@article { author = {Figallo-Orellano, A. and Slagter, J.S.}, title = {Possibility operators over n-valued Gödel logic}, journal = {Journal of Algebraic Hyperstructures and Logical Algebras}, volume = {3}, number = {2}, pages = {1-15}, year = {2022}, publisher = {University of Hatef (Hatef College University)}, issn = {2676-6000}, eissn = {2676-6019}, doi = {10.52547/HATEF.JAHLA.3.2.1}, abstract = {In the area of fuzzy logic, expansions of these logics by $\Delta$ operator have been intensively studied; the interest of $\Delta$ operator is due to the fact that it presents a fuzzy behavior, the associated systems were studied in propositional and first-order level.  On the other hand, the possibility operators that define Łukasiewicz-Moisil algebras have been studied over different classes of algebras; these operators are known as Moisil's operators in the literature. One of these operators coincides with $\Delta$, showing there are other operators with fuzzy behavior.   In this paper, we present the study of Moisil's operators over an extension of a fuzzy logic; namely, n-valued Gödel logic, thus opening the possibility to explore more fuzzy operators.}, keywords = {n-valued Gödel logic,$Delta$ operator,Moisil operators,first-order logics}, url = {https://jahla.hatef.ac.ir/article_148521.html}, eprint = {https://jahla.hatef.ac.ir/article_148521_c9b1ad25ccdaf2f8533eaea572a15d08.pdf} } @article { author = {Smarandache, F.}, title = {Introduction to SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra}, journal = {Journal of Algebraic Hyperstructures and Logical Algebras}, volume = {3}, number = {2}, pages = {17-24}, year = {2022}, publisher = {University of Hatef (Hatef College University)}, issn = {2676-6000}, eissn = {2676-6019}, doi = {10.52547/HATEF.JAHLA.3.2.2}, abstract = {In this paper we recall our concepts of $n^{\text{th}}$-Power Set of a Set, SuperHyperOperation, SuperHyperAxiom, SuperHyperAlgebra, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom and Neutrosophic SuperHyperAlgebra.In general, in any field of knowledge, one actually encounters SuperHyperStructures (or more accurately $(m,n)$-SuperHyperStructures). }, keywords = {SuperHyperOperation,SuperHyperAlgebra,Neutrosophic SuperHyperAlgebra,SuperHyperStructures}, url = {https://jahla.hatef.ac.ir/article_146683.html}, eprint = {https://jahla.hatef.ac.ir/article_146683_a7416664bad37a295e2df085d780901c.pdf} } @article { author = {Yannick Lea, T. and Joseph, D. and Temgoua, E.}, title = {Residuated lattices derived from filters(ideals) in double Boolean algebras}, journal = {Journal of Algebraic Hyperstructures and Logical Algebras}, volume = {3}, number = {2}, pages = {25-45}, year = {2022}, publisher = {University of Hatef (Hatef College University)}, issn = {2676-6000}, eissn = {2676-6019}, doi = {10.52547/HATEF.JAHLA.3.2.3}, abstract = {Double Boolean algebras (dBas) are algebraic structures D = (D, v, ^, ‌, ', ⊥, T) of type (2, 2, 1, 1, 0, 0), introduced by Rudolf Wille to capture the equational theory of the algebra of protoconcepts. Our goal is an algebraic investigation of  dBas, based on similar results on Boolean algebras. In this paper, first we characterize filters on dBas as deductive systems and we give many characterization of primary filters(ideals). Second, for a given dBa, we show that the set of its filters F(D) (resp.ideals I(D)) is endowed with the structure of distributive pseudo-complemented lattices, Heyting algebras and residuated lattices. We finish by introducing the notions of annihilators and co-annihilators on dBas and investigate some relalted properties of them. We show that pseudo-complement of an ideal I (filter F) is the annihilator I* of I ( co-annihilator F*) and the set of annihilators (co-annihilators) forms a Boolean algebra. }, keywords = {Double Boolean algebra,Filter,ideal,primary,protoconcepts}, url = {https://jahla.hatef.ac.ir/article_147668.html}, eprint = {https://jahla.hatef.ac.ir/article_147668_6df71ee93581fe74427beecd82efd9e2.pdf} } @article { author = {Song, S.Z. and Jun, Y.B.