New definition of the indefinite integral of fuzzy valued function linearly generated by structural elements

摘要

This paper proposes a new definition of the indefinite integral of fuzzy valued function linearly generated by structural elements using a kind of fuzzy distance. Then the new definition is used to study the basic properties of the indefinite integral of fuzzy valued function linearly generated by structural elements. They are the existence of the original function, addition together with multiplication, integration by substitution and integration by parts. Subsequently, by giving the Cauchy convergence criterion for the anomalous integral of fuzzy value function linearly generated by structural elements, the integrable conditions of the anomalous integral of fuzzy value function linearly generated by structural elements are discussed. They are absolute convergence, Dirichlet test and Abel test.