On fuzzy paranormed spaces

Abstract

It is well-known that Paranormed spaces have more general properties than normed spaces. Until recently, the concept of paranorm has not been considered with the set of fuzzy numbers and there are no studies in literature from this point of view. So, our main aim in this work is to apply this notion to the set of fuzzy numbers and give the new concepts of fuzzy paranorm and fuzzy paranormed space. In addition, we discuss in detail the statistical convergence and statistically Cauchy sequence in a fuzzy paranormed space.