Quasilinearity of the classical sets of sequences of fuzzy numbers and some related results

In the present study, we prove that the classical sets `∞(F ), c(F ), c0(F ) and `p(F ) of sequences of fuzzy numbers are normed quasilinear spaces and the β−, α−duals of the set `1(F ) is the set `∞(F ). Besides this, we show that `∞(F ) and c(F ) are normed quasialgebras and an operator defined by an infinite matrix belonging to the class (`∞(F ) : `∞(F )) is bounded and quasilinear. Finally, as an application, we characterize the class (`1(F ) : `p(F )) of infinite matrices of fuzzy numbers and establish the perfectness of the spaces `∞(F ) and `1(F ).