2023/04/08 by Huan Huang, Huang, Huan
Decision Sciences · Mathematics · #FOS: Mathematics #Fixed Point Theorems Analysis #Fuzzy Systems and Optimization #Fuzzy and Soft Set Theory #General Mathematics (math.GM)
paper · pdf · doi:10.48550/arxiv.2304.03876
openalex publication_date 2023/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper discusses the properties the spaces of fuzzy sets in a metric space equipped with the endograph metric and the sendograph metric, respectively. We first give some relations among the endograph metric, the sendograph metric and the Γ-convergence, and then investigate the level characterizations of the endograph metric and the Γ-convergence. By using the above results, we give some relations among the endograph metric, the sendograph metric, the supremum metric and the dp^* metric, p≥ 1. On the basis of the above results, we present the characterizations of total boundedness, relative compactness and compactness in the space of fuzzy sets whose α-cuts are compact when α>0 equipped with the endograph metric, and in the space of compact support fuzzy sets equipped with the sendograph metric, respectively. Furthermore, we give completions of these metric spaces, respectively.