In order to create a dynamic measure that describes distances between spatiotemporal points whose positions change over time as well as between the data represented by these points, a temporal INTUITIONISTIC fuzzy METRIC SPACE is created in this paper. The notions of temporal fuzzy t-norm, temporal fuzzy tconorm, and temporal fuzzy negation which have not previously been discussed in the literature are defined, and some of their fundamental characteristics are investigated, in order to define this new method. The idea that the degrees of nearness and non-nearness change with time is the basis for a novel definition of the concept of temporal INTUITIONISTIC fuzzy METRIC SPACEs. However, the basic topological characteristics of the temporal INTUITIONISTIC fuzzy metric SPACE are also looked at. We demonstrate how this new temporal METRIC SPACE preserves the basic characteristics offered by both classical and fuzzy METRIC SPACEs. As a result, a new, more flexible, and dynamic METRIC topology is created while maintaining the fundamental topological characteristics of fuzzy and INTUITIONISTIC fuzzy METRIC SPACEs.

The purpose of this article is to introduce the triple sequences and its convergence over instuitionistic fuzzy METRIC SPACE (IFMS). The article also discusses ideal convergence of triple sequences, the uniqueness of ideal limits, the relationship between Pringsheim’, s limit and ideal limits, the ideal Cauchy sequences, and various specific SPACEs of triple sequences with respect to IFMS.

In this paper, we introduce a new concept named generalized (j-k)-B contraction and prove a theorem about existence and uniqueness of fixed point in generalized (j-k)-B contraction on complete Menger SPACE.

The aim of this research paperto use the concept of Intimate mappings to demonstrate the existence and uniqueness of common fixed point theorems for self-mappings in INTUITIONISTIC fuzzy METRIC SPACE.

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.

The idea of PROBABILISTIC METRIC SPACE was introduced by Menger and he showed that PROBABILISTIC METRIC SPACEs are generalizations of METRIC SPACEs. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in METRIC SPACEs. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining PROBABILISTIC METRIC SPACEs. Then the Dirac function is presented as an important example of distributions functions. We also, introduced Sibley’ s METRIC or Levy METRIC on the set of distance distribution functions and so this SPACE becomes a METRIC SPACE. In the following, PROBABILISTIC METRIC SPACEs are defined from the Serstnev’ s view, and some examples such as Menger PROBABILISTIC METRIC SPACEs, are introduced. In this paper, the strong topology induced by distance distribution functions is introduced, and then PROBABILISTIC diameter, PROBABILISTIC bounded, PROBABILISTIC semi-bounded, PROBABILISTIC unbounded and PROBABILISTIC totally bounded sets are introduced. Also, we prove that in every PROBABILISTIC METRIC, every PROBABILISTIC totally bounded set is PROBABILISTIC bounded set. We also present the cantor intersection theorem and a formulation of Bair’ s Theorem in complete PROBABILISTIC METRIC SPACEs. In addition, we prove that the Heine-Borel property and the Bolzano-Wierestrass property are equivalent.