Journal of Algebraic Hyperstructures and Logical Algebras
Volume:4 Issue: 1, Winter 2023

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.

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 (α, β)-fuzzy hyperideals in Krasner (m, n)-hyperrings. In particular, some fundamental aspects of interval valued  (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.

In this paper, by considering the notion of L-algebra,  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  aim of this paper is to find  under what conditions L-algebras are equivalent to these logical algebras.

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  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.

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  distributive) lattices and we prove that a coherent quantale A is weakly zipped iff the reticulation L(A) of A is a zip lattice.  From this result we obtain the following corollary: the coherent quantale A is weakly zipped iff the frame R(A) of the  radical elements of A is zipped. Such theorems allow us to extend to quantale framework a lot of results obtained by  Dube and Blose for the zipped frames and for the weak zip rings.

This research targets the investigation of characteristics within the maximal product of two RL-graphs by scrutinizing  particular types of RL-graphs. Our first step in this quest entails introducing RL-graph concepts, followed by defining  what constitutes a strong RL-graph, further elucidated by a practical example. Subsequently, we lay out the connection  between RL-graphs and their maximal products. In particular, a theorem establishes that two RL-graphs are regular if  their maximal product maintains regularity, and a parallel rule applies to α-regular RL-graphs. Contrarily, the reverse is  not inherently true, a claim supported by a specific example. Nonetheless, by incorporating an additional condition, we  validate the converse. Lastly, we assert that two RL-graphs are connected only if their maximal product is also a  connected RL-graph. In conclusion, the maximal product of two RL-graphs holds potential in modeling societal health  metrics and road accident rates.