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Fuzzy proximal relator spaces

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Abstract

This paper introduces fuzzy Lodato–Smirnov proximal relator spaces. We define fuzzy proximity relation to evaluate the proximity of the sets. Also, it is shown that the max–min composition of fuzzy proximity relations is associative and the Smirnov proximity measure on the Lodato proximity space is a fuzzy spatial Lodato proximity relation. Fuzzy proximity relation approach can be applied to some problems. Therefore, it is used to solve a few issues such as precise sorting of near sets, solution of classification problems and given examples for the problems.

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References

  1. Dochviri I, Peters JF (2015) Topological Sorting of finitely many near sets. Math Comput Sci. 1–6, communicated

  2. Efremoviĉh VA (1952) The geometry of proximity. Math Sb (N.S) 73(1):189–200 (in Russian)

    MathSciNet  MATH  Google Scholar 

  3. Hussain M (2010) Fuzzy Relations. Master Thesis, Department of Mathematics and Science, Supervisor E. R. Andersson

  4. İnan E (2017) Approximately semigroups and ideals: an algebraic view of digital images. Afyon Kocatepe University J Sci Eng 17:479–487

    Article  Google Scholar 

  5. Kaufmann A (1975) Introduction to the theory of fuzzy subsets, vol 1. Academic Press, New York

    MATH  Google Scholar 

  6. Leader S (1959) On clusters in proximity spaces. Fundam Math 47:205–213

    Article  MathSciNet  MATH  Google Scholar 

  7. Lodato MW (1962) On topologically induced generalized proximity relations. Ph.D. thesis, Rutgers University, 42pp, supervisor: S. Leader

  8. Lodato MW (1964) On topologically induced generalized proximity relations I. Proc Am Math Soc 15:417–422

    Article  MathSciNet  MATH  Google Scholar 

  9. Lodato MW (1966) On topologically induced generalized proximity relations II. Pacific J Math 17:131–135

    Article  MathSciNet  MATH  Google Scholar 

  10. Naimpally SA, Warrack BD (1970) Proximity spaces. Cambridge University, Cambridge

    MATH  Google Scholar 

  11. Peters JF (2016) Computational proximity. Excursions in the topology of digital images. Intelligent Systems Reference Library, Springer, Berlin

  12. Peters JF (2013) Near sets: an introduction. Math Comp Sci 7:3–9

    Article  MathSciNet  MATH  Google Scholar 

  13. Peters JF (2016) Proximal relator spaces. Filomat 30(2):469–472

    Article  MathSciNet  MATH  Google Scholar 

  14. Peters JF (2014) Topology of digital images. Visual pattern discovery in proximity spaces. Intelligent Systems Reference Library, vol. 63, Springer, Berlin

  15. Smirnov JM (1964) On proximity spaces. Math Sb (N.S.) 31(73):543–574. English translation: Am Math Soc Trans Ser 2(38):5–35 (1964)

  16. Szás À (1987) Basic tools and mild continuties in relator spaces. Acta Math Hungar 50:177–201

    Article  MathSciNet  Google Scholar 

  17. Szás À, Zakaria A (2016) Mild continuity properties of relations and relators in relator spaces. Essays Math Appl 439–511

  18. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MATH  Google Scholar 

  19. Zadeh LA (1971) Similarity relations and fuzzy orderings. Inform Sci 3:177–206

    Article  MathSciNet  MATH  Google Scholar 

  20. Zhan J, Liu Q, Davvaz B (2015) A new rough set theory: rough soft hemirings. J Intell Fuzzy Syst 28:1687–1697

    MathSciNet  MATH  Google Scholar 

  21. Zhan J, Bin Y, Fotea VE (2016) Characterizations of two kinds of hemirings based on probability spaces. Soft Comput 20:637648

    Article  MATH  Google Scholar 

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Acknowledgements

The authors are thankful for financial support from the Research Fund of Adiyaman University by the Project FEFMAP/2015-0010.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Sciences, Adıyaman University, Adıyaman, Turkey

    Mehmet Ali Öztürk, Ebubekir İnan & Özlem Tekin

  2. Computational Intelligence Laboratory, Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MB, Canada

    James Francis Peters

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  1. Mehmet Ali Öztürk
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  2. Ebubekir İnan
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  3. Özlem Tekin
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  4. James Francis Peters
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Correspondence to Özlem Tekin.

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All authors of this article have no relationships or interests that could have direct or potential influence or impart bias on any aspect of this work.

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Öztürk, M.A., İnan, E., Tekin, Ö. et al. Fuzzy proximal relator spaces. Neural Comput & Applic 31, 3201–3210 (2019). https://doi.org/10.1007/s00521-017-3268-1

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  • DOI: https://doi.org/10.1007/s00521-017-3268-1

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