This chapter is devoted to the sequences of fuzzy numbers. After presenting
the fundamental facts concerning convergent sequences of fuzzy numbers, some
results on statistical convergence of sequences of fuzzy numbers and related results
are given. Also the α-,fi β-, γ- duals of the classical sets l∞(F), c(F),
c0(F) and lp(F) of all bounded, convergent, null and absolutely p-summable sequences
of fuzzy numbers are determined and the classes (µ(F) : l∞(F)), (c0(F) :
c(F)), (c0 F) : c0(F)), (c(F) : c(F); p), (lp(F) : c(F)), (lp(F) : c0(F)) and
(l∞F) : c0(F)) of in nite matrices of fuzzy numbers are characterized, where
µ Ε {l∞, c; c0; lp}. Finally, the quasilinearity of the classical sets of sequences of
fuzzy numbers is investigated.
Keywords: Fuzzy number, level set, fuzzy valued sequences, statistical convergence
of fuzzy sequences, bounded set from above and below, infinite matrix of fuzzy
numbers, convergence and boundedness of a fuzzy sequence, limit superior and limit
inferior and core of a sequence of fuzzy numbers, statistical monotonic and bounded
sequences of fuzzy numbers, statistical cluster point and limit point of a sequence
of fuzzy numbers, statistical limit superior and limit inferior of a sequence of fuzzy
numbers, α-, β-, γ- duals of the classical sets l∞(F), c(F), c0(F) and lp(F) of
all bounded, convergent, null and absolutely p-summable sequences of fuzzy numbers,
characterization of matrix transformations between the sets of sequences of
fuzzy numbers, quasilinearity of the classical sets of sequences of fuzzy numbers,
sets of sequences of fuzzy numbers de ned by a modulus.
