Integrated and Differentiated Spaces of Triangular Fuzzy Numbers

Fuzzy sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics, fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. In this paper, we use the triangular fuzzy numbers for matrix domains of sequence spaces with infinite matrices. We construct the new space with triangular fuzzy numbers and investigate to structural, topological and algebraic properties of these spaces.Comment: 10 pages, 17 reference

Comparison theorems for summability methods of sequences of fuzzy numbers

In this study we compare Ces\`{a}ro and Euler weighted mean methods of summability of sequences of fuzzy numbers with Abel and Borel power series methods of summability of sequences of fuzzy numbers. Also some results dealing with series of fuzzy numbers are obtained.Comment: publication information is added, typos correcte

On a new type of Double Sequences of Fuzzy Numbers

ABSTRACT In this article we introduce the notion of -statistically pre-Cauchy double sequence of fuzzy numbers and establish a criterion for arbitrary double sequence of fuzzy numbers to be -statistically pre-Cauchy

On the resummation of series of fuzzy numbers via generalized Dirichlet and generalized factorial series

We introduce semicontinuous summation methods for series of fuzzy numbers and give Tauberian conditions under which summation of a series of fuzzy numbers via generalized Dirichlet series and via generalized factorial series implies its convergence. Besides, we define the concept of level Fourier series of fuzzy valued functions and obtain results concerning the summation of level Fourier series.Comment: publication information is adde

On the Zweier Sequence Spaces of Fuzzy Numbers

It was given a prototype constructing a new sequence space of fuzzy numbers by means of the matrix domain of a particular limitation method. That is we have constructed the Zweier sequence spaces of fuzzy numbers [ℓ∞(F)]Zη, [c(F)]Zη, and [c0(F)]Zη consisting of all sequences u=(uk) such that Zηu in the spaces ℓ∞(F), c(F), and c0(F), respectively. Also, we prove that [ℓ∞(F)]Zη, [c(F)]Zη, and [c0(F)]Zη are linearly isomorphic to the spaces ℓ∞(F), c(F), and c0(F), respectively. Additionally, the α(r)-, β(r)-, and γ(r)-duals of the spaces [ℓ∞(F)]Zη, [c(F)]Zη, and [c0(F)]Zη have been computed. Furthermore, two theorems concerning matrix map have been given