

The theory of rough sets, Proposed by Pawlak in1982, is powerful mathematical toolto deal with uncertainty problem. Intuitionistic fuzzy set Proposed by Atanassov in1983, isan extension of the fuzzy set theory, It is more precision than fuzzy set to describing thefuzzy phenomena. This thesis mainly studies intuitionistic fuzzy rough set by combiningintuitionistic fuzzy set theory and rough set theory in intuitionistic fuzzy T equivalenceinformation systems, the main results in this thesis are summarized as follows:1. Uncertainty Measures of Knowledge in intuitionistic fuzzy approximation space arestudied by introducing some basic concept which are knowledge granulation, knowledgeinformation entropy, knowledge rough entropy, Uncertainty measure of knowledge, and soon. Some properties and relarionships of these concept are discussed. Moreover, wepropose the extension of the rourh entropy of rough set in intuitionistic fuzzyT equivalence information systems, some important conlusions are obtained.2. Intuitionistic fuzzy rough set are studied by intuitionistic fuzzy T equivalencerelation, based on Intuitionistic fuzzy implication,(Θ, Φ)-intuitionistic fuzzy rough setsare established. Moreover, an axiomatic approach is proposed to characterize theintuitionistic approximation operators.3. The notions of attibute reduction and approximation reduction in intuitionisticfuzzy information systems are proposed, the judgement theorems and discernibility matrixassociated with the two reduction are examined, from which we can obtain an approach tothe two reductions in intuitionistic fuzzy T equivalence information systems.4. Intuitionistic fuzzy ordered information systems are studied by introducingdominance relation. Ranking method for all objects by using dominance degree of eachobject are given. The properties of rough approximation are discussed in intuitionisticfuzzy ordered information system with decision. In order to extract much simplerdominance rules, based on the discernibility matrices, we have proposed approximationreduction of intuitionistic fuzzy ordered information system with decision, and presentedmethod of the reduction respectively.