Connectedness in Fuzzy Soft Topological Spaces

  • S. E. Abbas
  • El-sayed El-sanowsy
  • A. AtefEmail author


In this paper, we define the fuzzy soft operator \(\;\phi \;\) constructed from a fuzzy soft grill \(\;\mathcal {G}_{_{E}}\;\) and a fuzzy soft topological space \((X, \tau _{_{E}}).\) Also, we introduce and study the notion of connectedness to fuzzy soft topological spaces with fuzzy soft grills. Furthermore, we extend the notion of \(\alpha \)-connectedness related to a fuzzy soft operator \(\;\alpha \;\) on the set X.


Fuzzy soft grill Fuzzy soft operator Fuzzy soft connectedness Fuzzy soft component 

Mathematics Subject Classification

54A40 54C10 54D05 



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


  1. Abbas, S.E., El-sanowsy, E., Atef, A.: On fuzzy soft irresolute functions. J. Fuzzy Math. 24(2), 465–482 (2016)zbMATHGoogle Scholar
  2. Abbas, S.E., El-sanowsy, E., Atef, A.: Fuzzy soft \((\alpha,\beta,\theta,\delta,\cal{I})\)-continuous functions. J. Egypt. Math. Soc. 25, 59–64 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  3. Abbas, S.E., El-sanowsy, E., Atef, A.: Stratified modeling in soft fuzzy topological structures. Soft Computing 22, 1603–1613 (2018)CrossRefzbMATHGoogle Scholar
  4. Ahmad, B., Kharal, A.: On fuzzy soft sets. Adv. Fuzzy Syst. 2009, 586507 (2009). MathSciNetzbMATHGoogle Scholar
  5. Aygünoglu, A., C̣etkin, V., Aygün, H.: An introduction to fuzzy soft topological spaces. Hacet. J. Math. Stat. 43(2), 193–204 (2014)MathSciNetGoogle Scholar
  6. C̣etkin, V., Šostak, A.P., Aygűn, H.: An approach to the concept of soft fuzzy proximity. Abstract Appl. Anal. 3, 1–9 (2014)MathSciNetCrossRefGoogle Scholar
  7. Gunduz, C., Bayramov, S.: Some Results on Fuzzy Soft Topological Spaces. Math. Prob. Eng. 2013, 835308 (2013). MathSciNetzbMATHGoogle Scholar
  8. Kharal, A., Ahmad, B.: Mappings on fuzzy soft classes. Adv. Fuzzy Syst. 2009, 407890 (2009). MathSciNetzbMATHGoogle Scholar
  9. Maji, P.K., Biswas, R., Roy, A.R.: Fuzzy soft sets. J. Fuzzy Math. 9, 589–602 (2001)MathSciNetzbMATHGoogle Scholar
  10. Maji, P.K., Roy, A.R., Biswas, R.: An application of soft sets in a decision making problem. Comput. Math. Appl. 44(8–9), 1077–1083 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  11. Molodtsov, D.: Soft set theory-first results. Comput. Math. Appl. 37, 19–31 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  12. Molodtsov, D.: Describing dependences using soft sets. J. Computer Syst. Sci. Int. 40(6), 975–982 (2001)zbMATHGoogle Scholar
  13. Sabir, H.: A note on soft connectedness. J. Egypt. Math. Soc. 23, 6–11 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  14. Šostak, A.P.: On a fuzzy topological structure. Rendiconti del Circolo Matematico di Palermo 1(11), 53–64 (2004)Google Scholar
  15. Tanay, B., Kandemir, M.B.: Topological structure of fuzzy soft sets. Computer Math. Appl. 61, 2952–2957 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  16. Tripathy, B.C., Das, P.C.: On convergence of series of fuzzy real numbers. Kuwait J Sci Eng 39(1A), 57–70 (2012)MathSciNetGoogle Scholar
  17. Tripathy, B.C., Ray, G.C.: On mixed fuzzy topological spaces and countability. Soft Computing 16(10), 1691–1695 (2012)CrossRefzbMATHGoogle Scholar
  18. Tripathy, B.C., Ray, G.C.: Mixed fuzzy ideal topological spaces. Appl. Math. Comput. 220, 602–607 (2013)MathSciNetzbMATHGoogle Scholar
  19. Tripathy, B.C., Ray, G.C.: On \(\delta \)-continuity in mixed fuzzy topological spaces. Boletim da Sociedade Paranaense de Matematica 32(2), 175–187 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  20. Tripathy, B.C., Acharjee, S.: Some results on soft bitopology. Boletim da Sociedade Paran- aense de Matematica 35(1), 269–279 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  21. Zadeh, L.A.: Fuzzy sets. Inform and Control 8, 338–353 (1965)CrossRefzbMATHGoogle Scholar

Copyright information

© Sociedade Brasileira de Matemática 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceJazan UniversityJizanSaudi Arabia
  2. 2.Department of MathematicsFaculty of ScienceSohagEgypt

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