R-order Convergence And Dual Convergence Of Uncertain Sequences

In this paper, on the basis of uncertainty theory,the purpose of this paper is to studysome properties of convergence in r-order for uncertain sequence and the dual convergenceof uncertain variables.First of all, in uncertainty theory, the concepts of convergence in mean andconvergence in mean square for uncertain sequence have been built. In this paper, theconcept of convergence in r-order for uncertain sequence is presented firstly. Then somemathematical properties of convergence in r-order is proved. Furthermore, the concept ofCauchy in r-order for uncertain variable is presented. Then, the relation betweenconvergence in r-order and Cauchy in r-order is discussed,get necessary and sufficientcondition of convergence in r-order.Secondly，Based on definition of the uncertainty variables,some properties of limits foruncertain sequence and the dual limits theory of uncertain variables,this paper is to make afurther research on the dual limits of uncertain variables,and the nested theory about theconnection among convergence almost everywhere, convergence uniformly almost surelyand convergence in measure is received.The paper consists of four parts. The main results of this paper are summarized asfollowing：In the first chapter, we simply narrate the academic background and relevantdevelopment of the issue. And the main content is introduced.In the second chapter, some definitions, lemmas and related results used in the articleare introduced in the preparation.In the third chapter, some properties of convergence in r-order for uncertain sequenceare.investigated.In the fourth chapter, the dual convergence of uncertain variables is studied...