Neutrosophic Quadruple BCI-Positive Implicative Ideals

Young Bae Jun, Seok-Zun Song and Seon Jeong Kim
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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

Mathematics, 2019, vol. 7, issue 5, 1-9

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.

Keywords: neutrosophic quadruple BCK/BCI-number; neutrosophic quadruple BCK/BCI-algebra; neutrosophic quadruple (BCI-positive implicative) ideal (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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