Metric Characterizations Of Convergences Of Fuzzy Number Series

This thesis mainly studies metric characterizations of convergences of fuzzy number series,it consists of the following four parts:The first chapter is about introduction to some basic problems including the background,significance,the situation of current study both domestic and abroad.The second chapter presents the related preliminary knowledge.Chapter three and chapter four are the main parts of this thesis.It is proved that the convergence of a fuzzy number series with respect to most of the metrics can be converted into the convergence of the corresponding remainder sequence,in the case of convergence the limit of the latter must be 0.Also,the levelwise convergence of a fuzzy number series is equivalent to the convergence of its remainder.The convergence of a fuzzy number series with respect to endograph metric is not equivalent to the convergence of its remainder.It is proved that the limit of a convergent fuzzy number series is also a fuzzy number.It is shown that fuzzy number sequence and fuzzy number series can not be transformed each other.It is proved that the convergence of a fuzzy number series with respect to the sendograph metric D,the endograph metric D?,the supremum metric d_?,the skorokhod metric d_s,the d_p metrics and the convergence of support sets sequence with Hausdorff metric are all equivalent to each other.Fuzzy number sequence is decomposed into the sum of interval number sequence and unimodal fuzzy number sequence the normal point of which is 0.The convergence of fuzzy number series sum from n=1 to ?(u_n) is equivalent to both sum from n=1 to ?(a_m) and sum from n=1 to ?(v_n) are convergent.Discussing the convergence of fuzzy number sequences on both sides of the equation under this decomposition and counter example shows that it is not equivalent.It is proved that metric and the supremum metric d_? are not equivalent.Topological properties of unimodal fuzzy number space the normal point of which is 0 are discussed.By this kind of decomposition,a new metric d_? is induced.We discuss the convergence of fuzzy number sequences with respect to metric d and metric d_?.It is show that the convergence of fuzzy number sequence with respect to the supremum metric d_? and metric(d_?)_? is equivalent.