A Study on Fuzzy Riesz Spaces

Abstract

Fuzzy Riesz Space is an attempt to study vector spaces with a fuzzy order for more com- plicated scenarios. In this dissertation, we study the fuzzy order convergence, fuzzy Riesz homomorphisms, and fuzzy order continuous positive operator, which help to prove the exis- tence of fuzzy Dedekind completion of Archimedean fuzzy Riesz spaces. Theory of the fuzzy Riesz space of all fuzzy order bounded linear operators are investigated. We de ne and study unbounded fuzzy order convergence and some of its applications. Furthermore, study the fuzzy norms compatible with fuzzy ordering (fuzzy normed Riesz space) and discuss the rela- tionship between the fuzzy order dual and topological dual of a locally convex solid fuzzy Riesz space. Besides, we throw light on the unbounded fuzzy norm convergence and its applications in fuzzy Banach lattice, which is topological.