Very true pseudo-BCK algebras

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-BCKvt,st\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {BCK}_{vt,st}$$\end{document} 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, FLw\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {FL}_w$$\end{document}-algebras and pseudo-MTL algebras.