Weak Fuzzy Topology on Vector Spaces

Abstract

‎In this paper‎, ‎we study the concept of weak linear fuzzy topology on a fuzzy topological vector space as a generalization of usual weak topology‎. ‎We prove that this fuzzy topology consists of all weakly lower semi-continuous fuzzy sets on a given vector space when $ \mathbb{K} $ ($ \mathbb{R} $ or $ \mathbb{C} $) endowed with its usual fuzzy topology‎. ‎In the case that the fuzzy topology of $ \mathbb{K} $ is different from the usual fuzzy topology‎, ‎we show that the weak fuzzy topology is not equivalent with the fuzzy topology of weakly lower semi-continuous fuzzy sets‎.