Fuzzy metric spaces

FUZZY METRIC SPACES(M.Sc. Thesis)Yasemin AKMANGAZ UNIVERSITYINSTITUTE OF SCIENCE AND TECHNOLOGYJanuary 2007ABSTRACTIn this study, definitions of some fuzzy metric spaces are investigated. The thesisconsists of four sections. In the first part the introduction takes places. In thesecond part fuzzy set and some definitions and theorems related to fuzzy setsare studied. Also fuzzy topological space and fuzzy compact space are given. Inthe third part definition of the fuzzy metric space-I is investigated and it isshown that every metric space is fuzzy metric space. Definitions of the topologyinduced by fuzzy metric-I and complete fuzzy metric space are given. Also it isproven that every fuzzy metric space is a Hausdorff space. In the last partdefinition of fuzzy metric space-II and some basic concepts in the metric spacesare given in the fuzzy metric space-II. Finally, relations between these two fuzzymetric spaces are investigated.Science Code : 204.1.132Key Words : Fuzzy set, fuzzy metric space, complete fuzzy metric spacePage Number : 63Adviser : Prof. Dr. Cemil YILDIZ