Some Studies Of Fuzzy Integral Generated Linearly By Structural Elements

The fuzzy limit has different forms according to the difference of the fuzzy distance,so the different properties,the existence conditions and the application of the fuzzy limit can be obtained.The content of this article is roughly divided into three parts:The first part.Based on the extension principle,this paper defines a new fuzzy distance of fuzzy numbers,which is more optimized than the fuzzy distance used in general.Because the calculation result of the fuzzy distance is the fuzzy number and the the model length of the fuzzy distance is more shorter.Then we use this fuzzy distance to define the limit of the fuzzy sequence generated linearly by structural element,and use this fuzzy limit to study the new fuzzy distance.We get the conclusion that the new fuzzy distance is horizontal convergence and completeness.After that,we study these properties of the fuzzy sequence generated linearly by structural elements,which are monotone boundedness,theorem of nested interval,Cauchy convergence criterion,limit uniqueness,boundedness,local preserving number etc,and study the convergence of the fuzzy number term series generated linearly by structural element.The second part.Use the new fuzzy distance to define the limit of the fuzzy value function generated linearly by the structure element.Then the limit definition is used to prove six the-orems,which are addition together with multiplication,local boundedness,uniqueness,local protection,local protection and forcing convergence of the limit of the fuzzy value function generated linearly by the structure element.Afterwards a Cauchy criterion theorem for the ex-istence of the limit of the fuzzy value function generated linearly by the structure element is given.Then This limit of the fuzzy value function generated linearly by the structure element is used to study the continuity and differentiability of the fuzzy value function generated linearly by the structure element.The third part.Combined with the fuzzy linear generated value function limit,continuity and differentiability.The definite integral of the fuzzy value function generated linearly by the structure element are defined.and the property theorems and existence condition of definite integral of the fuzzy value function generated linearly by the structure element are studied.Finally,we apply the fuzzy definite integral of the fuzzy value function generated linearly by the structure element to the calculation of the fuzzy area,the fuzzy volume,the fuzzy curve and the fuzzy surface.