Hatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60002420211101Implication Zroupoids and Birkhoff Systems11213081010.52547/HATEF.JAHLA.2.4.1ENJ.M.CornejoDepartamento de Matem'atica, Universidad Nacional del Sur, Alem 1253, Bah'ia Blanca, Argentina, INMABB - CONICET.H.P.SankappanavarHanamantagouda P. Sankappanavar, Department of Mathematics, State University of New York, New Paltz, New York 12561, U.S.A.Journal Article20210520An algebra $\mathbf A = \langle A, \to, 0 \rangle$, where $\to$ is binary and $0$ is a constant, is called an implication zroupoid ($\mathcal{I}$-zroupoid, for short) if $\mathbf{A}$ satisfies the identities: $(x \to y) \to z \approx [(z' \to x) \to (y \to z)']'$, where $x' : = x \to 0$, and $ 0'' \approx 0$. These algebras generalize De Morgan algebras and $\vee$-semilattices with zero. Let $\mathcal{I}$ denote the variety of implication zroupoids. The investigations into the structure of $\mathcal{I}$ and of the lattice of subvarieties of $\mathcal{I}$, begun in 2012, have continued in several papers (see the Bibliography at the end of the paper). The present paper is a sequel to that series of papers and is devoted to making further contributions to the theory of implication zroupoids. The main purpose of this paper is to prove that if $\mathbf{A}$ is an algebra in the variety $\mathcal{I}$, then the derived algebra $\mathbf{A}_{mj} := \langle A; \wedge, \vee \rangle$, where $a \land b := (a \to b')'$ and $a \lor b := (a' \land b')'$, satisfies the Birkhoff's identity (BR): $x \land (x \lor y) \approx x \lor (x \land y)$. As a consequence, the implication zroupoids $\mathbf A$ whose derived algebras $\mathbf{A}_{mj}$ are Birkhoff systems are characterized. Another interesting consequence of the main result is that there are bisemigroups that are not bisemilattices but satisfy the Birkhoff's identity, which leads us naturally to define the variety of "Birkhoff bisemigroups'' as bisemigroups satisfying the Birkhoff identity, as a generalization of Birkhoff systems. The paper concludes with some open problems.http://jahla.hatef.ac.ir/article_130810_54f16a4d1639a37455de773b217c6191.pdfHatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60002420211101On block commutative groupoids132313851610.52547/HATEF.JAHLA.2.4.2ENY. J.SeoDepartment of Mathematics, Daejin University, Pochen 11159, KoreaJ.NeggersDepartment of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, U.S.A.H.S.KimDepartment of Mathematics, Research Institute of Natural Sciences, Hanyang University, Seoul 04763, KoreaJournal Article20211010In this paper, we introduce the notion of a block commutativity in several groupoids, and show that the class of block commutative groupoids and the class of d/BCK-algebras are Smarandache disjoint. The block commutativity in linear/quadratic groupoids is investigated, and we prove that every group is a normal groupoid. Moreover, we discuss block n-commutative groupoids and block ranks.<br /> http://jahla.hatef.ac.ir/article_138516_6ba221cd343204aad7fc9e9ba63b3ea5.pdfHatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60002420211101The investigate of ΓUP-algebras253713995710.52547/HATEF.JAHLA.2.4.3ENS.Ostadhadi-DehkordiDepartment of Mathematics, University of Hormozgan, Bandar Abbas, Iran.K.P.ShumInstitute of Mathematics,Yunnan University, Kunming, 650091, P.R. ChinaJournal Article20211111We first define a new concept, namely, the ΓUP-algebra. Then, we study and investigate the properties of its ΓUP-ideals and ΓUP-subalgebras. As a consequence, we construct a covariant functor between the ΓUP-category and the UP algebra-category. Some possible connections between these categories are also considered.http://jahla.hatef.ac.ir/article_139957_74e866e68d6ec6b0aa67516eae4b3d7b.pdfHatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60002420211101On autosolvable and autonilpotent polygroups394914062610.52547/HATEF.JAHLA.2.4.4ENA.Mosayebi DorchehDepartment of