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 the theory of rings and near-rings, the properties of derivations are an important topic to study, see [2, 3, 7, 10]. In [6], Jun and Xin applied the notions in rings and nearrings theory to BCI-algebras, and obtained some related properties. In this paper, the notion of left-right (resp., right-left) f -derivation of a BCI-algebra is introduced, and some related properties are investigated....

BZ-algebra, as the common generalization of BCI-algebra and BCC-algebra, is a kind important logic algebra. Herein, new concepts QM-BZ-algebra quasi-hyper BZ-algebra are proposed their structures constructions studied. First, definition presented, structure obtained: Each KG-union quasi-alter BCK-algebra anti-grouped BZ-algebra. Second, generalized quasi-left alter (hyper) BZ-algebras QM-hyper ...

The notion of symmetric left bi-derivation of a BCI-algebra X is introduced, and related properties are investigated. Some results on componentwise regular and d-regular symmetric left bi-derivations are obtained. Finally, characterizations of a p-semisimple BCI-algebra are explored, and it is proved that, in a p-semisimple BCI-algebra, F is a symmetric left bi-derivation if and only if it is a...

In this paper, for any non-empty subset C of a pseudo BCI-algebra X, the concept of p-closure of C, denoted by C(pc), is introduced and some related properties are investigated. Applying this concept, a characterization of the minimal elements of X is given. It is proved that C(pc) is the least closed pseudo BCI-ideal of X containing C and K(X) for any ideal C of X...

In the present paper we introduced the notion of (θ ,φ)-derivations of a BCI-algebra X . Some interesting results on inside (or outside) (θ ,φ)-derivations in BCI-algebras are discussed. It is shown that for any commutative BCI-algebra X , every inside (θ ,φ)derivation of X is isotone. Furthermore it is also proved that for any outside (θ ,φ)-derivation d(θ ,φ) of a BCI-algebra X , d(θ ,φ)(x) =...

Using the notion of anti fuzzy points and its besideness to and non-quasi-coincidence with a fuzzy set, new concepts of an anti fuzzy subalgebras in BCK/BCI-algebras are introduced and their inter-relations and related properties are investigated in [3]. The notion of the new fuzzy subalgebra with thresholds are introduced and relationship between this notion and the new fuzzy subalgebra of a B...

The aim of this paper is to introduce the notions of ($epsilon, epsilon vee q$)-fuzzy p-ideals, ($epsilon, epsilon vee q$)-fuzzy q-ideals and ($epsilon, epsilon vee q$)-fuzzy a-ideals in BCIalgebras and to investigate some of their properties. Several characterizationtheorems for these generalized fuzzy ideals are proved and the relationshipamong these generalized fuzzy ideals of BCI-algebras i...

Some new properties of fuzzy associative filters (also known as fuzzy associative pseudo-filters), fuzzy p-filter (also known as fuzzy pseudo-p-filters), and fuzzy a-filter (also known as fuzzy pseudo-a-filters) in pseudo-BCI algebras are investigated. By these properties, the following important results are proved: (1) a fuzzy filter (also known as fuzzy pseudo-filters) of a pseudo-BCI algebra...

We consider the notion of an isomorphism between two hyper BCI-algebras and obtain all of the hyper BCI-algebras of order 3. It is shown that there exist 14 proper hyper BCI-algebras and 5 proper weak hyper BCI-algebras of order 3 up to isomorphism. Finally, further study on the theory of hyper BCI-algebra and its related hyper structure and applications of our results in information sciences a...