Showing papers by "Bijan Davvaz published in 2022"
5 citations
TL;DR: In this paper , the authors studied ordered semigroups through some new substructures, namely quasi-filters and (m,n)-quasi-filter, and investigated properties of the new concepts, different examples, and relations between quasi-filter and quasi-ideal.
Abstract: Ordered semigroups are understood through their subsets. The aim of this article is to study ordered semigroups through some new substructures. In this regard, quasi-filters and (m,n)-quasi-filters of ordered semigroups are introduced as new types of filters. Some properties of the new concepts are investigated, different examples are constructed, and the relations between quasi-filters and quasi-ideals as well as between (m,n)-quasi-filters and (m,n)-quasi-ideals are discussed.
4 citations
TL;DR: In this paper , a generalization of both soft graph and hypergraph for important application in social media networking is presented, where various techniques and operations are provided including soft sub-hypergraph, extended union, extended intersection, cartesian product and complement with elucidatory examples.
Abstract: Soft set theory is a map of a set of parameters to the subsets of a universe which can be utilized to parametrically model the uncertainty. On the other hand, Graph (hypergraph) theory is used to simplify some practical problems. Inspired by these concepts, the notion of “soft hypergraph” is developed as the generalization of both soft graph and hypergraph for important application in social media networking. Based on the structure of soft hypergraph, various techniques and operations are provided including soft sub-hypergraph, extended union, extended intersection, cartesian product and complement with elucidatory examples. As per the current global spread of COVID, most of the national and international interactions and social affairs have been virtually conducted via social media networks, such as Skype, Microsoft Teams, WhatsApp, Telegram, Zoom, Instagram, WeChat, etc. For the purpose of Intelligent management of network systems, we use the “generalized soft hypergraph” to model the global e-communication networking of individuals in online platforms.
3 citations
TL;DR: In this article , the multi-fuzzy soft set and polygroup structure are combined to obtain a new soft structure called the multifuzzy polygroup, which is a special subcategory of hypergroups and is used in many branches of mathematics and basic sciences.
Abstract: The combination of two elements in a group structure is an element, while, in a hypergroup, the combination of two elements is a non-empty set. The use of hypergroups appears mainly in certain subclasses. For instance, polygroups, which are a special subcategory of hypergroups, are used in many branches of mathematics and basic sciences. On the other hand, in a multi-fuzzy set, an element of a universal set may occur more than once with possibly the same or different membership values. A soft set over a universal set is a mapping from parameters to the family of subsets of the universal set. If we substitute the set of all fuzzy subsets of the universal set instead of crisp subsets, then we obtain fuzzy soft sets. Similarly, multi-fuzzy soft sets can be obtained. In this paper, we combine the multi-fuzzy soft set and polygroup structure, from which we obtain a new soft structure called the multi-fuzzy soft polygroup. We analyze the relation between multi-fuzzy soft sets and polygroups. Some algebraic properties of fuzzy soft polygroups and soft polygroups are extended to multi-fuzzy soft polygroups. Some new operations on a multi-fuzzy soft set are defined. In addition to this, we investigate normal multi-fuzzy soft polygroups and present some of their algebraic properties.
3 citations
TL;DR: In this article , the relationship between algebraic hyperstructures and linear Diophantine fuzzy sets through polygroups has been discussed, and some properties of these properties have been characterized in relation to level and ceiling sets.
Abstract: Linear Diophantine fuzzy sets were recently introduced as a generalized form of fuzzy sets. The aim of this paper is to shed the light on the relationship between algebraic hyperstructures and linear Diophantine fuzzy sets through polygroups. More precisely, we introduce the concepts of linear Diophantine fuzzy subpolygroups of a polygroup, linear Diophantine fuzzy normal subpolygroups of a polygroup, and linear Diophantine anti-fuzzy subpolygroups of a polygroup. Furthermore, we study some of their properties and characterize them in relation to level and ceiling sets.
