Hatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60002120210201Cover-Vol 2- Issue 1- February 2021127926ENJournal Article20210308http://jahla.hatef.ac.ir/article_127926_3db8194d0cc71342f10ab4547b43b5e1.pdfHatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60002120210201The Belluce lattice associated with a bounded BCK -algebra11612163810.52547/HATEF.JAHLA.2.1.1END.BusneagFaculty of Sciences, Department of Mathematics, University of Craiova, Craiova, RomaniaD.PiciuFaculty of Sciences, Department of Mathematics, University of Craiova, Craiova, RomaniaM.IstrataFaculty of Sciences, Department of Mathematics, University of Craiova, Craiova, RomaniaJournal Article20201229In this paper, we introduce the notions of Belluce lattice associated with a bounded $BCK$-algebra and reticulation of a bounded $BCK$-algebra. To do this, first, we define the operations $curlywedge ,$ $curlyvee $ and $sqcup $ on $BCK$-algebras and we study some algebraic properties of them. Also, for a bounded $BCK$-algebra $A$ we define the Zariski topology on $ Spec(A)$ and the induced topology $tau _{A,Max(A)}$ on $Max(A)$. We prove $(Max(A),tau_{A,Max(A)})$ is a compact topological space if $A$ has Glivenko property. Using the open and the closed sets of $Max(A)$, we define a congruence relation on a bounded $BCK$-algebra $A$ and we show $L_{A}$, the quotient set, is a bounded distributive lattice. We call this lattice the Belluce lattice associated with $A.$ Finally, we show $(L_{A},p_{A})$ is a reticulation of $A$ (in the sense of Definition ref{d7}) and the lattices $L_{A}$ and $S_{A}$ are isomorphic. http://jahla.hatef.ac.ir/article_121638_52a4d7eea12e1cb5a876c0b3ff04f800.pdfHatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60002120210201Crossing cubic ideals of BCK/BCI-algebras173112789910.52547/HATEF.JAHLA.2.1.2ENY.B.JunDepartment of Mathematics Education, Gyeongsang National University, Jinju 52828, KoreaS.Z.SongDepartment of Mathematics, Jeju National University, Jeju 63243, KoreaJournal Article20210307The notions of a crossing cubic ideal in a BCK/BCI-algebra, a closed crossing cubic ideal in a BCI-algebra, and a crossing cubic $circ$-subalgebra of a BCK-algebra with the condition (S) are introduced, and several properties are investigated. The relationship between them is established. Conditions for a crossing cubic structure to be a closed crossing cubic ideal are provided. Conditions under which crossing cubic ideals are closed are explored. Characterizations of crossing cubic ideals are discussed. The translation of crossing cubic subalgebras and crossing cubic ideals are studied. Conditions for the translation of a crossing cubic structure to be a crossing cubic subalgebra (ideal) are provided, and its characterization is established. http://jahla.hatef.ac.ir/article_127899_d9d3042bfd7f48bb6abea4a21a254c31.pdfHatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60002120210201Tense and dynamic algebras related to GFA334612710010.52547/HATEF.JAHLA.2.1.3ENKh.AbolpourDepartment of Mathemathics, Shiraz Branch, Islamic Azad University, Shiraz, IranM.M.ZahediDepartment of Mathemathics, Graduate University of Advanced Technology, Kerman, IranM.ShamsizadehKhatam Alanbia University of Technology, Behbahan, IranJournal Article20210226The present paper is an attempt to suggest and scrutinize tense operators in the dynamic logic $textbf{B}$ which is regarded as a set of propositions about the general fuzzy automaton $ tilde{F} $, in which its underlying structure has been a bounded poset. Here, the operators $ T_{delta}, P_{delta}, H_{delta}$ and $ F_{delta} $ are proposed regardless of what propositional connectives the logic comprises. For this purpose, the axiomatization of universal quantifiers is applied as a starting point and these axioms are modified. In this study, firstly, we demonstrate that the operators can be identified as modal operators and the pairs $ (T_{delta},P_{delta}) $ are examined as the so-called dynamic pairs. In addition, constructions of these operators are attained in the corresponding algebra and in the following a transition frame is suggested. Besides, the problem of finding a transition frame is solved in the case when the tense operators are given. Specifically, this study shows that the tense algebra $ textbf{B} $ is representable in its Dedekind-MacNeille completion. Representation theorems for dynamic and tense algebra are explicated in details in the related given