Fréchet Spaces via Fuzzy Structures

The concept of fuzzy Fréchet space Z introduced in two equivalent ways, the first way when Z considered as a fuzzy F − locally convex topological vector space and the second one when Z defined as a complete fuzzy topological vector space whose fuzzy topology generated by a countable separating collection of fuzzy seminorms. Moreover, many classes of continuous mappings between these spaces are established and specified that the class of continuous, strongly continuous and sequentially continuous mappings between these spaces are equivalent. (paper)