Soft Computing

, Volume 23, Issue 21, pp 10587–10600 | Cite as

Very true pseudo-BCK algebras

  • Lavinia Corina CiunguEmail author


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 (Av), 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 (Av) 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.


Very true pseudo-BCK algebra Interior operator Very true deductive system Very true homomorphism Truth-depressing hedge 



The author is very grateful to the referees for the valuable suggestions in obtaining the final form of this paper. The author would also like to thank Professor Wenjuan Chen for his useful remark that helped to improve the result from Proposition 5.4.

Compliance with ethical standards

Conflicts of interest

The author declares that she has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by the author.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IowaIowa CityUSA

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