The Product Fuzzy Metric Space and its Basic Properties

Abstract

A new type of FMS, known as a product FMS (or simply p-FMS) is introduced, the reason behind this name is the continuous t-norm used here is binary operation usually product between number in [0, 1]. To show that this type of spaces is exists we give some examples, then some important basic properties, of this space are introduced with its proves. Moreover we study fuzzy continuous and uniformly fuzzy continuous function by proving basic properties of these notions. Furthermore the prove of cross product of finite number of p-FMS is again a p-FMS is introduced.