2 citations
TL;DR: The determination of patients medical status where diseases and patients are represented as q-rung orthopair fuzzy values in the feature space of some clinical manifestations is discussed.
2 citations
TL;DR: The notion of hypergraphs, introduced around 1960, is a generalization of that of graphs and one of the initial concerns was to extend some classical results of graph theory as mentioned in this paper .
Abstract: The notion of hypergraphs, introduced around 1960, is a generalization of that of graphs and one of the initial concerns was to extend some classical results of graph theory. In this paper, we present some connections between hypergraph theory and hypergroup theory. In this regard, we construct two hypergroupoids by defining two new hyperoperations on ℍ, the set of all hypergraphs. We prove that our defined hypergroupoids are commutative hypergroups and we define hyperrings on ℍ by using the two defined hyperoperations. Moreover, we study the fundamental group, complete parts, automorphism group and strongly regular relations of one of our hypergroups.
2 citations
TL;DR: In this article , it was shown that a fuzzy set of an ordered semigroup is a fuzzy filter if and only if its complement is a prime generalized fuzzy [formula: see text]-ideal.
Abstract: The aim of this paper is to generalize the results related to fuzzy filters of ordered semigroups. In this regard, the concept of fuzzy [Formula: see text]-filters of ordered semigroups is initiated, nontrivial examples are presented, and its properties are investigated. It is known that a fuzzy set of an ordered semigroup is a fuzzy filter if and only its complement is a fuzzy prime ideal. As a generalization of the latter result, it is proved that a fuzzy set of an ordered semigroup is a fuzzy [Formula: see text]-filter if and only if its complement is a prime generalized fuzzy [Formula: see text]-ideal. Furthermore, it is shown that in an [Formula: see text]-regular semigroup, fuzzy [Formula: see text]-filters and fuzzy bi-filters coincide.
1 citations
TL;DR: This article presents the notion of multi-polar fuzzy sets in ordered semihypergroups and defines multi- polar fuzzy hyperideal (bi-hyperideals, quasi hyperideals) in an ordered semikhypergroup.
Abstract: An multi-polar fuzzy set is a robust mathematical model to examine multipolar, multiattribute, and multi-index data. The multi-polar fuzzy sets was created as a useful mechanism to portray uncertainty in multiattribute decision making. In this article, we consider the theoretical applications of multi-polar fuzzy sets. We present the notion of multi-polar fuzzy sets in ordered semihypergroups and define multi-polar fuzzy hyperideals (bi-hyperideals, quasi hyperideals) in an ordered semihypergroup. Relations between multi-polar fuzzy hyperideals, multi-polar fuzzy bi-hyperideals and multi-polar fuzzy quasi hyperideals are discussed.
1 citations
TL;DR: In this article , the authors demonstrate that L-group theory is capable of capturing most of the refined ideas and concepts of classical group theory, and demonstrate this by extending the notion of subnormality to the L-setting and investigating its properties.
Abstract: The main focus in this work is to establish that L-group theory, which uses the language of functions instead of formal set theoretic language, is capable of capturing most of the refined ideas and concepts of classical group theory. We demonstrate this by extending the notion of subnormality to the L-setting and investigating its properties. We develop a mechanism to tackle the join problem of subnormal L-subgroups. The conjugate L-subgroup as is defined in our previous paper [4] has been used to formulate the concept of normal closure and normal closure series of an L-subgroup which, in turn, is used to define subnormal L-subgroups. Further, the concept of subnormal series has been introduced in L-setting and utilized to establish the subnor-mality of L-subgroups. Also, several results pertaining to the notion of subnormality have been established. Lastly, the level subset characterization of a subnormal L-subgroup is provided after developing a necessary mechanism. Finally, we establish that every subgroup of a nilpotent L-group is subnormal. In fact, it has been exhibited through this work that L-group theory presents a modernized approach to study classical group theory.
