Infinite Dimensional Banach Spaces of Fuzzy Numbers

Banach spaces of fuzzy numbers of infinite dimension are constructed based on Strong Linear Independence (SLI). First, enumerable SLI sets of fuzzy numbers are identified with a subspace of the space of absolutely convergent real sequences through an isomorphism with the space generated by infinite linear combinations of the given fuzzy numbers. The resulting image space of fuzzy numbers, equipped with induced arithmetic operations and an induced norm, becomes a complete normed vector space, a Banach space of infinite dimension, with a Schauder basis whose cardinality equals that of the natural numbers. Moreover, an equivalence relation on the set of SLI fuzzy number sets establishes a bijection between the positive cone of the space of bounded real sequences and the quotient set of equivalence classes.