Hahn-Banach type theorems and the separation of convex sets for fuzzy quasi-normed spaces

Abstract

In this paper, we first study continuous linear functionals on a fuzzy quasi-normed space, obtain a characterization of continuous linear functionals, and point out that the set of all continuous linear functionals forms a convex cone and can be equipped with a weak fuzzy quasi-norm. Next, we prove a theorem of Hahn-Banach type and two separation theorems for convex subsets of fuzzy quasinormed spaces.

Keywords

• fuzzy quasi-normed space
• continuous linear functional
• hahn-banach extension theorem
• separation theorem