Mathematies, Payame Noor University (PNU), IranJournal Article20211122Polygroups are another important class of hypergroups. The importance of polygroups is their connection to graphs, relations and Boolean algebras. In this paper, we study notions of autosolvable and autonilpotent polygroups by using the heart of a polygroup. This study introduces the concept of autosolvable and autonilpotent polygroups with respect to the automorphism of polygroups. We also prove that autonilpotent polygroups are autosolvable. http://jahla.hatef.ac.ir/article_140626_791f115d3349d6067f6b34342b6aeb51.pdfHatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60002420211101Modal representation of coalgebras over local BL-algebras516214174510.52547/HATEF.JAHLA.2.4.5ENC.T.NganteuDepartment of Mathematics, Faculty of sciences, University of Yaound&amp;eacute; 1, Yaound&amp;eacute;, CameroonM.KianpiDepartment of mathematics, Faculty of sciences, University of Yaounde 1, CameroonO.AmassayogaDepartment of mathematics, faculty of sciences, University of Yaounde 1, CameroonJournal Article20211214We consider the category Coalg(∏) of ∏-coalgebras where ∏ is the endofunctor on the category of local BL-algebras and L-morphisms which assigns to each local BL-algebra its quotient by its unique maximal filter and we characterize homomorphisms and subcoalgebras in Coalg(∏) . Moreover, we introduce local BL-frames based on local BL-algebras, and show that the category of local BL-frames is isomorphic to Coalg(∏).http://jahla.hatef.ac.ir/article_141745_545d45b8753d536e59470f810393bb2e.pdfHatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60002420211101Neutrosophic soft metric matrices with applications in decision-making638113637410.52547/HATEF.JAHLA.2.4.6ENM.KhanDepartment of Mathematics
COMSATS University Islamabad, Abbottabad Campus, PakistanM.ZeeshanCOMSATS University IslamabadS.IqbalDepartment of Mathematics
COMSATS University Islamabad, Islamabad Campus, PakistanJournal Article20210906In this paper, we introduce neutrosophic soft metric matrices and define some new operations on these matrices. Moreover, we develop an algorithm using neutrosophic soft metric matrices and apply it to a decision-making problem.http://jahla.hatef.ac.ir/article_136374_b654141ce4eb49916fc616db4631a0c2.pdfHatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60002420211101Generalized fuzzy sets with complexities and applications in decision-making problems8310813895410.52547/HATEF.JAHLA.2.4.7ENM.KhanDepartment of Mathematics
COMSATS University Islamabad, Abbottabad Campus, PakistanA.MukhtarCOMSATS University Islamabad, Abbottabad Campus, KPK, PakistanM.ZEESHANCOMSATS University IslamabadJournal Article20211018All the prevailing theories based on FS and their modifications, inconsistency, and uncertainties are involved in the form of truth grade TG whose value is also in the form of real numbers and certain user information may be lost and the decision-maker is affected by this. The principle of a complex fuzzy set (CFS) is a valuable procedure to manage inconsistent and awkward information genuine life troubles. CFS gives the TG against the value which is taken from the set of attributes in the form of a complex number whose real and unreal parts are limited to the unit interval. In this paper, we discussed some operations and formulas of set theory for complex fuzzy sets. We established the basic results of complex fuzzy sets using bounded sum, bounded product, bounded difference, simple difference, Cartesian product, algebraic product, and algebraic sums. We discussed particular examples of these operations and results. Moreover, a multicriteria decision-making (MCDM) technique is explored based on the elaborated complex fuzzy dominance matrix by using the complex fuzzy information. The application has been effectively demonstrated with numerical examples.http://jahla.hatef.ac.ir/article_138954_c3b2009baa3a5ef2899ed6c2e36b2cca.pdf