QUASILINEARITY OF THE CLASSICAL SETS OF SEQUENCES OF FUZZY NUMBERS AND SOME RELATED RESULTS

Abstract

In the present paper, we prove that the classical sets $\ell_{\infty}(F)$, $c(F)$, $c_0(F)$ and $\ell_p(F)$ of sequences of fuzzy numbers are normed quasilinear spaces and the $\beta−$, $\alpha−$duals of the set $\ell_1(F)$ is the set $\ell_{\infty}(F)$. Besides this, we show that $\ell_{\infty}(F)$ and $c(F)$ are normed quasialgebras and an operator defined by an infinite matrix belonging to the class $(\ell_{\infty}(F) : \ell_{\infty}(F))$ is bounded and quasilinear. Finally, as an application, we characterize the class $(\ell_1(F) : \ell_p(F))$ of infinite matrices of fuzzy numbers and establish the perfectness of the spaces $\ell_{\infty}(F)$ and $\ell_1(F)$.