Journal of Algebraic Hyperstructures and Logical Algebras
https://jahla.hatef.ac.ir/
Journal of Algebraic Hyperstructures and Logical Algebrasendaily1Mon, 01 May 2023 00:00:00 +0430Mon, 01 May 2023 00:00:00 +0430Positive implicative BE-filters of BE-algebras based on Lukasiewicz fuzzy sets
https://jahla.hatef.ac.ir/article_170311.html
Lukasiewicz fuzzy set is applied to positive implicative filter of BE-algebra. The notion of positive implicative Lukasiewiczfuzzy BE-filters is introduced, and its properties are investigated. The relationship between fuzzy positive implicative BE-filter and positive implicative Lukasiewicz fuzzy BE-filter is discussed, and conditions under which Lukasiewicz fuzzy BE-filter can be positive implicative Lukasiewicz fuzzy BE-filter are explored. Characterizations of positive implicative Lukasiewicz fuzzy BE-filter are provided. Conditions for Lukasiewicz fuzzy set to be positive implicative Lukasiewicz fuzzy BE-filter are considered. Conditions are found where E-set, q-set, and O-set of the Lukasiewicz fuzzy set can be positive implicative BE-filter.&nbsp;Modal operators on BCK-algebras
https://jahla.hatef.ac.ir/article_178610.html
In this paper, modal operators on BCK-algebras, especially BCK-algebras with condition (S) are introduced and several properties and characterizations of them are investigated. Also, it is investigated under what conditions these modal&nbsp; operators form a lattice. Furthermore, some special modal operators are introduced and their properties and&nbsp; characterizations of them are obtained, especially in some classes of BCK-algebras such as positive implicative BCK- algebras.On L-fuzzy approximation operators and L-fuzzy relations on residuated lattices
https://jahla.hatef.ac.ir/article_180761.html
We consider properties of $L$-fuzzy relations and $L$-normal operators for a residuated lattice $L$ in detail and show that the class $\mathcal{R}_L(U)$ of all $L$-fuzzy relations on $U$ and the class $\mathcal{N}_L(U)$ of all $L$-normal operators are residuated lattices and they are isomorphic as lattices. Moreover, we prove that for any $L$-normal operators $\mathcal{F}$, it is reflexive (or transitive) if and only if the $L$-fuzzy relation $R_{\mathcal{F}}$ induced by $\mathcal{F}$ is reflexive (or transitive) respectively.Integral and obstinate prefilters of hyper EQ-algebras
https://jahla.hatef.ac.ir/article_183210.html
The main goal of this paper is to introduce integral hyper EQ-algebras, integral (pre)filters and obstinate (pre)filters of hyper EQ-algebras. In the following, some characterizations of these (pre)filters in hyper EQ-algebras are investigated and it is proved that the quotient hyper EQ-algebras induced by a filter F is an integral hyper EQ-algebra if and only if F is an integral filter. Moreover, the concept obstinate (pre)filter in hyper EQ-algebras is introduced and some related properties are provided. Finally, the relationship among obstinate (pre)filters and some type of other (pre)filters such integral, maximal, (positive) implicative and fantastic (pre)filters in hyper EQ-algebras are studied.Quotient bipolar fuzzy soft sets of hypervector spaces and bipolar fuzzy soft sets of quotient hypervector spaces
https://jahla.hatef.ac.ir/article_183323.html
In this paper, two related quotient structures are investigated utilizing the concept of coset. At first, a new hypervector space F/V = (F/V,\circ,\circledcirc,K) is created, which is composed of all cosets of a bipolar fuzzy soft set (F;A) over a hypervector space V . Then it will be shown that dim F/V = dim V/W, where the quotient hypervector space V/W includes all cosets of an especial subhyperspace W of V. Also, three bipolar fuzzy soft sets over the quotient hypervector space V/W are presented and in this way some new bipolar fuzzy soft hypervector spaces are defined.Ideals of roughness in L-algebras
https://jahla.hatef.ac.ir/article_184525.html
