Fuzzy bounded linear maps and quotient spaces

Abstract

Abstract. In this paper fuzzy norm on a real or complex vector space is introduced. Fuzzy nonned space and fuzzy Banach space are defined. Boundedness of a linear transfonnation in F-nonned space (fuzzy nonned space) is also difined i.e., Fboundedness. The quotient space of an F-nonned space is defined. It is proved that B(X, X'), the set of all bounded linear transfonnation from F-nonned space (X, N ,*) to (X', N. *) is a F-Banach space if X' is a F-Banach space. It is also proved that if X is F-Banach then so is the quotient space X/M, where M is a closed linear subspace of X