Properties And Relativity Of The Set Of Logical Operator And Fuzzy Set And Rough Set

In this dissertation, we try to srudy the organic combination of the t-norm operator set, rough set and fuzzy set. Its content are divided into two chapters.In chapter one, we give the definition of upper fuzzy rough approximation operator decided by t-nonn operator, discuss its properties. In addition, we solve its inverse problem, that is, we give the construction method of t-norm operator from the upper general fuzzy rough approximation operator φ, which contents φ_l = φ. Next, we prove the construction theorem of negator operator. After, we study the properties of dual t-norm operator and t-cononn operator and their corresponding general upper and lower fuzzy rough approximation operator. At last, we we prove the decomposition and synthetize theorems of general fuzzy rough approximation operator.In chapter two, we propose the definition of t-fuzzy equivalent, relation and discuss its properties. And, for arbitrary t-norm operator, we geive. the construction method of its corresponding n × n t-fuzzy equivalent matrix, and the method of new n×n t-fuzzy equivalent matrix from two different n × n t-fuzzy equivalent matrices. In addition, we give the definition of t-fuzzy knowledge base and its corresponding t-fuzzy quotient space, discuss their properties, and prove that all the t-fuzzy equivalent relation and all the t-fuzzy knowledge base construct isomorphism complete lattice.