Rough is an exceptional mathematical tool for effectively analyzing and addressing the complexities of vague action descriptions in decision problems. This paper explores the concept of an L-algebra, which leads to the introduction of&nbsp; lower and upper approximations. The properties of these approximations are also discussed and elucidated. Furthermore, it is proven that the lower and upper approximations serve as interior and closure operators, respectively. Additionally, by employing A-lower and A-upper approximations, this paper presents and examines conditions for a nonempty&nbsp; subset to be definable. Furthermore, we investigated the circumstances under which the A-lower and A-upper approximations can be rough ideals. Finally, we define an operation &lrm;" --&gt;"&lrm; on the set of all upper approximations of L&nbsp; &lrm;and &lrm;prove &lrm;that &lrm;it &lrm;is &lrm;made &lrm;an &lrm;&lrm;L-algebra.&nbsp;L-fuzzy algebraic substructure
https://jahla.hatef.ac.ir/article_184655.html
This article aims to provide a method for defining $L$-fuzzy algebraic substructures on general algebras. Concretely, the&nbsp; properties of L-fuzzy sets are first reviewed, and their representations are then provided. Next, algebraic substructures&nbsp; are generalised as the closure systems on the power set of the algebra, and the properties of the prime and maximal elements in the above closure system are investigated. Based on these facts, L-fuzzy algebraic substructures with respect to the closure system are defined and studied. Two equivalence characterisations of the sup property of the ordered set L are provided using L-fuzzy substructures. Similarly, some properties of L-fuzzy prime and maximal substructures with respect to the closure system are discussed. Finally, to demonstrate the broad applicability of the theory of L-fuzzy&nbsp; algebraic substructures, the theory is applied to some specific algebraic structures, such as groups and pseudo MV-algebras.Interval valued (α, β)-fuzzy hyperideals in Krasner (m, n)-hyperrings
https://jahla.hatef.ac.ir/article_170310.html
In this paper, the notion of quasicoincidence of a fuzzy interval valued with an interval valued fuzzy set, which generalizes the concept of quasicoincidence of a fuzzy point in a fuzzy set is concentrated. Based on the idea, we study the concept of interval valued (&alpha;, &beta;)-fuzzy hyperideals in Krasner (m, n)-hyperrings. In particular, some fundamental aspects of interval valued &nbsp;(E, EVq)-fuzzy hyperideals will be considered. Moreover, we examine the notion of implication-based interval valued fuzzy hyperideals in a Krasner (m, n)-hyperring.&nbsp;Relations between L-algebras and other logical algebras
https://jahla.hatef.ac.ir/article_166948.html
In this paper, by considering the notion of L-algebra, &nbsp;we show that there are relations between L-algebras and some of other logical algebras such as residuated lattices, MTL-algebras, BL-algebras, MV-algebras, BCK-algebras, equality algebras, EQ-algebras and Hilbert algebras. The &nbsp;aim of this paper is to find &nbsp;under what conditions L-algebras are equivalent to these logical algebras.Block code on L-algebras
https://jahla.hatef.ac.ir/article_170471.html
By using the notion of L-algebras as an important part of the ordered algebra, we introduce the notions of block code, x-function and x-subsets on an arbitrary L-algebra. Then some related properties and examples are provided. Also, by&nbsp; using these notions, we define an equivalence relation on L-algebra and we introduce a new order on the generated code based on L-algebras. Finally, we will provide a method which allows us to find an L-algebra starting from a given arbitrary binary block code.&nbsp;Zipped coherent quantales
https://jahla.hatef.ac.ir/article_171997.html
