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Neutrosophic Quadruple BCI-Positive Implicative Ideals

Author

Listed:
  • Young Bae Jun

    (Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea)

  • Seok-Zun Song

    (Department of Mathematics, Jeju National University, Jeju 63243, Korea)

  • Seon Jeong Kim

    (Department of Mathematics, Natural Science of College, Gyeongsang National University, Jinju 52828, Korea)

Abstract

By considering an entry (i.e., a number, an idea, an object, etc.) which is represented by a known part ( a ) and an unknown part ( b T , c I , d F ) where T , I , F have their usual neutrosophic logic meanings and a , b , c , d are real or complex numbers, Smarandache introduced the concept of neutrosophic quadruple numbers. Using the concept of neutrosophic quadruple numbers based on a set, Jun et al. constructed neutrosophic quadruple BCK/BCI-algebras and implicative neutrosophic quadruple BCK-algebras. The notion of a neutrosophic quadruple BCI-positive implicative ideal is introduced, and several properties are dealt with in this article. We establish the relationship between neutrosophic quadruple ideal and neutrosophic quadruple BCI-positive implicative ideal. Given nonempty subsets I and J of a BCI-algebra, conditions for the neutrosophic quadruple ( I , J ) -set to be a neutrosophic quadruple BCI-positive implicative ideal are provided.

Suggested Citation

  • Young Bae Jun & Seok-Zun Song & Seon Jeong Kim, 2019. "Neutrosophic Quadruple BCI-Positive Implicative Ideals," Mathematics, MDPI, vol. 7(5), pages 1-9, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:385-:d:226664
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