Fuzzy set approach to ideal theory on Sheffer stroke BE-algebras

Volume 34, Issue 3, pp 283--294 https://dx.doi.org/10.22436/jmcs.034.03.07

Publication Date: March 29, 2024 Submission Date: February 05, 2024 Revision Date: February 18, 2024 Accteptance Date: February 29, 2024

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 119 Downloads
• 238 Views

Authors

N. Chunsee - Faculty of Science and Technology, Uttaradit Rajabhat University, Uttaradit 53000, Thailand. P. Julatha - Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok 65000, Thailand. A. Iampan - Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand.

Abstract

This paper aims to apply fuzzy set theory to Sheffer stroke BE-algebras. The concepts of fuzzy SBE-ideals and anti-fuzzy SBE-ideals of Sheffer stroke BE-algebras are introduced, and their important properties are investigated. Characterizations of SBE-ideals of SBE-algebras are given in terms of fuzzy SBE-ideals and anti-fuzzy SBE-ideals. Relationships between fuzzy SBE-ideals and anti-fuzzy SBE-ideals and their level subsets are discussed. We especially characterize fuzzy SBE-ideals and anti-fuzzy SBE-ideals by their level subsets.

Share and Cite

Keywords

• SBE-ideal
• fuzzy SBE-ideal
• anti-fuzzy SBE-ideal
• level subset
• Sheffer stroke BE-algebra

MSC

•  03G25
•  03E72

References

• [1] T. Katican, Branches and obstinate SBE-filters of Sheffer stroke BE-algebras, Bull. Int. Math. Virtual Inst., 12 (2022), 41–50
  • View Article
  • Google Scholar


• [2] T. Katican, T. Oner, A. B. Saeid, On Sheffer stroke BE-algebras, Discuss. Math. Gen. Algebra Appl., 42 (2022), 293–314
  • View Article
  • Google Scholar
  • MATH


• [3] B. Kesorn, K. Maimun, W. Ratbandan, A. Iampan, Intuitionistic fuzzy sets in UP-algebras, Ital. J. Pure Appl. Math., 34 (2015), 339–364
  • View Article
  • Google Scholar
  • MATH


• [4] H. S. Kim, Y. H. Kim, On BE-algebras, Sci. Math. Jpn., 66 (2007), 113–116
  • View Article
  • Google Scholar
  • MATH


• [5] T. Oner, T. Katican, A. Rezaei, Neutrosophic N-structures on Sheffer stroke BCH-algebras, Neutrosophic Sets Syst., 50 (2022), 459–479
  • View Article
  • Google Scholar


• [6] T. Oner, T. Katican, A. Rezaei, Neutrosophic N-structures on strong Sheffer stroke non-associative MV-algebras, Neutrosophic Sets Syst., 40 (2021), 235–252
  • View Article
  • Google Scholar


• [7] T. Oner, T. Katican, A. B. Saeid, On Sheffer stroke up-algebras, Discuss. Math. Gen. Algebra Appl., 41 (2021), 381–394
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] T. Oner, T. Katican, A. B. Saeid, Relation between Sheffer stroke and Hilbert algebras, Categ. Gen. Algebr. Struct. Appl., 14 (2021), 245–268
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] T. Oner, T. Kalkan, A. B. Saeid, Class of Sheffer stroke BCK-algebras, An. S¸tiint¸. Univ. “Ovidius” Constant¸a Ser. Mat., 30 (2022), 247–270
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] T. Oner, T. Katican, A. B. Saeid, (Fuzzy) filters of Sheffer stroke BL-algebras, Kragujevac J. Math., 47 (2023), 39–55
  • View Article
  • Google Scholar
  • MATH


• [11] T. Oner, T. Katican, A. B. Saeid, On fuzzy Sheffer stroke BE-algebras, New Math. Nat. Comput., (2023),
  • View Article
  • Google Scholar


• [12] T. Oner, T. Katican, S. Svanidze, A. Rezaei, Neutrosophic N-structures on Sheffer stroke BE-algebras, J. Math. Res. Center, 11 (2022), 121–143
  • View Article
  • Google Scholar


• [13] H. M. Sheffer, A set of five independent postulates for Boolean algebras, with application to logical constants, Trans. Amer. Math. Soc., 14 (1913), 481–488
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [14] J. Somjanta, N. Thuekaew, P. Kumpeangkeaw, A. Iampan, Fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform., 12 (2016), 739–756
  • View Article
  • Google Scholar


• [15] K. Tanamoon, S. Sripaeng, A. Iampan, Q-fuzzy sets in UP-algebras, Songklanakarin J. Sci. Technol., 40 (2018), 9–29
  • View Article
  • Google Scholar


• [16] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338–353
  • View Article
  • Google Scholar