robabilistic metric spaces have been first defined by Menger in 1942 . Menger's idea was to replace the distance between two points and q in a metric space by a distribution functio . The value of at x is then to be interpreted as the probability that the distance between and is less tha x . Menger's work was subsequent by Wald , who modified Menger's idea . I 1964 erstnev gave the first definition of a probabilistic normed space . The theory had little progress however since its introduction . This motivated Alsina , Schweizer and Sklar to redefine probabilistic normed spaces in 1993. Their definition included the previous definitions as special cases . In this thesis we adopt the definition of a probabilistic normed spaces as given by Alsina , Schweizer and Sklar given in the following .