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Applications of partial belong and total non-belong relations on soft separation axioms and decision-making problem

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Abstract

This study introduces a new family of soft separation axioms and a real-life application utilizing partial belong and natural non-belong relations. First, we initiate the concepts of w-soft \(T_i\)-spaces \((i=0, 1, 2, 3, 4)\) with respect to distinct ordinary points. These concepts generate a wider family of soft spaces compared with soft \(T_i\)-spaces, p-soft \(T_i\)-spaces and e-soft \(T_i\)-spaces. We illustrate the relationships between w-soft \(T_i\)-spaces with the help of examples and discuss some sufficient conditions of soft topological spaces to be w-soft \(T_i\)-spaces. Additionally, we point out that stable or soft regular spaces are sufficient conditions for the equivalence among the concepts of soft \(T_i\), p-soft \(T_i\) and w-soft \(T_i\). We highlight on explaining the links between w-soft \(T_i\)-spaces and their parametric topological spaces and studying the role of enriched spaces in these links. Furthermore, we prove that w-soft \(T_i\)-spaces are hereditary and topological properties, and they are preserved under finite product soft spaces. Finally, we propose an algorithm to bring out the optimal choices. This algorithm is based on dividing the whole parameters set into parameter sets and then apply a partial belong relation in the favorite soft sets. This application is supported with an interesting example to show how to implement this algorithm.

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References

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

    MathSciNet  MATH  Google Scholar 

  • Al-shami TM (2018b) Corrigendum to “separation axioms on soft topological spaces, annals of fuzzy mathematics and informatics, 11 (4) (2016) 511–525”. Ann Fuzzy Math Inf 15(3):309–312

  • Al-shami TM (2019a) Comments on “soft mappings spaces”. Sci World J Vol 2019, Article ID 6903809:2 pages

  • Al-shami TM (2019b) Investigation and corrigendum to some results related to g-soft equality and gf-soft equality relations. Filomat 33(11):3375–3383

    MathSciNet  Google Scholar 

  • Al-shami TM, El-Shafei (2019) On supra soft topological ordered spaces. Arab J Basic Appl Sci 26(1):433–445

  • Al-shami TM, El-Shafei (2020) Partial belong relation on soft separation axioms and decision making problem: two birds with one stone. Soft Comput 24:5377–5387

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

  • Al-shami TM, El-Shafei ME, Abo-Elhamayel M (2019) On soft topological ordered spaces. J King Saud Univ Sci 31(4):556–566

    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

    MathSciNet  MATH  Google Scholar 

  • Aygünoǧlu A, Aygün H (2012) Some notes on soft topological spaces. Neural Comput Appl 21:113–119

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

    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 

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

    MathSciNet  Google Scholar 

  • Das S, Samanta SK (2013) Soft metric. Ann Fuzzy Math Inf 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

    MathSciNet  Google Scholar 

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

    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

    MATH  Google Scholar 

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

    MathSciNet  Google Scholar 

  • Hussain S, Ahmad B (2015) Soft separation axioms in soft topological spaces. Hacettepe 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 Volume 2016, Article ID 1584528:11 pages

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

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    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

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Tahat MK, Sidky F, Abo-Elhamayel M (2018) Soft topological soft groups and soft rings. Soft Comput 22:7143–7156

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Varol BP, Aygün H (2013) On soft hausdorff spaces. Ann Fuzzy Math Inf 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

    MathSciNet  MATH  Google Scholar 

  • Zorlutuna I, Akdag M, Min WK, Atmaca S (2012) Remarks on soft topological spaces. Ann Fuzzy Math Inf 2:171–185

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors are thankful to the anonymous referees for their valuable comments and suggestions.

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Authors and Affiliations

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

    M. E. El-Shafei & T. M. Al-shami

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

    T. M. Al-shami

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  1. M. E. El-Shafei
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  2. T. M. Al-shami
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Correspondence to T. M. Al-shami.

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Communicated by Anibal Tavares de Azevedo.

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El-Shafei, M.E., Al-shami, T.M. Applications of partial belong and total non-belong relations on soft separation axioms and decision-making problem. Comp. Appl. Math. 39, 138 (2020). https://doi.org/10.1007/s40314-020-01161-3

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  • DOI: https://doi.org/10.1007/s40314-020-01161-3

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