A Study on Fuzzy Order Bounded Linear Operators in Fuzzy Riesz Spaces

This paper aims to study fuzzy order bounded linear operators between two fuzzy Riesz spaces. Two lattice operations are defined to make the set of all bounded linear operators as a fuzzy Riesz space when the codomain is fuzzy Dedekind complete. As a special case, separation property in fuzzy order dual is studied. Furthermore, we studied fuzzy norms compatible with fuzzy ordering (fuzzy norm Riesz space) and discussed the relation between the fuzzy order dual and topological dual of a locally convex solid fuzzy Riesz space.

Automated summary

This paper focuses on fuzzy order bounded linear operators between two fuzzy Riesz spaces and defines lattice operations to make the set of all bounded linear operators as a fuzzy Riesz space. It also studies the separation property in fuzzy order dual as a special case and discusses the relation between fuzzy order dual and topological dual of a locally convex solid fuzzy Riesz space.