In this paper, we introduce a new class of contractive mappings in FUZZY METRIC SPACEs and we present some fixed point results for this class of maps.

In this paper, we study the existence of integral solutions of FUZZY fractional differential systems with nonlocal conditions under Caputo generalized Hukuhara derivatives. These models are considered in the framework of complete generalized METRIC SPACEs in the sense of Perov. The novel feature of our approach is the combination of the convergent matrix technique with Schauder fixed point principle of vector valued operators in semilinear Banach SPACEs. Some computational examples are represented to demonstrate our theoretical results.

For a class of FUZZY METRIC SPACEs (in the sense of George and Veeramani) with an H-type t-norm, we present a method to construct a METRIC on a FUZZY METRIC SPACE. The induced METRIC SPACE shares many important properties with the given FUZZY METRIC SPACE. Specifically, they generate the same topology, and have the same completeness. Our results can give the constructive proofs to some problems for FUZZY METRIC SPACEs in the literature, which are shown by examples in this paper.

In this paper, we propose a new definition of intuitionistic FUZZY quasi-METRIC and pseudo-METRIC SPACEs based on intuitionistic FUZZY points. We prove some properties of intuitionist FUZZY quasi- METRIC and pseudo-METRIC SPACEs, and show that every intuitionist FUZZY pseudo-METRIC SPACE is intuitionist FUZZY regular and intuitionistic FUZZY completely normal and hence intuitionistic FUZZY normal. These are the intuitionistic FUZZY generalization of the corresponding properties of FUZZY quasi-METRIC and pseudo- METRIC SPACEs.

Many authors have introduced the concept of FUZZY METRIC SPACEs in different ways. In this paper, we get a special structure for some separable FUZZY METRIC and M-FUZZY METRIC SPACEs, where the METRIC SPACE has been introduced by George and Veermani.

The aim of this paper is to study induced (quasi-) uniformities in Kramosil and Michalek's FUZZY METRIC SPACEs. Firstly, I-uniformity in the sense of J. Gutierrez Garcia and I-neighborhood system in the sense of Hohle and Sostak are induced by the given FUZZY METRIC. It is shown that the FUZZY METRIC and the induced I-uniformity will generate the same I-neighborhood system. Secondly, the relationship between Hutton quasi-uniformities and I-quasi-uniformities is given and it is proved that the category of strongly stratified I-quasi-uniform SPACEs can be embedded in the category of Hutton quasi-uniform SPACEs as a bicoreflective subcategory. Also it is shown that two kinds of Hutton quasi-uniformities can generate the same I-uniformity in FUZZY METRIC SPACEs.