theorems.http://jahla.hatef.ac.ir/article_127100_9b1bdd27cdcb2dfb1e4146b534417f0b.pdfHatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60002120210201On hyper BI-algebras476712790010.52547/HATEF.JAHLA.2.1.4ENS.NiazianFaculty of Medicine, Tehran Medical Sciences, Islamic Azad University, Tehran, IranJournal Article20210307In this paper, we introduce the notion of hyper BI-algebra and investigate some properties of it. Also, we state and prove some theorems which determine the relationship among $R/ C/ D/ T$ and V-hyper BI-algebras under some conditions. Then we study the relation among hyper BI-algebra with some of other hyper logical algebras such as hyper BCI/BCK/K/B/BCC-algebras and show that under which condition these hyper structures coincide. In addition, we define hyper subalgebra and (weak) ideal of a hyper BI-algebra and obtain some results and the relation between them. Finally, we construct the quotient structure of hyper BI-algebra and examine the isomorphism theorems.http://jahla.hatef.ac.ir/article_127900_6cc984dde904b40f9d72054206a47e6b.pdfHatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60002120210201Commutative MBJ-neutrosophic ideals of $BCK$-algebras698112790110.52547/HATEF.JAHLA.2.1.5ENY.B.JunDepartment of Mathematics Education, Gyeongsang National University, Jinju 52828, KoreaM.Mohseni TakalloDepartment of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran0000-0002-4113-3657Journal Article20210307The notion of commutative MBJ-neutrosophic ideal is introduced, and several properties are investigated. Relations between MBJ-neutrosophic ideal and commutative MBJ-neutrosophic ideal are considered. Characterizations of commutative MBJ-neutrosophic ideal are discussed.http://jahla.hatef.ac.ir/article_127901_3938ad64fbc2847e4687ae2528345c24.pdfHatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60002120210201Fuzzy n-fold obstinate and maximal (pre)filters of EQ-algebras839812826710.52547/HATEF.JAHLA.2.1.6ENB.Ganji SaffarDepartment of Mathematics
Faculty of Mathematical Sciences
Alzahra University
Tehran
Iran0000000257055331Journal Article20210316In this paper, we defined the concepts of fuzzy $n$-fold obstinate (pre)filter and maximal fuzzy (pre)filter of $EQ$-algebras and discussed the properties of them. We show that every maximal fuzzy (pre)filter of $mathcal{LomE}$ is normalized and takes only the values ${0, 1}$. Also we show that in good $EQ$-algebra, if $m$ is a normalized fuzzy (pre)filter of $mathcal{LomE}$, then $m$ is a fuzzy $n$-fold obstinate (pre)filter of $mathcal{LomE}$ if and only if every normalized fuzzy (pre)filter of quotient algebra $mathcal{LomE}/m$ is a fuzzy $n$-fold obstinate (pre)filter of $mathcal{LomE}/m$.<br /> Also, we verify relation between fuzzy obstinate $n$-fold (pre)filters and other fuzzy (pre)filters of $EQ$-algebras. http://jahla.hatef.ac.ir/article_128267_4a8f7927bf30d1bb537601f0f14e96e1.pdfHatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60002120210201A graph associated to a polygroup with respect to an automorphism9911212826810.52547/HATEF.JAHLA.2.1.7ENE.MohammadzadehDepartment of Mathematics, Faculty of Science, Payame Noor University, Tehran, IranJournal Article20210316In this paper, we introduce and study, $zeta^alpha(P)$, the $alpha$-center of a polygroup $(P, cdot )$ with respect to an automorphism $alpha$. Then we associate to $P$ a graph $Gamma^alpha_{P}$, whose vertices are elements of $P setminus zeta^alpha(P)$ and $x$ connected to $y$ by an edge in case $x cdot y cdot omega neq y cdot x^alpha cdot omega $ or $y cdot x cdot omega neq x cdot y^alpha cdot omega$, where $omega $ is the heart of $P$. We obtain some basic properties of this graph. In particular, we prove that if $zeta^alpha(P) neq P$, then $dim(Gamma^alpha _{P})=2$. Moreover, we define a weak $alpha$-commutative polygroup to state that if $Gamma^alpha_{H} cong Gamma^beta_{K}$ and $H$ is a weak $alpha$-commutative, then $ K$ is a weak $beta $-commutative. Also, we show that if $H$ and $K$ are two polygroups such that $Gamma^alpha_{H} cong Gamma^beta_{K}$, then for some automorphisms $eta$ and $lambda$, $Gamma^eta_{H times A} cong Gamma^lambda_{K times B}$, where $A$ and $B$ are two weak commutative polygroups.http://jahla.hatef.ac.ir/article_128268_56f10d768f4215a0c28ba8ab4b515e4a.pdfHatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60002120210201Persian translation of abstracts113121128269ENJournal Article20210316http://jahla.hatef.ac.ir/article_128269_f4212b43538810b69270a80c95335d69.pdf