A study on fuzzy connectedness and fuzzy continuity in fuzyy topological spaces

Abstract

Fuzzy connectedness and fuzzy continuity are important concepts in the field of fuzzy mathematics, and have been studied in various types of fuzzy spaces. In this review paper, we have explored several recent research articles that investigate these concepts in different types of fuzzy spaces, including intuitionistic fuzzy topological spaces, quasi-metric spaces, generalized metric spaces, generalized fuzzy topological spaces, intuitionistic fuzzy soft metric spaces, fuzzy normed linear spaces, fuzzy quasi-metric spaces, fuzzy metric spaces, and b-metric spaces. The methodology and results of each study vary based on the type of fuzzy space under consideration, but all papers aim to provide a better understanding of the properties and behavior of fuzzy connectedness and fuzzy continuity. Common theme across these articles includes the use of various types of fuzzy functions, fuzzy sets, and the extension of classical concepts to fuzzy spaces. This review paper provides a comprehensive overview of the recent advances in the study of fuzzy connectedness and fuzzy continuity, highlighting similarities and differences among the various types of fuzzy spaces and suggesting directions for future research.