In this paper, we introduce the concept of bipolar-valued fuzzification of ordered 𝓐𝓖-groupoids and discuss some structural properties of bipolar-valued fuzzy two-sided ideals of an intra-regular ordered 𝓐𝓖-groupoid.
In this paper, we introduce the notion of a bi-BL-algebra, bi-filter, bi-deductive system and bi-Boolean elements of a bi-BL-algebra and deal with bi-filters in bi-BL-algebra. We study this structure and construct the quotient of bi-BL-algebra. Also present a classification for examples of proper bi-BL-algebras.
The present study aimed to introduce -fold interval valued residuated lattice (IVRL for short) filters in triangle algebras. Initially, the notions of -fold (positive) implicative IVRL-extended filters and -fold (positive) implicative triangle algebras were defined. Afterwards, several characterizations of the algebras were presented, and the correlations between the -fold IVRL-extended filters, -fold (positive) implicative algebras, and the Gödel triangle algebra were discussed.
We introduce Engel elements in a BCI-algebra by using left and right normed commutators, and some properties of these elements are studied. The notion of -Engel BCI-algebra as a natural generalization of commutative BCI-algebras is introduced, and we discuss Engel BCI-algebra, which is defined by left and right normed commutators. In particular, we prove that any nilpotent BCI-algebra of type is an Engel BCI-algebra, but solvable BCI-algebras are not Engel, generally. Also, it is proved that...
The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized...
The notions of a dual pseudo-Q algebra and a dual pseudo-QC algebra are introduced. The properties and characterizations of them are investigated. Conditions for a dual pseudo-Q algebra to be a dual pseudo-QC algebra are given. Commutative dual pseudo-QC algebras are considered. The interrelationships between dual pseudo-Q/QC algebras and other pseudo algebras are visualized in a diagram.
Hilbert algebras are important tools for certain investigations in intuitionistic logic and other non-classical logic and as a generalization of Hilbert algebra a new algebraic structure, called a GE-algebra (generalized exchange algebra), is introduced and studied its properties. We consider filters, upper sets and congruence kernels in a GE-algebra. We also characterize congruence kernels of transitive GE-algebras.
In this paper, we introduce the notion of pseudo BE-algebra which is a generalization of BE-algebra. We define the concepts of pseudo subalgebras and pseudo filters and prove that, under some conditions, pseudo subalgebra can be a pseudo filter. We prove that every homomorphic image and pre-image of a pseudo filter is also a pseudo filter. Furthermore, the notion of pseudo upper sets in pseudo BE-algebras introduced and is proved that every pseudo filter is an union of pseudo upper sets.
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