Some remarks concerning on a fuzzy real normed space

Abstract

In mathematics, computer science, statistics, and other fields, the notion of fuzzy metric and fuzzy normed is crucial. Finding an acceptable fuzzy metric or norm for making some measurements can solve a lot of difficulties. In the sense of Mohammedali, fuzzy real normed spaces (FRNS) are the issue of this paper. Real normed and fuzzy real normed are advanced together with a ground-breaking analysis of their interactions. The structure of FRNS in terms of families of sublinear functional is established. After investigating some properties of "sublinear functional" that corresponding to an FRN, the concept of the family of star sublinear funtional based on the popular t-conorm (a parameter some families) is introduced with proved that a descending and separating family of star sublinear functional, denoted by produces a FRNS. In addition, the concept of generating space of quasinorm and quasi-norm family (GSQNF) has been presented. Furthermore, the decomposition theorem of a FRN  into a family of quasinorm is formulated. The correlation between FRNS and the quasinorm family's generating space is explored and demonstrated.