On the Cesàro convergence of sequences of fuzzy numbers

Talo, Özer; Çakan, Celal

doi:10.1016/j.aml.2011.09.002

Cited by 28 publications

(17 citation statements)

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“…Subrahmanyam [6] has defined the Cesàro summability method for sequences of fuzzy numbers and obtained fuzzy analogues of some classical Tauberian theorems. Talo and Çakan [7] have presented some Tauberian theorems for sequences of fuzzy numbers that convergence follows from Cesàro convergence under some Tauberian conditions.…”

Section: Introductionmentioning

confidence: 99%

Tauberian theorems for statistically (C,1,1) summable double sequences of fuzzy numbers

2017

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Abstract:In this paper, we prove that a bounded double sequence of fuzzy numbers which is statistically convergent is also statistically .C; 1; 1/ summable to the same number. We construct an example that the converse of this statement is not true in general. We obtain that the statistically .C; 1; 1/ summable double sequence of fuzzy numbers is convergent and statistically convergent to the same number under the slowly oscillating and statistically slowly oscillating conditions in certain senses, respectively.

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Section: Introductionmentioning

confidence: 99%

Tauberian theorems for statistically (C,1,1) summable double sequences of fuzzy numbers

2017

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“…Subrahmanyam [15] has defined the Cesàro summability method for sequences of fuzzy numbers and obtained fuzzy analogues of some classical Tauberian theorems. Also, Talo and Çakan [17], Talo and Basar [16] and Çanak [6] have established some Tauberian theorems for Cesàro summability method of sequences of fuzzy numbers. In addition, Altin et al [1] have defined the statistical Cesàro summability and obtained some Tauberian results for sequences of fuzzy numbers.…”

Section: Introductionmentioning

confidence: 99%

A Tauberian theorem for the weighted mean method of summability of sequences of fuzzy numbers

Önder

Sezer

Çanak

2015

Journal of Intelligent &Amp; Fuzzy Systems

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“…This open set is called fuzzy b − θ open set, which is a generalization of b − θ open set. Quite recently, the matrix domains of the sequence spaces derived by FN are studied [9,10,15,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

“…Matloka's sequences were used in the classical sequence spaces by Nanda [8]. Quite recently, the matrix domains of the sequence spaces derived by FN are studied [9,10,15,18,19,20].…”

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Integrated and Differentiated Spaces of Triangular Fuzzy Numbers

Kirişçi¹

2017

Fasciculi Mathematici

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Abstract. 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. Fuzzy sets have become popular in every branch of mathematics such as analysis, topology, algebra, applied mathematics etc. Thus fuzzy sets triggered the creation of a wide range of research topics in all areas of science in a short time. 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.Key words: fuzzy numbers, integrated matrix, differentiated matrix, real duals.AMS Mathematics Subject Classification: 03E72, 46A45, 40C05. IntroductionFuzziness has revolutionized many areas such as mathematics, science, engineering, medicine. This concept was initiated by Zadeh [17]. Not only Zadeh discovered this concept, but he also developed the infrastructure of today's popular forms of use such as relations of similarity, decision making, and fuzzy programming in a short time.Just like in the theory of sets, fuzzy sets(FS) also have led to the emergence of new mathematical concepts, research topics, and the design of engineering applications. Therefore, the nature of the classical set theory must be well known and understood. In particular, consider the two fundamental laws of Boolean algebra the law of excluded middle and law of contradiction. In logic, the proposition every proposition is either true or falseť excludes any third, or middle, possibility, which gave this principle the name of the law of excluded middle. When look at the principles of Boolean algebra, there are two items as prediction: "True" or "False". Whether classical, Unauthenticated Download Date | 5/9/18 6:25 PM 76Murat Kirişci Boolean or crisp, set theory can be defined as a characteristic function of the membership of an element x in a set A. For each elements of universal set X, the function that generates the values 0 and 1 is called the characteristic function.Today, the studies and applications related to the fuzziness are increasing rapidly and this concept is finding in every scientific areas. Zadeh's FS theory succeeded in attracting mathematicians as well as other scientists and was adopted. The most important feature of FS is to generalize the values of "true" and "false" in traditional logic and to produce a logic that can use multi-valued results.Any change or transition in real life takes place between membership and non-membership. This transition is clear, well-defined. Despite this certainty in classical sets, this is somewhat different in FS. This difference arises because the transition is gradual. The uncertainty of the boundaries of the FS implies that this transition will vary from one membership to another. In that case, membership of an element from the universe in this set is measured by a function that attempts to describe vagueness and ambiguity.Matlok...

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On the Cesàro convergence of sequences of fuzzy numbers

Cited by 28 publications

References 10 publications

Tauberian theorems for statistically (C,1,1) summable double sequences of fuzzy numbers

Tauberian theorems for statistically (C,1,1) summable double sequences of fuzzy numbers

A Tauberian theorem for the weighted mean method of summability of sequences of fuzzy numbers

Integrated and Differentiated Spaces of Triangular Fuzzy Numbers

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