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Some properties of sequences in gradual normed spaces

Mina Ettefagh

Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran

E-mail Address: etefagh@iaut.ac.ir

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Sina Etemad

Young Researchers and Elite Club, Tabriz Branch, Islamic Azad University, Tabriz, Iran

E-mail Address: sina.etemad@gmail.com

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, and

Farnaz Y. Azari

Department of Mathematics, Sahand University of Technology, Tabriz, Iran

E-mail Address: fyaqubazari@gmail.com

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https://doi.org/10.1142/S1793557120500850Cited by:9 (Source: Crossref)

Abstract

In this paper, we investigate some properties of sequences in a gradual normed space. We define some new notions such as gradual convergent sequences, gradual Cauchy sequences, etc., and then we state some theorems about these notions. Finally, in the last section, we bring some illustrative examples.

Communicated by W. S. Cheung

Keywords:

AMSC: 03E72, 28E10

References

1. F. Aiche and D. Dubois , Possibility and gradual number approaches to ranking methods for random fuzzy intervals, Commun. Comput. Inf. Sci. 299 (2012) 9–18. Google Scholar
2. P. Brass , On the nonexistence of Hausdorff-like metrics for fuzzy sets, Pattern Recognit. Lett. 23 (2002) 39–43. Crossref, Web of Science, Google Scholar
3. D. Dubois and H. Prade , Gradual elements in a fuzzy set, Soft Comput. A Fusion of Found. Methodolog. Appl. 12 (2007) 165–175. Google Scholar
4. M. Ettefagh, F. Y. Azari and S. Etemad, On some topological properties in gradual normed spaces, submitted. Google Scholar
5. J. Fortin, D. Dubois and H. Fargier , Gradual numbers and their application to fuzzy interval analysis, IEEE Trans. Fuzzy Syst. 16 (2008) 388–402. Crossref, Web of Science, Google Scholar
6. J. Fortin, A. Kasperski and P. Zielinski , Some methods for evaluating the optimality of elements in matroids, Fuzzy Sets Syst. 160 (2009) 1341–1354. Crossref, Web of Science, Google Scholar
7. A. Kasperski and P. Zielinski , Using gradual numbers for solving fuzzy-valued combinatorial optimization problems, in Foundations of Fuzzy Logic and Soft Computing, Lecture Notes in Computer Sciences (Springer, 2007) pp. 656–665. Crossref, Google Scholar
8. L. Lietard and D. Rocacher , Conditions with aggregates evaluated using gradual numbers, Control Cybernetics 38 (2009) 395–417. Google Scholar
9. I. Sadeqi and F. Y. Azari , Gradual normed linear space, Iranian J. Fuzzy Syst. 8 (2011) 131–139. Web of Science, Google Scholar
10. G. F. Simmons , Introduction to Topology and Modern Analysis (Tata McGraw-Hill Education, 2004), ISBN: 10:0070597847. Google Scholar
11. E. A. Stock, Gradual numbers and fuzzy optimization, Ph.D. Thesis, University of Colorado Denver, Denver, America (2010). Google Scholar
12. A. L. Zadeh , Fuzzy sets, Inf. Control 8 (1965) 338–353. Crossref, Google Scholar
13. C. Zhou , Gradual metric spaces, Appl. Math. Sci. 14 (2015) 689–701. Google Scholar
14. C. Zhou and J. Li , New fuzzy measure based on gradual numbers, Int. J. Math. Anal. 9 (2015) 101–110. Crossref, Google Scholar