Journal of Algebraic Hyperstructures and Logical Algebras
https://jahla.hatef.ac.ir/
Journal of Algebraic Hyperstructures and Logical Algebrasendaily1Wed, 01 Feb 2023 00:00:00 +0330Wed, 01 Feb 2023 00:00:00 +0330Positive 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;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;