Characterizations of compactness of fuzzy set space with endograph metric

分类： 数学 >> 数学（综合） 提交时间： 2023-01-14

黄欢

摘要： In this paper, we present the characterizations of total boundedness, relative compactness and compactness in fuzzy set spaces equipped with the endograph metric.The conclusions in this papersignificantly improvethe corresponding conclusions given in our previous paper H. Huang, Characterizations of endograph metric and $ Gamma$-convergence on fuzzy sets, Fuzzy Sets and Systems 350 (2018), 55-84 . The results in this paper are applicable tofuzzy sets in a general metric space. The results in our previous paper are applicable tofuzzy sets in the $m$-dimensional Euclidean space $ mathbb{R}^m$,which is a special type of metric space.Furthermore, based on the above results,wegivethe characterizations of relative compactness,total boundedness and compactness in a kind of common subspaces of general fuzzy sets according to the endograph metric.As an application, we investigate some relationship betweenthe endograph metric and the $ Gamma$-convergence on fuzzy sets.

同行评议状态:待评议

 点击量 5483  下载量 341  评论