Soft Computing

, Volume 22, Issue 5, pp 1603–1613 | Cite as

Stratified modeling in soft fuzzy topological structures

  • S. E. Abbas
  • E. El-sanowsy
  • A. Atef


In this paper, we introduce the concepts of stratified fuzzy soft topogenous, stratified fuzzy soft filter, stratified fuzzy soft quasi-proximity and stratified fuzzy soft grill. Also, we introduce the concept of fuzzy soft topogenous structures by combining fuzzy soft topogenous with fuzzy soft filter and we introduce the concept of fuzzy soft quasi-proximity by combining fuzzy soft quasi-proximity with fuzzy soft grill and give their properties. Furthermore, we establish the relationship among these fuzzy soft topological structures and their stratifications.


Stratified Fuzzy soft quasi-uniformity Fuzzy soft topogenous order Fuzzy soft quasi-proximity 



The authors would like to thank the referees for their valuable comments and suggestions which have improved this paper.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


  1. Abbas SE, Abd-Allah AA (2011) Stratified double \(L\)-topological structures. Math Comput Modell 54:423–439MathSciNetCrossRefzbMATHGoogle Scholar
  2. Abbas SE, Ibedou I (2017) Fuzzy soft uniform spaces. Soft Comput 21:6073–6083CrossRefGoogle Scholar
  3. Ahmad B, Kharal A (2009) On fuzzy soft sets. Adv Fuzzy Syst 2009(2009).
  4. Aygünoglu A, C̣etkin V, Aygün H (2014) An introduction to fuzzy soft topological spaces. Hacettepe J Math Stat 43(2):193–204MathSciNetGoogle Scholar
  5. C̣etkin V, Šostak AP, Aygűn H (2014) An approach to the concept of soft fuzzy proximity. Hindawi Publishing Corparation 2014, Article ID 782583, pp 1–9Google Scholar
  6. Deng W, Zhao HM, Yang XH, Xiong JX, Sun M, Li B (2017) Study on an improved adaptive PSO algorithm for solving multi-objective gate assignment. Appl Soft Comput 59:288–302CrossRefGoogle Scholar
  7. Deng W, Zhao HM, Zou L, Li GY, Yang XH, Wu DQ (2017) A novel collaborative optimization algorithm in solving complex optimization problems. Soft Comput 21(15):4387–4398CrossRefGoogle Scholar
  8. Gu B, Sheng VS (2016) A robust regularization path algorithm for \(v\)-support vector classification. IEEE Trans Neural Netw Learn Syst. Google Scholar
  9. Gu B, Sheng VS, Tay KY, Romano W, Li S (2015) Incremental support vector learning for ordinal regression. IEEE Trans Neural Netw Learn Syst 26(7):1403–1416MathSciNetCrossRefGoogle Scholar
  10. Gu B, Sun X, Sheng VS (2016) Structural minimax probability machine. IEEE Trans Neural Netw Learn Syst. Google Scholar
  11. Gunduz C, Bayramov S (2013) Some results on fuzzy soft topological spaces. Math Prob Eng 2013, Article ID 835308, 10 pagesGoogle Scholar
  12. Kharal A, Ahmad B (2009) Mappings on fuzzy soft classes. Adv Fuzzy Syst 2009(2009).
  13. Maji PK, Biswas R, Roy AR (2001) Fuzzy soft sets. J Fuzzy Math 9:589–602MathSciNetzbMATHGoogle Scholar
  14. Maji PK, Roy AR, Biswas R (2002) An application of soft sets in a decision making problem. Comput Math Appl 44(8–9):1077–1083MathSciNetCrossRefzbMATHGoogle Scholar
  15. Molodtsov D (1999) Soft set theory-first results. Comput Math Appl 37:19–31MathSciNetCrossRefzbMATHGoogle Scholar
  16. Molodtsov D (2001) Describing dependences using soft sets. J Comput Syst Sci Int 40(6):975–982MathSciNetzbMATHGoogle Scholar
  17. Šostak AP (2004) On a fuzzy topological structure. Rendiconti del Circolo Matematico di Palermo 1(11):53–64Google Scholar
  18. Sun Y, Gu F (2017) Compressive sensing of piezoelectric sensor response signal for phased array structural health monitoring. Int J Sens Netw 23(4):258–264CrossRefGoogle Scholar
  19. Tanay B, Kandemir MB (2011) Topological structure of fuzzy soft sets. Comput Math Appl 61:2952–2957MathSciNetCrossRefzbMATHGoogle Scholar
  20. Tripathy BC, Das PC (2012) On convergence of series of fuzzy real numbers. Kuwait J Sci Eng 39(1A):57–70MathSciNetGoogle Scholar
  21. Tripathy BC, Debnath S (2013) \(\gamma \)-open sets and \(\gamma \)-continuous mappings in fuzzy bitopological spaces. J Intell Fuzzy Syst 24(3):631–635MathSciNetzbMATHGoogle Scholar
  22. Tripathy BC, Ray GC (2012) On mixed fuzzy topological spaces and countability. Soft Comput 16(10):1691–1695CrossRefzbMATHGoogle Scholar
  23. Tripathy BC, Ray GC (2013) Mixed fuzzy ideal topological spaces. Appl Math Comput 220:602–607MathSciNetCrossRefzbMATHGoogle Scholar
  24. Tripathy BC, Ray GC (2014) On \(\delta \)-continuity in mixed fuzzy topological spaces. Boletim da Sociedade Paranaense de Matematica 32(2):175–187MathSciNetCrossRefGoogle Scholar
  25. Wang B, Gu X, Ma L, Yan S (2017) Temperature error correction based on BP neural network in meteorological WSN. Int J Sens Netw 23(4):265–278CrossRefGoogle Scholar
  26. Wang J, Lian S, Shi YQ (2017) Hybrid multiplicative multi-watermarking in DWT domain. Multidimens Syst Signal Process 28(2):617–636CrossRefzbMATHGoogle Scholar
  27. Xiong L, Xu Z, Shi Y-Q (2017) An integer wavelet transform based scheme for reversible data hiding in encrypted images. Multidimens Syst Signal Process. Google Scholar
  28. Xue Y, Jiang J, Zaho B, Ma T (2017) A self-adaptive artificial bee colony algorithm based on global best for global optimization. Soft Comput. Google Scholar
  29. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceJazan UniversityJazanSaudi Arabia
  2. 2.Department of Mathematics, Faculty of ScienceSohag UniversitySohâgEgypt

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