Fuzzy Complex-valued Measures And Fuzzy Complex-valued Integral

The paper has two parts.The first part:On the basis of the theory of fuzzy complex numbers being introd-uced by J.J.Buckley, we first define the concept of fuzzy complex-valued measurable, and null additivity, null subtraction, pseudo-null additivity, pseudo-null subtraction, auto continuity and pseudo-auto continuity are discussed in the fuzzy complex-valued measures space. Then, through introducing the concept of the fuzzy complex distance, we study uniform auto continuity and pseudo-uniform auto continuity for the fuzzy complex-valued measures.The second part:At first, aiming at measurable function for fuzzy complex value in fuzzy complex measure space, the definition of fuzzy complex valued integral is given. Then its reasonableness and some basic properties are discussed. At last, in given conditions some important theorems similar to classic Lebesgue integral such as monotone convergence theorem, fatou lemma and dominated convergence theorem are abtained. These results are significant for studying and enriching fuzzy integral theory.