The aim of this paper is to define an abstract quantale framework for extending some properties of the zip rings (studied by Faith, Zelmanowitz, etc.) and the weak zip rings (defined by Ouyang). By taking as prototype the quantale of ideals of a zip ring (resp. a weak zip ring) we introduce the notion of zipped quantale (resp. weakly zipped quantale). The zipped quantales also generalize the zipped frames, defined by Dube and Blose in a recent paper. We define the zip (bounded&nbsp; distributive) lattices and we prove that a coherent quantale A is weakly zipped iff the reticulation L(A) of A is a zip lattice.&nbsp; From this result we obtain the following corollary: the coherent quantale A is weakly zipped iff the frame R(A) of the&nbsp; radical elements of A is zipped. Such theorems allow us to extend to quantale framework a lot of results obtained by&nbsp; Dube and Blose for the zipped frames and for the weak zip rings.&nbsp;Some applications of maximal product in RL-graphs
https://jahla.hatef.ac.ir/article_172284.html
This research targets the investigation of characteristics within the maximal product of two RL-graphs by scrutinizing&nbsp; particular types of RL-graphs. Our first step in this quest entails introducing RL-graph concepts, followed by defining&nbsp; what constitutes a strong RL-graph, further elucidated by a practical example. Subsequently, we lay out the connection&nbsp; between RL-graphs and their maximal products. In particular, a theorem establishes that two RL-graphs are regular if&nbsp; their maximal product maintains regularity, and a parallel rule applies to &alpha;-regular RL-graphs. Contrarily, the reverse is&nbsp; not inherently true, a claim supported by a specific example. Nonetheless, by incorporating an additional condition, we&nbsp; validate the converse. Lastly, we assert that two RL-graphs are connected only if their maximal product is also a&nbsp; connected RL-graph. In conclusion, the maximal product of two RL-graphs holds potential in modeling societal health&nbsp; metrics and road accident rates.&nbsp;Mathematical Model for some Chemical Redox Reactions
https://jahla.hatef.ac.ir/article_177214.html
Algebraic hyperstructures have many applications in various sciences. The main purpose of this paper is to provide a new&nbsp; application of weak hyperstructures in Chemistry. The Motivation for the study of hyperstructures comes from chemical&nbsp; reactions. By hyperstructures theory, we provide mathematical models for chemical reactions. We study chemical&nbsp; hyperstructures of standard reduction potentials for consecutive oxidation states of elements of Cm; Er; Pm; Mg; Tm; Au and&nbsp; Cf.Some results on graded prime and primary hyperideals
https://jahla.hatef.ac.ir/article_177303.html
&lrm;Let G be a group with identity e and R be a multiplicative hyperring&lrm;. &lrm;W&lrm;e introduce the concept of G-graded multiplicative hyperring R and present some &lrm;new&lrm; results and examples&lrm;. &lrm;This &lrm;&lrm;&lrm;&lrm;&lrm;article &lrm;aim &lrm;is &lrm;&lrm;&lrm;to &lrm;introduce &lrm;and &lrm;study&lrm; &lrm;&lrm;&lrm;&lrm;&lrm;&lrm;&lrm;&lrm;&lrm;graded &lrm;&lrm;prime &lrm;and&nbsp; &lrm;&lrm;graded &lrm;&lrm;p&lrm;rimary &lrm;hy&lrm;perideals &lrm;which &lrm;are&lrm; &lrm;different &lrm;generalizations &lrm;of&lrm; &lrm;&lrm;prime &lrm;and&lrm;&lrm; &lrm;&lrm;&lrm;&lrm;p&lrm;rimary &lrm;hyperideals. &lrm;Several&lrm; &lrm;basic&nbsp; &lrm;properties&lrm;, &lrm;examples and characterizations of graded &lrm;prime (graded &lrm;primary)&lrm; hyperideals of a graded multiplicative&nbsp; hyperring R are &lrm;presented &lrm;such &lrm;as &lrm;investigating&lrm; of this structure under homogeneous components&lrm;, &lrm;graded hyperring&nbsp; homomorphisms&lrm;, &lrm;quotient graded hyperrings and fundamental relations&lrm;.&nbsp;Hausdorff (quasi)topological MV-algebras
https://jahla.hatef.ac.ir/article_177299.html
In this paper, the relations between separation axioms and (quasi)topological MV-algebras are studied. It is proved that&nbsp; T0-spaces and (T1) Hausdorff spaces are equivalent in (quasi) topological MV-algebras. Also, some topologies on MV-algebras are generated by ideals, filters and prefilters. It is shown that the MV-algebras equipped with these topologies&nbsp; are (para)topological MV-algebras and (T0) normal spaces. In addition, some conditions are derived for locally compact&nbsp; Hausdorff MV-algebras to make them into normal paratopological MV-algebras. Finally, quotient MV-algebras are&nbsp; studied to get a Hausdorff topological quotient MV-algebra.&nbsp;