2019/10/05 by Huan Huang, Huang, Huan
Computer Science · Decision Sciences · Mathematics · #FOS: Mathematics #Fixed Point Theorems Analysis #Fuzzy and Soft Set Theory #General Mathematics (math.GM) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1910.02205
openalex publication_date 2019/10/05 · 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 fist 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 compact positive \al-cuts fuzzy sets 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.