Fuzzy Limited Operation And In The Fuzzy Value Function Integral Applied Research Based On Structured Element

For the problems solved by fuzzy limited operation and the integral of fuzzy-valued function,This article research to address these issues and their application based on fuzzy structured element.First of all,this article research mutual conversion of the transform function and its membership function of the fuzzy numbers based on fuzzy structured element theory,and conversion method through graphical transformation,then research mutual conversion of the representation of fuzzy-valued function, providing two effective tools for the generalized fuzzy numbers limited operation and fuzzy-valued function study.Secondly, this article expansion of the generalized fuzzy numbers limited operation by the fuzzy number is expressed by using structured element when it is non-monotonic transformation, then discussed the nature of the fuzzy numbers limited operation,and expand applied research of the theory which its get in the article, get some results which include representation of the structured element of the first class of fuzzy probability, a class of complex fuzzy queuing system structured element method.Finally, this article launched a further study for the integral of fuzzy-valued function based on theory of the foregoing, this article give a new definition about the integral of fuzzy-valued function, and prove that the fuzzy-valued function has limited additivity through the property of limited operation, in the end illustrates effectiveness of the approach through two examples.