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

Young Bae Jun, Eun Hwan Roh and Mehmet Ali Öztürk
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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

Mathematics, 2018, vol. 6, issue 9, 1-16

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.

Keywords: intuitionistic random set; intuitionistic falling shadow; (positive implicative) (?, ?)-intuitionistic fuzzy ideal; (positive implicative) falling intuitionistic fuzzy ideal (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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