Compactness in ech Fuzzy Soft Closure Spaces

In this paper, the concepts of compactness, almost compactness, and nearly compactness for ech fuzzy soft closure spaces are introduced and discussed. Their characterizations in terms of the finite intersection property are established, and their hereditary properties are investigated for compactness and almost compactness types. The relationships between the three types of compactness are investigated and illustrated with examples. The sufficient condition for the equivalence between compactness and almost compactness has been provided. In addition, new types of fuzzy soft mappings on ech fuzzy soft closure spaces, namely ech fuzzy soft strongly (respectively ech fuzzy soft θ, and ech fuzzy soft almost) continuous mapping, are introduced to study the behavior of the presented compactness types under fuzzy soft mappings.