Özer Talo

Determination of the duals of classical sets of sequences of fuzzy numbers and related matrix transformations

The convergence of a series of fuzzy sets was examined via Zadehs Extension Principle by M. Stojakovic and Z. Stojakovic [M. Stojakovic, Z. Stojakovic, Addition and series of fuzzy sets, Fuzzy Sets and Systems 83 (1996), 341-346]. Since the utilization of this approach is quite difficult in practice, we prefer the idea of using the sum of the series of @l-level sets. The main purpose of the present paper is to determine the @a-, @b- and @c-duals of the classical sets of sequences of fuzzy numbers and is to give the necessary and sufficient conditions on an infinite matrix of fuzzy numbers transforming one of the classical sets to the another one.

On the Slowly Decreasing Sequences of Fuzzy Numbers

We introduce the slowly decreasing condition for sequences of fuzzy numbers. We prove that this is a Tauberian condition for the statistical convergence and the Cesaro convergence of a sequence of fuzzy numbers.

On the Cesàro convergence of sequences of fuzzy numbers

Abstract In this paper we have determined necessary and sufficient Tauberian conditions under which convergence follows from ( C , 1 ) -convergence of sequences of fuzzy numbers.

Abel summability of sequences of fuzzy numbers

In the present study, we have introduced the concept of Abel summability for sequences and series of fuzzy numbers. Also, some tauberian results in classical analysis have been generalized to fuzzy analysis.

Certain spaces of sequences of fuzzy numbers defined by a modulus function

The main purpose of the present paper is to introduce the spaces £oo(F, /), c(F, / ) , co(F, / ) and ip{F, f , s) of sequences of fuzzy numbers defined by a modulus function. Furthermore, some inclusion theorems related to these sets are given and shown that 4o (F, f), co(F, f) and £P(F, f , s) are solid. 1. Preliminaries, background and notation Let W be the set of all closed bounded intervals A of real numbers with endpoints A and A, i.e. A :— [̂ 4, A]. The operations addition and multiplication by a real number on W are defined, as follows: A + B-.= {a + b:a<=A,beB}:= [A + B,A + B], aA := {aa : a € A}. One can extend the natural order relation on the real line to intervals as follows: A < B if and only if A < B and A<B. Define the relation d on W by d(A, B) : = max{|A B\, \A Then it can easily be observed that d is a metric on W (cf. Diamond and Kloeden [3]) and (W,d) is a complete metric space, (cf. Nanda [8]). A fuzzy number is a fuzzy set on the real axis, i.e. a mapping u : R —> [0,1] associating with each real number t its grade of membership u(t) which satisfies the following four conditions. (i) u is normal, i.e. there exists an to G R such that u(to) = 1. 2000 Mathematics Subject Classification: Primary 46S40; Secondary 40A05.

The extension of the Knopp core theorem to the sequences of fuzzy numbers

The concept of the core of a sequence of fuzzy numbers has been introduced by Aytar et al. in The core of a sequence of fuzzy numbers, Fuzzy Sets and Systems, 159(24) (2008) 3369-3379]. Quite recently, some matrix transformations on the classical sets of sequences of fuzzy numbers have been characterized by Talo and Basar in Determination of the duals of classical sets of sequences of fuzzy numbers and related matrix transformations, Comput. Math. Appl. 58 (2009) 717-733]. In this paper, we have proved a core theorem for sequences of fuzzy numbers which is analogous to the famous Knoop Core Theorem for real sequences. To achieve this goal, we have studied some properties of the lim sup and lim inf of sequences of fuzzy numbers. Also, we have characterized a class of positive regular matrices of fuzzy numbers such that these matrices leave the core of any bounded sequence of fuzzy numbers invariant.

Regularly -Convergence and Regularly -Cauchy Double Sequences of Fuzzy Numbers

In this paper, we introduce the notions of regularly , -convergence and regularly , -Cauchy double sequence of fuzzy numbers. Also, we study some properties of these concepts.

Approximation of Continuous Periodic Functions of Two Variables via Power Series Methods of Summability

We prove a Korovkin-type approximation theorem via power series methods of summability for continuous

Tauberian Theorems for Statistically (C; 1)-Convergent Sequences of Fuzzy Numbers

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