Abstract
In this paper, we introduce the notions of fuzzy soft uniform spaces as a view point of the entourage approach. We investigate the relationship among fuzzy soft uniformities, fuzzy soft topologies and fuzzy soft interior operators. We study several fuzzy soft topologies induced by a fuzzy soft uniform space.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Abbas SE, El-Sanousy E, Atef A (2016) On fuzzy soft irresolute functions. J Fuzzy Math 24(2):465–482
Abdülkadir A, Cetkin V, Aygun H (2014) An introduction to fuzzy soft topological spaces. Hacet J Math Statist 43(2):193–204
Ahmed B, Kharal A (2009) On fuzzy soft sets. Adv Fuzzy Syst 2009(ID 586507):6
Aktas H, Caǧman N (2007) Soft sets and soft groups. Inf Sci 177(3):2726–2735
Ali MI, Feng F, Liu X, Min WK, Shabir M (2009) On some new operation in soft set theory. Comput Math Appl 57(9):1547–1553
Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96
Atanassov KT (1994) Operators over interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst 64(2):159–174
Aygünoglu A, Aygun H (2009) Introduction to fuzzy soft groups. Comput Math Appl 58:1279–1286
Chang CL (1968) Fuzzy topological spaces. J Math Anal Appl 24(1):182–190
Chen D, Tsang EC, Yeung DS, Wang X (2005) The parameterization reduction of soft sets and its applications. Comput Mat Appl 49(5–6):757–763
Feng F, Jun YB, Zhao X (2008) Soft semi rings. Comput Math Appl 56(10):2621–2628
Gorzalczany MB (1987) A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 21(1):1–17
Gunduz C, Bayramov S (2013) Some results on fuzzy soft topological spaces. Math Probl Eng 2013(ID 835308):10
Hutton B (1977) Uniformities in fuzzy topological spaces. J Math Anal Appl 58:559–571
Kharal A, Ahmed B (2009) Mappings on fuzzy soft classes. Adv Fuzzy Syst 2009(ID 407890):6
Kotzé W (1999) Uniform spaces handbook of fuzzy sets series, Chapter 8, vol 3. Kluwer Academic Publisher, Dordrecht, Boston, London, pp 553–580
Lowen R (1981) Fuzzy uniform spaces. J Math Anal Appl 82:370–385
Maji BK, Biswas R, Roy AR (2001) Fuzzy soft sets. J Fuzzy Math 9(3):589–602
Maji PK, Roy AR, Biswas R (2002) An application of soft sets in a decision making problem. Comput Math Appl 44(8–9):1077–1083
Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45(4–5):555–562
Molodtsov DA (1999) Soft set theory-first results. Comput Math Appl 37(4–5):19–31
Pawlak Z (1982) Rough sets. Int J Comp Inform Sci 11(5):341–356
Pazar Varol B, Aygun H (2012) Fuzzy soft topology. Hacet J Math Statist 41(3):407–419
Shabir M, Naz M (2011) On soft topological spaces. Comput Math Appl 61(7):1786–1799
Sun QM, Zhang ZL, Liu J (2008) Soft sets and soft modules. Lect Notes Comput Sci 5009:403–409
Tanay B, Kandemir MB (2011) Topological structure of fuzzy soft sets. Comput Math Appl 61(10):2952–2957
Yang X, Lin TS, Yang J, Li Y, Yu D (2011) Combination of interval-valued fuzzy set and soft set. Comput Math Appl 58(3):521–527
Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353
Acknowledgments
The author would like to thank the referees for their valuable comments and suggestions which have improved this paper. The authors are partially supported by Deanship of Scientific Research, Jazan University, Saudi Arabia.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
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.
Additional information
Communicated by A. Di Nola.
Rights and permissions
About this article
Cite this article
Abbas, S.E., Ibedou, I. Fuzzy soft uniform spaces. Soft Comput 21, 6073–6083 (2017). https://doi.org/10.1007/s00500-016-2327-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-016-2327-3