About the Compactness of Fuzzy Cone Metric Spaces

The generalization of metric spaces from ordinary sets to fuzzy set theoryand then to the so called cone metric spaces is a promising topics of theoreticalmathematics.  
Therefore, this thesis has two objectives. The first objective is to studycone metric spaces and then constructing the so called fuzzy cone metric spacesusing a new direction which is based on fuzzy point. The second objective is tostudy the compactness of fuzzy sets in fuzzy cone metric spaces and then givethe relationship among different types of compactness, such as compact fuzzysets, pre-compact fuzzy sets, sequentially compact fuzzy sets, countablecompact fuzzy sets and locally compact fuzzy set.