Quasilinearity of the Classical Sets of Sequences of Fuzzy Numbers and Some Related Results
نویسندگان
چکیده
In the present paper, 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 ).
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