Intuitionistic Fuzzy Rough Set Over Two Universes And Its Uncertainty Measures

The theories of rough sets and intuitionistic fuzzy sets, proposed by Pawlak andAtanassove, are mathmatic tools to deal with the uncertain and vague problems. In fact,intuitionistic fuzzy set is an extension of fuzzy set and it can describe fuzzy phenomenonsbetter. On the basis of two universes, this paper proposes intuitionistic fuzzy rough set modelsby combining rough set theory and intuitionistic fuzzy set theory, and discusses the reductionby using the evidence theory and investigates the uncertainty measures. The main ideas in thisthesis are listed in the following.1. From the perspective of two universes, we establish rough intuitionistic fuzzy set model ingeneralized approximation space and intuitionistic fuzzy rough set model in intuitionisticfuzzy approximation space. Then we investigate the important properties of the twomodels, and use practical examples to prove the practicabilities and universalities of thetwo models.2. The uncertainty problems are discussed in two universes inituitionistic fuzzyapproximation space and we introduce the notions of four uncertainty measures,knowledge granularity, rough entropy, information entropy and the uncertainty measure ofknowledge. Next, we explore their properties and the relationships between them, andgeneralize the rough entropy of rough set by combining the roughness of rough set andknowledge granularity in intuitionistic fuzzy approximation space.3. Combined the rough set theory and envidence theory, the concepts of object belief andplausibility consistent reductions and belief and plausibility significance reductions are putforward in generalized approximation space. In addition, we probes into the connectionsbetween them and these reduction methods are very important to knowledge acquisitionand rules extraction.4. In order to study the uncertainty of intuitionistic fuzzy decision table, six kinds ofsimilarity measures of intuitionistic fuzzy set are introduced. Based on the new method forclassifying objects, the new upper and lower approximation of rough set are setted up andwe extend the similar measures to describe the uncertainty better. Lastly, we discuss theproperties and inner relations between them.