Extension of fuzzy linear operators on fuzzy Riesz spaces

Abstract

Let E be a fuzzy order vector space, (F,v) be a fuzzy Riesz space with F fuzzy Dedekind complete, K⊂E is a non-empty convex subset, we show that for every fuzzy sublinear θ:K→F, there exists a fuzzy linear operator T:E→F such that T≤θ. This is the generalization of Hahn-Banach theorem in case where the range space is a fuzzy Dedekind complete fuzzy Riesz space. Related extension problems are also studied. Let K be a fuzzy Riesz subspace of E, T:K→F be a fuzzy positive operator, we give a characterization of extreme point of ε(T). We also prove that if K is a fuzzy majorizing vector subspace of E, and T:K→F is a fuzzy positive operator, then the convex set ε(T) has an extreme point.