Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (5)

Search Parameters:
Keywords = Wajsberg-algebra

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
14 pages, 275 KiB  
Article
Paraconsistency in the Logic sqŁ*
by Lei Cai and Wenjuan Chen
Axioms 2025, 14(4), 241; https://doi.org/10.3390/axioms14040241 - 21 Mar 2025
Viewed by 264
Abstract
The logic sqŁ* is closely related to complex fuzzy sets. In this paper, we continue our study on sqŁ* by establishing a system that includes all formulas with values 0 in sqŁ*. This system has paraconsistent formulas within sqŁ [...] Read more.
The logic sqŁ* is closely related to complex fuzzy sets. In this paper, we continue our study on sqŁ* by establishing a system that includes all formulas with values 0 in sqŁ*. This system has paraconsistent formulas within sqŁ*. Moreover, we show that this logical system is both sound and weakly complete. Full article
(This article belongs to the Special Issue Advances in Fuzzy Logic with Applications)
19 pages, 351 KiB  
Article
Graphs of Wajsberg Algebras via Complement Annihilating
by Necla Kırcalı Gürsoy
Symmetry 2023, 15(1), 121; https://doi.org/10.3390/sym15010121 - 1 Jan 2023
Cited by 2 | Viewed by 1805
Abstract
In this paper, W-graph, called the notion of graphs on Wajsberg algebras, is introduced such that the vertices of the graph are the elements of Wajsberg algebra and the edges are the association of two vertices. In addition to this, commutative W-graphs are [...] Read more.
In this paper, W-graph, called the notion of graphs on Wajsberg algebras, is introduced such that the vertices of the graph are the elements of Wajsberg algebra and the edges are the association of two vertices. In addition to this, commutative W-graphs are also symmetric graphs. Moreover, a graph of equivalence classes of Wajsberg algebra is constructed. Meanwhile, new definitions as complement annihilator and ∆-connection operator on Wajsberg algebras are presented. Lemmas and theorems on these notions are proved, and some associated results depending on the graph’s algebraic properties are presented, and supporting examples are given. Furthermore, the algorithms for determining and constructing all these new notions in each section are generated. Full article
Show Figures

Figure 1

13 pages, 260 KiB  
Article
Constructing Some Logical Algebras with Hoops
by M. Aaly Kologani, Seok-Zun Song, R. A. Borzooei and Young Bae Jun
Mathematics 2019, 7(12), 1243; https://doi.org/10.3390/math7121243 - 16 Dec 2019
Cited by 3 | Viewed by 3617
Abstract
In any logical algebraic structures, by using of different kinds of filters, one can construct various kinds of other logical algebraic structures. With this inspirations, in this paper by considering a hoop algebra or a hoop, that is introduced by Bosbach, the notion [...] Read more.
In any logical algebraic structures, by using of different kinds of filters, one can construct various kinds of other logical algebraic structures. With this inspirations, in this paper by considering a hoop algebra or a hoop, that is introduced by Bosbach, the notion of co-filter on hoops is introduced and related properties are investigated. Then by using of co-filter, a congruence relation on hoops is defined, and the associated quotient structure is studied. Thus Brouwerian semilattices, Heyting algebras, Wajsberg hoops, Hilbert algebras and BL-algebras are obtained. Full article
(This article belongs to the Special Issue Algebra and Discrete Mathematics)
20 pages, 258 KiB  
Article
Some Results in Weak Pseudo-Quasi-Wajsberg Algebras
by Wenjun Liu and Wenjuan Chen
Symmetry 2019, 11(4), 447; https://doi.org/10.3390/sym11040447 - 29 Mar 2019
Cited by 1 | Viewed by 2680
Abstract
In this paper we continue to investigate weak pseudo-quasi-Wajsberg algebras which are called weak PQW-algebras for short. First, some definitions are recalled and the basic properties of weak PQW-algebras are presented. Next, we define the notions of type-I filters, type-II filters, left weak [...] Read more.
In this paper we continue to investigate weak pseudo-quasi-Wajsberg algebras which are called weak PQW-algebras for short. First, some definitions are recalled and the basic properties of weak PQW-algebras are presented. Next, we define the notions of type-I filters, type-II filters, left weak filters and right weak filters of a weak PQW-algebra and study related properties of them. We also discuss the relation between normal filters and filter congruences on a weak PQW-algebra. Finally, we characterize the relationship between weak PQW-algebras and some bounded residuated quasi-ordered monoids with supplementary conditions. Full article
(This article belongs to the Special Issue Mathematical Fuzzy Logic and Fuzzy Set Theory)
13 pages, 215 KiB  
Article
On Solutions to the Set-Theoretical Yang-Baxter Equation in Wajsberg-Algebras
by Tahsin Oner and Tugce Katican
Axioms 2018, 7(1), 6; https://doi.org/10.3390/axioms7010006 - 20 Jan 2018
Cited by 9 | Viewed by 4413
Abstract
In this work, we introduce Wajsberg algebras which are equivalent structures to MV-algebras in their implicational version, and then we define new notions and give new solutions to the set-theoretical Yang-Baxter equation by using Wajsberg algebras. Full article
(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang–Baxter Equations 2017)
Back to TopTop