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 p...

the notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  probabilistic metric space was  introduced by karl menger. alsina, schweizer and sklar gave a general definition of  probabilistic normed space based on the definition of menger [1]. in this note we study the pn spaces which are  topological vector spaces and the open mapping an...

In this paper, the connection between Menger probabilistic norms and H"{o}hle probabilistic norms is discussed. In addition, the correspondence between probabilistic norms and Wu-Fang fuzzy (semi-) norms is established. It is shown that a probabilistic norm (with triangular norm $min$) can generate a Wu-Fang fuzzy semi-norm and conversely, a Wu-Fang fuzzy norm can generate a probabilistic norm.

in this paper, a new enhanced version of the particle swarm optimization (pso) is presented. an important modification is made by adding probabilistic functions into pso, and it is named probabilistic particle swarm optimization (ppso). since the variation of the velocity of particles in pso constitutes its search engine, it should provide two phases of optimization process which are: explorati...

In this paper, we give a probabilistic counterpart of  Mazur-Ulam theorem  in probabilistic normed groups. We show, under some conditions, that every surjective isometry between two probabilistic normed groups is a homomorphism.

In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...

in this paper, we formalize the menger probabilistic normed space as a category in which its objects are the menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. so, we can easily apply the results of topological vector spaces...

in this paper, we introduce the  probabilistic normed groups. among other results, we investigate the continuityof inner automorphisms of a group and the continuity of left and right shifts in probabilistic group-norm. we also study midconvex functions defined  on probabilistic normed groups and  give  some results about locally boundedness of such  functions.

In this paper, we define the concepts of modified intuitionistic probabilistic metric spaces, the property (E.A.) and  the common property (E.A.) in   modified  intuitionistic probabilistic metric spaces.Then, by the commonproperty (E.A.), we prove some common fixed point theorems in modified intuitionistic Menger probabilistic metric spaces satisfying an implicit relation.