The notion of a positive implicative pseudo-valuation on a BCKalgebra is introduced, and its characterizations are investigated. The relationship between a pseudo-valuation and a positive implicative pseudovaluation is examined. Reduction property for a positive implicative pseudo-valuation is established. Mathematics Subject Classification: 06F35, 03G25

In this paper, by considering the notion of ∧-closed set in BCK-algebras, we construct the fractions of BCK-algebras and we get some related results.

The notion of positive implicative vague ideals in BCKalgebras is introduced. A relation between a vague ideal and a positive implicative vague ideal is discussed. Characterizations of a positive implicative vague ideal are considered. 2010 AMS Classification: 06F35, 03G25, 03E72

This study focuses on combining the theories of m -polar fuzzy sets over id="M2"> BCK -algebras and establishing a new framework id="M3"> id="M4"> -algebras. In this paper, we define idea id="M5"> positive implicative ideals in id="M6"> investigate some related properties. Then, introduce concepts id="M7">...

 In this paper, we aresupposed to introduce the definitions of n-fold commutative, andimplicative hyper K-ideals. These definitions are thegeneralizations of the definitions of commutative, andimplicative hyper K-ideals, respectively, which have been definedin [12]. Then we obtain some related results. In particular wedetermine the relationships between n-fold implicative hyperK-ideal and n-fol...