A fuzzy methodology for approaching fuzzy sets of the real line by fuzzy numbers

Under an interpretation of the principles of non-contradiction and excluded-middle based on the concept of self-contradiction, this paper mainly deals with the principles' verification in the case of the unit interval of the real line. Such verification is done in the three following cases: (1) The unit interval is totally ordered by the restriction to it of the usual order of the real line, (2) the unit interval is partially ordered by the sharpened order, and (3) the unit interval is under a new particular preorder. The first case is immediately extended to characterize the case of fuzzy sets.

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Fuzzy sets of the real line

Statistics with Vague Data ◽

10.1007/978-94-009-3943-1_3 ◽

1987 ◽

pp. 10-23

Author(s):

Rudolf Kruse ◽

Klaus Dieter Meyer

Keyword(s):

Fuzzy Sets ◽

Real Line ◽

The Real

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The properties of Bessel-type fractional derivatives and integrals

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v11i8.203 ◽

2016 ◽

pp. 3973-3982

Author(s):

V. R. Lakshmi Gorty

Keyword(s):

Fractional Order ◽

Real Line ◽

Computer Algebra System ◽

Fractional Derivatives ◽

Graphical Representation ◽

Fractional Integrals ◽

The Real ◽

Fractional Derivatives And Integrals ◽

Half Axis ◽

Derivatives Of

The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis. The Bessel-type fractional derivatives are also established. The properties of Fractional derivatives and integrals are studied. The fractional derivatives of Bessel-type of fractional order on finite of the real-line are studied by graphical representation. Results are direct output of the computer algebra system coded from MATLAB R2011b.

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AN OSCILLATION FUNCTION ON THE REAL LINE

Real Analysis Exchange ◽

10.2307/44153160 ◽

2000 ◽

Vol 26 (1) ◽

pp. 237

Author(s):

Duszyński

Keyword(s):

Real Line ◽

The Real

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DERIVATION BASES ON THE REAL LINE (I)

Real Analysis Exchange ◽

10.2307/44151585 ◽

1982 ◽

Vol 8 (1) ◽

pp. 67 ◽

Cited By ~ 21

Author(s):

Thomson

Keyword(s):

Real Line ◽

The Real

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One Class of Systems of Linear Fredholm Integral Equations of the Third Kind on the Real Line with Multipoint Singularities

Differential Equations ◽

10.1134/s00122661200100122 ◽

2020 ◽

Vol 56 (10) ◽

pp. 1363-1370

Author(s):

A. Asanov ◽

R. A. Asanov

Keyword(s):

Integral Equations ◽

Real Line ◽

Fredholm Integral Equations ◽

The Real ◽

The Third

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ERP selection using picture fuzzy CODAS method

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-202564 ◽

2021 ◽

pp. 1-11

Author(s):

Hacer Yumurtacı Aydoğmuş ◽

Eren Kamber ◽

Cengiz Kahraman

Keyword(s):

Decision Analysis ◽

Fuzzy Sets ◽

Fuzzy Numbers ◽

Ideal Solution ◽

Application Area ◽

Erp System ◽

Mcdm Method ◽

Negative Ideal Solution ◽

Picture Fuzzy Sets ◽

System Selection

The purpose of this study is to develop an extension of CODAS method using picture fuzzy sets. In this respect, a new methodology is introduced to figure out how picture fuzzy numbers can be applied to CODAS method. COmbinative Distance-based Assessment (CODAS) is a new MCDM method proposed by Ghorabaee et al. Picture fuzzy sets (PFSs) are a new extension of ordinary fuzzy sets for representing human’s judgments having possibility more than two answers such as yes, no, refusal and neutral. Compared with other studies, the proposed method integrates multi-criteria decision analysis with picture fuzzy uncertainty based on Euclidean and Taxicab distances and negative ideal solution. ERP system selection problem is handled as the application area of the developed method, picture fuzzy CODAS. Results indicate that the new proposed method finds meaningful rankings through picture fuzzy sets. Comparative analyzes show that the presented method gives successful and robust results for the solutions of MCDM problems under fuzziness.

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On finite sums of periodic functions

Georgian Mathematical Journal ◽

10.1515/gmj-2019-2076 ◽

2020 ◽

Vol 27 (2) ◽

pp. 265-269

Author(s):

Alexander Kharazishvili

Keyword(s):

Analytic Function ◽

Real Line ◽

Real Analytic Function ◽

Periodic Functions ◽

Uniform Limit ◽

The Real ◽

Pointwise Limit ◽

Finite Sums ◽

Real Analytic

AbstractIt is shown that any function acting from the real line {\mathbb{R}} into itself can be expressed as a pointwise limit of finite sums of periodic functions. At the same time, the real analytic function {x\rightarrow\exp(x^{2})} cannot be represented as a uniform limit of finite sums of periodic functions and, simultaneously, this function is a locally uniform limit of finite sums of periodic functions. The latter fact needs the techniques of Hamel bases.

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