}, title = {Lukasiewicz fuzzy positive implicative ideals in BCK-algebras}, journal = {Journal of Algebraic Hyperstructures and Logical Algebras}, volume = {3}, number = {2}, pages = {47-58}, year = {2022}, publisher = {University of Hatef (Hatef College University)}, issn = {2676-6000}, eissn = {2676-6019}, doi = {10.52547/HATEF.JAHLA.3.2.4}, abstract = {In BCK-algebras, the notion of Lukasiewicz fuzzy positive implicative ideal is introduced, and several properties are investigated. The relationship between Lukasiewicz fuzzy ideal and Lukasiewicz fuzzy positive implicative ideal is discussed, and characterizations of a Lukasiewicz fuzzy positive implicative ideal are considered. Conditions for a Lukasiewicz fuzzy ideal to be a Lukasiewicz fuzzy positive implicative ideal are provided, and conditions for the ∈-set, q-set and O-set to be positive implicative ideals are explored.}, keywords = {Lukasiewicz fuzzy set,Lukasiewicz fuzzy ideal,Lukasiewicz fuzzy positive implicative,∈-set,q-set,O-set}, url = {https://jahla.hatef.ac.ir/article_150122.html}, eprint = {https://jahla.hatef.ac.ir/article_150122_eadb1f3dcf4b30891d379b2d9818721b.pdf} } @article { author = {Bayrak Delice, D. and Erol, S.}, title = {On subhypergroups of cyclic hypergroups}, journal = {Journal of Algebraic Hyperstructures and Logical Algebras}, volume = {3}, number = {2}, pages = {59-68}, year = {2022}, publisher = {University of Hatef (Hatef College University)}, issn = {2676-6000}, eissn = {2676-6019}, doi = {10.52547/HATEF.JAHLA.3.2.5}, abstract = {The aim of this paper is to study of properties of subhypergroups of a cyclic hypergroup. It has been examined whether the theorems existing in cyclic groups exist in cyclic hypergroups. A characterization has been investigated to subhypergroups of a cyclic hypergroup be cyclic. }, keywords = {Cyclic hypergroup,subhypergroups}, url = {https://jahla.hatef.ac.ir/article_148102.html}, eprint = {https://jahla.hatef.ac.ir/article_148102_c9153feb8222459da4af5601fda4bd92.pdf} } @article { author = {Aaly Kologani, M. and Xin, X.L. and Jun, Y.B. and Mohseni Takallo, M.}, title = {Positive implicative equality algebras and equality algebras with some types}, journal = {Journal of Algebraic Hyperstructures and Logical Algebras}, volume = {3}, number = {2}, pages = {69-86}, year = {2022}, publisher = {University of Hatef (Hatef College University)}, issn = {2676-6000}, eissn = {2676-6019}, doi = {10.52547/HATEF.JAHLA.3.2.6}, abstract = {The notion of a positive implicative equality algebras are defined, and related properties are studied. Characterizations of a positive implicative equality algebra is investigated. Conditions for an equality algebra to be positive implicative are provided. Equality algebra with some types is considered, and several properties are investigated. Using equality algebra with some types, we characterize a commutative equality algebra and a positive implicative algebra. }, keywords = {(Commutative, positive implicative) equality algebra, &-equality algebra, equality algebra of type (m,n,i,j)}, url = {https://jahla.hatef.ac.ir/article_148301.html}, eprint = {https://jahla.hatef.ac.ir/article_148301_2c76b3baf6848a8d0f0dc689b1713291.pdf} } @article { author = {Mohammadzadeh, F. and Mohammadzadeh, E.}, title = {Nilpotent soft polygroups}, journal = {Journal of Algebraic Hyperstructures and Logical Algebras}, volume = {3}, number = {2}, pages = {87-97}, year = {2022}, publisher = {University of Hatef (Hatef College University)}, issn = {2676-6000}, eissn = {2676-6019}, doi = {10.52547/HATEF.JAHLA.3.2.7}, abstract = {In this paper, we introduce nilpotent soft (sub)polygroups. In addition, nilpotency of intersection, extended intersection, restricted union of two nilpotent soft polygroups are studied. Espesialy, a necessary and suficient condition between nilpotency of a polygroup and soft polygroups is obtained. Finally, we define two new soft polygroups (Sα)A∪{c} and (Qα)_A derived from a soft polygroup α_A and study on nilpotency of these structures. Also, we extend a soft homomorphism of groups to polygroups. This helps us to extend some properties of groups to polygroups.}, keywords = {Polygroups,nilpotent polygroups,soft polygroups}, url = {https://jahla.hatef.ac.ir/article_150212.html}, eprint = {https://jahla.hatef.ac.ir/article_150212_cc7d101a0734240780c69e0901efca22.pdf} }