The Ideal Convergence Of A Fuzzy Numerical Function Column

Fuzzy-valued function and its related problems is one of the important re-search subjects of fuzzy analytics.On the basis of the concept of ideal con-vergence,this paper studies the ideal convergence of fuzzy-valued function se-quence and its related analytic properties.And its main contents include the following two aspects:The first part of this article introduces the concept of uniform ideal conver-gence and uniform ideal* convergence of fuzzy-valued function sequence. It proves that in the situation of admissible ideal, the uniform ideal* convergence of fuzzy-valued function sequence implies the uniform ideal convergence of fuzzy-valued function sequence.And this part also introduces the Cauchy cri-terion and its related properties. The continuity and integrability of the lim-it function of uniform ideal convergent fuzzy-valued function sequence are discussed. Then,it proves Dini theorem of uniform ideal convergence of fuzzy-valued function sequence and gets a decomposition theorem of ideal* convergence of fuzzy-valued function sequence.And this proves that the ide-al convergence and equicontinuity of fuzzy-valued function sequence implies uniform ideal convergence.On the second part,it introduces the definition of level uniform ideal conver-gence of fuzzy-valued function sequence.And some properties of limit func-tion of level ?-uniform convergent fuzzy-valued function sequence are researched.With the conditions of Cauchy criterion of level ?-convergence of fuzzy number sequence and ideal equicontinuity, the Cauchy Criterion of level uniform I-convergence of fuzzy-valued function sequence is proved.