Summability Theory And Its Applications

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The theory of summability has many uses throughout analysis and applied mathematics. Engineers and physicists working with Fourier series or analytic continuation will also find the concepts of ...
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Sequences of Fuzzy Numbers

Pp. 315-378 (64)

Feyzi Basar

Abstract

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 innite 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 dened by a modulus.