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Mathematics 2018, 6(9), 149; https://doi.org/10.3390/math6090149

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

1
Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
2
Department of Mathematics Education, Chinju National University of Education, Jinju 52673, Korea
3
Department of Mathematics, Faculty of Arts and Sciences, Adiyaman University, 02040 Adiyaman, Turkey
*
Author to whom correspondence should be addressed.
Received: 9 August 2018 / Revised: 19 August 2018 / Accepted: 24 August 2018 / Published: 29 August 2018
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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. View Full-Text
Keywords: intuitionistic random set; intuitionistic falling shadow; (positive implicative) (∈, ∈)-intuitionistic fuzzy ideal; (positive implicative) falling intuitionistic fuzzy ideal intuitionistic random set; intuitionistic falling shadow; (positive implicative) (∈, ∈)-intuitionistic fuzzy ideal; (positive implicative) falling intuitionistic fuzzy ideal
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Jun, Y.B.; Roh, E.H.; Öztürk, M.A. Positive Implicative Ideals of BCK-Algebras Based on Intuitionistic Falling Shadows. Mathematics 2018, 6, 149.

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