Skip to main content
SpringerLink
Log in

Partial belong relation on soft separation axioms and decision-making problem, two birds with one stone

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Here, we employ partial belong and total non-belong relations to construct a study consisting of two parts: one of them is related to soft topologies, and the other one is concerned with real-life applications. In the first part, we define a new class of soft separation axioms, namely e-soft \(T_i\)-spaces \((i=0, 1, 2, 3, 4)\). We formulate these spaces with respect to distinct ordinary points using partial belong and total non-belong relations. The merits of using these two relations are that they help to generate a wider class of soft spaces and open up the way for more real-life applications. With the help of examples, we show the relationships between them and investigate the interrelations between them and their parametric topological spaces. Also, we study under what condition the concepts of soft \(T_i\), p-soft \(T_i\) and e-soft \(T_i\) are equivalent. Furthermore, we scrutinize their behaviours in terms of soft subspaces, soft topological properties and finite soft product spaces. In the second part, we introduce an algorithm using partial belong relations in a decision-making problem in order to bring out the optimal choices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  • Al-shami TM (2018a) Corrigendum to “On soft topological space via semi-open and semi-closed soft sets. Kyungpook Math. J. 54 (2014) 221–236”. Kyungpook Math J 58(3):583–588

  • Al-shami TM (2018b) Corrigendum to “Separation axioms on soft topological spaces. Ann. Fuzzy Math. Inform. 11(4) (2016) 511–525”. Ann Fuzzy Math Inform 15(3):309–312

  • Al-shami TM (2019) Comments on “Soft mappings spaces”. Sci World J. Article ID 6903809, 2 p

  • Al-shami TM, Kocinac LDR (2019) The equivalence between the enriched and extended soft topologies. Appl Comput Math 18(2):149–162

    MathSciNet  MATH  Google Scholar 

  • Al-shami TM, El-Shafei ME, Abo-Elhamayel M (2019) On soft topological ordered spaces. J King Saud Univ Sci. https://doi.org/10.1016/j.jksus.2018.06.005

    Article  MATH  Google Scholar 

  • Ali M, Khan H, Son LH, Smarandache F, Kandasamy WBV (2018) New soft sets based class of linear algebraic codes. Symmetry 10:1–10

    Google Scholar 

  • Ali MI, Feng F, Liu X, Min WK, Shabir M (2009) On some new operations in soft set theory. Comput Math Appl 57(9):1547–1553

    Article  MathSciNet  MATH  Google Scholar 

  • Babitha KV, Suntil JJ (2010) Soft set relations and functions. Comput Math Appl 60:1840–1849

    Article  MathSciNet  MATH  Google Scholar 

  • Bayramov S, Aras CG (2018) A new approach to separability and compactness in soft topological spaces. TWMS J Pure Appl Math 6(1):82–93

    MathSciNet  MATH  Google Scholar 

  • Cağman N, Enginoğlu S (2010) Soft matrix theory and its decision making. Comput Math Appl 59:3308–3314

    Article  MathSciNet  Google Scholar 

  • Chen D, Tsong EEC, Young DS, Wong X (2005) The parametrization reduction of soft sets and its applications. Comput Math Appl 49:757–763

    Article  MathSciNet  Google Scholar 

  • Das S, Samanta SK (2013) Soft metric. Ann Fuzzy Math Inform 6(1):77–94

    MathSciNet  MATH  Google Scholar 

  • El-Shafei ME, Abo-Elhamayel M, Al-Shami TM (2018a) Partial soft separation axioms and soft compact spaces. Filomat 32(13):4755–4771

    Article  MathSciNet  Google Scholar 

  • El-Shafei ME, Abo-Elhamayel M, Al-Shami TM (2018b) Two notes on “On soft hausdorff spaces”. Ann Fuzzy Math Inform 16(3):333–336

    Article  MathSciNet  MATH  Google Scholar 

  • Feng F, Li YM, Davvaz B, Ali MI (2010) Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Comput 14:899–911

    Article  MATH  Google Scholar 

  • Georgiou DN, Mergaritis AC, Petropoulos VI (2013) On soft topological spaces. Appl Math Inf Sci 5:1889–1901

    Article  MathSciNet  Google Scholar 

  • Hussain S, Ahmad B (2015) Soft separation axioms in soft topological spaces. Hacet J Math Stat 44(3):559–568

    MathSciNet  MATH  Google Scholar 

  • Karaaslan F (2016) Soft classes and soft rough classes with applications in decision making. Math Probl Eng. Article ID 1584528, 11 p

  • Kharal A, Ahmad B (2011) Mappings on soft classes. New Math Nat Comput 7(3):471–481

    Article  MathSciNet  MATH  Google Scholar 

  • Maji PK, Roy R, Biswas R (2002) An application of soft sets in decision making problem. Comput Math Appl 44:1077–1083

    Article  MathSciNet  MATH  Google Scholar 

  • Maji PK, Biswas R, Roy R (2003) Soft set theory. Comput Math Appl 45:555–562

    Article  MathSciNet  MATH  Google Scholar 

  • Matejdes M (2017) On soft regularity. Int J Pure Appl Math 116(1):197–200

    Google Scholar 

  • Min WK (2011) A note on soft topological spaces. Comput Math Appl 62:3524–3528

    Article  MathSciNet  MATH  Google Scholar 

  • Molodtsov D (1999) Soft set theory-first results. Comput Math Appl 37:19–31

    Article  MathSciNet  MATH  Google Scholar 

  • Nazmul S, Samanta SK (2013) Neighbourhood properties of soft topological spaces. Ann Fuzzy Math Inform 6(1):1–15

    MathSciNet  MATH  Google Scholar 

  • Shabir M, Naz M (2011) On soft topological spaces. Comput Math Appl 61:1786–1799

    Article  MathSciNet  MATH  Google Scholar 

  • Singh A, Noorie NS (2017) Remarks on soft axioms. Ann Fuzzy Math Inform 14(5):503–513

    Article  MathSciNet  MATH  Google Scholar 

  • Tantawy O, El-Sheikh SA, Hamde S (2016) Separation axioms on soft topological spaces. Ann Fuzzy Math Inform 11(4):511–525

    MathSciNet  MATH  Google Scholar 

  • Varol BP, Aygün H (2013) On soft Hausdorff spaces. Remarks Soft Topol Spaces 5(1):15–24

    MathSciNet  MATH  Google Scholar 

  • Yuksel S, Dizman T, Yildizdan G, Sert U (2013) Application of soft sets to diagnose the prostate cancer risk. J Inequal Appl 2013:229

    Article  MathSciNet  MATH  Google Scholar 

  • Zorlutuna I, Akdag M, Min WK, Atmaca S (2012) Remarks on soft topological spaces. Remarks Soft Topol Spaces 2:171–185

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Sana’a University, Sana’a, Yemen

    T. M. Al-shami

  2. Department of Mathematics, Mansoura University, Mansoura, Egypt

    T. M. Al-shami & M. E. El-Shafei

Authors
  1. T. M. Al-shami
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. E. El-Shafei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. M. Al-shami.

Ethics declarations

Conflict of interests

The authors declare that there is no conflict of interests regarding the publication of this article.

Human participants

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

Additional information

Communicated by V. Loia.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Al-shami, T.M., El-Shafei, M.E. Partial belong relation on soft separation axioms and decision-making problem, two birds with one stone. Soft Comput 24, 5377–5387 (2020). https://doi.org/10.1007/s00500-019-04295-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-019-04295-7

Keywords

Search

Navigation