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Positive Implicative Ideals of BCK -Algebras Based on Intuitionistic Falling Shadows

Author

Listed:
  • Young Bae Jun

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

  • Eun Hwan Roh

    (Department of Mathematics Education, Chinju National University of Education, Jinju 52673, Korea)

  • Mehmet Ali Öztürk

    (Department of Mathematics, Faculty of Arts and Sciences, Adiyaman University, 02040 Adiyaman, Turkey)

Abstract

The concepts of a positive implicative ( ∈ , ∈)-intuitionistic fuzzy ideal and a positive implicative falling intuitionistic fuzzy ideal are introduced, and several properties are investigated. Characterizations of a positive implicative ( ∈ , ∈)-intuitionistic fuzzy ideal are obtained, and relations between a positive implicative ( ∈ , ∈)-intuitionistic fuzzy ideal and an intuitionistic fuzzy ideal are discussed. Conditions for an intuitionistic fuzzy ideal to be a positive implicative ( ∈ , ∈)-intuitionistic fuzzy ideal are provided, and relations between a positive implicative ( ∈ , ∈)-intuitionistic fuzzy ideal, a falling intuitionistic fuzzy ideal and a positive implicative falling intuitionistic fuzzy ideal are considered. Conditions for a falling intuitionistic fuzzy ideal to be positive implicative are given.

Suggested Citation

  • Young Bae Jun & Eun Hwan Roh & Mehmet Ali Öztürk, 2018. "Positive Implicative Ideals of BCK -Algebras Based on Intuitionistic Falling Shadows," Mathematics, MDPI, vol. 6(9), pages 1-16, August.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:9:p:149-:d:166496
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    References listed on IDEAS

    as
    1. Young Bae Jun & Kyung Ho Kim, 2000. "Intuitionistic fuzzy ideals of BCK-algebras," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 24, pages 1-11, January.
    2. Young Bae Jun & Sun Shin Ahn, 2012. "The Theory of Falling Shadows Applied to ð ‘‘ -Ideals in ð ‘‘ -Algebras," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-10, March.
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