Pseudo-BCK algebras were introduced by G. Georgescu and A. Iorgulescu as a generalization of BCK algebras in order to give a corresponding structure to pseudo-MV algebras, since the bounded commutative BCK algebras corresponde to MV algebras. Properties of pseudo-BCK algebras and their connections with other fuzzy structures were established by A. Iorgulescu and J. Kühr. The aim of this paper i...

In this paper, we introduce the concepts of n-fold obstinate pseudo-hoop and n-fold obstinate filter in pseudo-hoops. Then we investigated these notions and proved some properties of them. Also, we discussed the relationship between n-fold obstinate pseudo-hoop and n-fold obstinate filter and other types of n-fold pseudo-hoops and n-fold filters such as n-fold (positive) implicative filter and ...

In this paper, by considering the notion of hyper hoop-algebras, we define the concepts of (strong) regular relations on hyper hoop-algebras and investigate some properties of them. Then we construct a quotient (hyper) hoop-algebra by a (strong)regular relation on hyper hoop-algebras. Finally, we define the notion of maximal filter and we investigate the relation between quotient simple hyper h...

The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties.We generalize some results proved by A. Walendziak for the case of commutative BE-algebras.We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-...

In this paper, we study pseudo-valuations on a BCI-algebra and obtain some related results. The relation between pseudo-valuations and ideals is investigated. We use a pseudo-metric induced by a pseudovaluation to introduce a congruence relation on a BCI-algebra. We define the quotient algebra induced by this relation and prove that it is also a BCI-algebra and study its properties.

In this paper,  pseudo-amenability and pseudo-Connes amenability of weighted semigroup algebra $ell^1(S,omega)$ are studied. It is proved that pseudo-Connes amenability and pseudo-amenability of weighted group algebra $ell^1(G,omega)$ are the same. Examples are given to show that the class of $sigma$-Connes amenable dual Banach algebras is larger than that of Connes amenable dual Banach algebras.

Pseudo-hoops are algebraic structures introduced in [1, 2] by B. Bosbach under the name of complementary semigroups. This is a formalization of the paper [4]. Following [4] we prove some properties of pseudo-hoops and we define the basic concepts of filter and normal filter. The lattice of normal filters is isomorphic with the lattice of congruences of a pseudo-hoop. We also study some importan...

We develop alternative semantics for à Lukasiewicz logic and for cancellative hoop logic according to the following idea. We formalize statements reflecting an inexact knowledge of certain (sharp) properties; we assume that all what can be known about a property is its expressive strength. To this end, we consider a Boolean algebra endowed with an automorphism group or, alternatively, with a me...

Hoop residuation algebras are the {→, 1}-subreducts of hoops; they include Hilbert algebras and the {→, 1}-reducts of MV-algebras (also known as Wajsberg algebras). The paper investigates the structure and cardinality of finitely generated algebras in varieties of kpotent hoop residuation algebras. The assumption of k-potency guarantees local finiteness of the varieties considered. It is shown ...