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Characterizations of ordered semihypergroups by the properties of their intersectional-soft generalized bi-hyperideals

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Abstract

Molodtsov’s soft set theory is a new mathematical model for dealing with uncertainty from a parameterization point of view. In soft set theory, the problem of setting the membership function does not arise, which makes the theory easily applied to many different fields. In this paper, we discuss a new approach to soft sets and compare soft sets to the related concepts of ordered semihypergroups. We define int-soft generalized bi-hyperideals in ordered semihypergroups and characterize regular and left weakly regular ordered semihypergroups by the properties of their int-soft generalized bi-hyperideals.

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References

  • Aktas H, Cağman N (2007) Soft sets and soft groups. Inf Sci 177(13):2726–2735

    Article  MathSciNet  MATH  Google Scholar 

  • Feng F, Jun YB, Zhao X (2008) Soft semirings. Comput Math Appl 56(10):2621–2628

    Article  MathSciNet  MATH  Google Scholar 

  • Feng F, Ali MI, Shabir M (2013) Soft relations applied to semigroups. Filomat 27(7):1183–1196

    Article  MathSciNet  MATH  Google Scholar 

  • Feng F, Li YM (2013) Soft subsets and soft product operations. Inf Sci 232:44–57

    Article  MathSciNet  MATH  Google Scholar 

  • Jun YB (2014) Song SZ (2014) Muhiuddin G (2014) Concave soft sets, critical soft points, and union-soft ideals of ordered semigroups. Sci World J 2014(2014):467968

  • Ma X, Zhan J (2013) Characterizations of three kinds of hemirings by fuzzy soft \(h\)-ideals. J Intell Fuzzy Syst 24:535–548

    MathSciNet  MATH  Google Scholar 

  • Molodtsov D (1999) Soft set theory—first results. Comput Math Appl 37(4–5):19–31

    Article  MathSciNet  MATH  Google Scholar 

  • Zhan J, Čağman N, Sezer AS (2014) Applications of soft union sets to hemirings via \(SU\)-\(h\)-ideals. J Intell Fuzzy Syst 26:1363–1370

    MathSciNet  MATH  Google Scholar 

  • Marty F (1934) Sur Une generalization de la notion de group. In: \(8^{iem}\) congress, Math Scandinaves Stockholm, pp 45–49

  • Song SZ, Kim, HS, Jun YB (2014) Ideal theory in semigroups based on intersectional soft sets. Sci World J. Article ID 136424

  • Khan A, Farooq M, Davvaz B (2017a) Int-soft left (right) hyperideals of ordered semihypergroups (submitted)

  • Khan A, Farooq M, Davvaz B (2017b) Prime Int-soft bi-hyperideals of ordered semihypergroups (submitted)

  • Naz S, Shabir M (2014) On soft semihypergroups. J Intell Fuzzy Syst 26:2203–2213

    MathSciNet  MATH  Google Scholar 

  • Naz S, Shabir M (2014) On prime soft bi-hyperideals of semihypergroups. J Intell Fuzzy Syst 26:1539–1546

    MathSciNet  MATH  Google Scholar 

  • Pibaljommee B, Davvaz B (2015) Characterizations of (fuzzy) bi-hyperideals in ordered semihypergroups. J Intell Fuzzy Syst 28:2141–2148

    Article  MATH  Google Scholar 

  • Heidari D, Davvaz B (2011) On ordered hyperstructures. UPB Sci Bull Ser A 73(2):85–96

    MathSciNet  MATH  Google Scholar 

  • Tang J, Khan A, Luo YF (2016) Characterization of semisimple ordered semihypergroups in terms of fuzzy hyperideals. J Intell Fuzzy Syst 30:1735–1753

    Article  MATH  Google Scholar 

  • Changphas T, Davvaz B (2015) Bi-hyperideals and quasi-hyperideals in ordered semihypergroups. Ital J Pure Appl Math 35:493–508

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Abdul Wali Khan University, Mardan, KP, Pakistan

    Muhammad Farooq & Asghar Khan

  2. Department of Mathematics, Yazd University, Yazd, Iran

    Bijan Davvaz

Authors
  1. Muhammad Farooq
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  2. Asghar Khan
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  3. Bijan Davvaz
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Corresponding author

Correspondence to Asghar Khan.

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The authors declare that they have no conflict of interest.

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Communicated by V. Loia.

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Farooq, M., Khan, A. & Davvaz, B. Characterizations of ordered semihypergroups by the properties of their intersectional-soft generalized bi-hyperideals. Soft Comput 22, 3001–3010 (2018). https://doi.org/10.1007/s00500-017-2550-6

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  • DOI: https://doi.org/10.1007/s00500-017-2550-6

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