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Erschienen in:
25.03.2019 | Foundations
Very true pseudo-BCK algebras
Erschienen in: Soft Computing | Ausgabe 21/2019
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Abstract
In this paper, we introduce the very true operators on pseudo-BCK algebras and we study their properties. We prove that the composition of two very true operators is a very true operator if and only if they commute. Moreover, given a very true bounded pseudo-BCK algebra (A, v), we define the pseudo-\(\hbox {BCK}_{vt,st}\) algebra by adding two truth-depressing hedge operators associated with v. We also define the very true deductive systems and the very true homomorphisms, and we investigate their properties. Also, given a normal v-deductive system H of a very true pseudo-BCK algebra (A, v) we construct a very true operator on the quotient pseudo-BCK algebra A / H. Some particular properties are proved for the case of very true operators on classes of pseudo-BCK algebras such as pseudo-BCK(pP) algebras, \(\hbox {FL}_w\)-algebras and pseudo-MTL algebras.