Banach spaces generated by strongly linearly independent fuzzy numbers

Abstract

This article introduces the notion of strong linear independence (SLI) for a set of fuzzy numbers. Based on this notion, we prove that there exist isomorphisms between Rn and special classes of fuzzy numbers generated by SLI sets of n fuzzy numbers. Such a bijection can be used to induce the structure of Banach space on its range. We prove that the finite SLI sets are dense in the set of finite fuzzy numbers. Moreover, we proposed two methods to produce SLI sets based on consecutive powering hedges and Zadeh extension of polynomials.