1 citations
TL;DR: In this article , the authors used the natural equivalence relation on the set of fuzzy (normal) subgroups of finite groups, which has a consistent group theoretical foundation, to account for the number of fuzzy subgroups.
30 Sep 2022-Communications Faculty of Sciences University of Ankara. Series A1: mathematics and statistics
TL;DR: In this article , the inverse function continuity condition is removed for soft topological polygroups and the inverse functions are allowed to have more freedom of action in soft topology polygroups.
Abstract: By removing the condition that the inverse function is continuous in soft topological polygroups, we will have less constraint to obtain the results. We offer different definitions for soft topological polygroups and eliminate the inverse function continuity condition to have more freedom of action.
TL;DR: In this paper , the concepts of fundamental relation, complete part and complete closure are studied regarding to ( R, S )-hyper bi-modules and some properties of these bi-modalities are investigated.
Abstract: . In this article, we investigate several aspects of ( R, S )-hyper bi-modules and describe some their properties. The concepts of fundamental relation, completes part and complete closure are studied regarding to ( R, S )-hyper bi-modules. In particular, we show that any complete ( R, S )-hyper bi-module has at least an identity and any element has an inverse. Finally, we obtain a few results related to the heart of ( R, S )-hyper bi-modules.
TL;DR: This paper studies constacyclic codes over finite Krasner hyperfields in which they are characterized by their generating polynomial, and studies the dual of these codes by finding their parity check polynomials.
Abstract: The class of constacyclic codes plays an important role in the theory or error-correcting codes. They are considered as a remarkable generalization of cyclic codes. In this paper, we study constacyclic codes over finite Krasner hyperfields in which we characterize them by their generating polynomial. Moreover, we study the dual of these codes by finding their parity check polynomial.
TL;DR: The notion of ternary (cid:2) -semirings as discussed by the authors is a generalization of semirings, and it has been shown that there is a covariant function for the category of Relocation-ternary Semirings.
Abstract: The notion of ternary (cid:2) -semihyperrings is a generalization of semirings. In a ternary (cid:2) - semihyperring, addition is a hyperoperation and multiplication is a ternary hyperoperation. Our main purpose of this paper is to introduce regular and simple ternary (cid:2) -semihyperrings and study the notions of right (left) fundamental semirings, and we show that there is a covariantfunctorbetweenthecategoryofrelocationternary (cid:2) -semihyperringsandsemirings.
TL;DR: In this paper , the transfer of the property of coherence to the bi-amalgamation module M⋈φ,ψ(JN, J'P) was investigated.
Abstract: In this paper, we introduce and investigate the transfer of the property of coherence to the bi-amalgamation module M⋈φ,ψ(JN, J'P). We provide necessary and sufficient conditions for M⋈φ,ψ(JN, J'P) to be a coherent module.
TL;DR: In this article , the authors define a soft topology including concepts such as soft neighborhood, soft continuity, soft compact, soft connected, soft Hausdorff space and their relationship with soft continuous functions in soft topological polygroups.
Abstract: Soft topological polygroups are defined in two different ways. First, it is defined as a usual topology. In the usual topology, there are five equivalent definitions for continuity, but not all of them are necessarily established in soft continuity. Second it is defined as a soft topology including concepts such as soft neighborhood, soft continuity, soft compact, soft connected, soft Hausdorff space and their relationship with soft continuous functions in soft topological polygroups.
25 Dec 2022
TL;DR: In this paper , a Jacobson topology on the set of primitive hyperideals of a hyperring R and its corresponding hyperstructure space is studied. But it is not shown how to obtain a topological relation between the hyperring and R itself.
Abstract: . We introduce primitive hyperideals of a hyperring R and show relations with R itself, and with maximal and prime hyperideals of R . We endow a Jacobson topology on the set of primitive hyperideals of R and study topological properties of the corresponding hyperstructure space.
DOI•
01 Jan 2022TL;DR: In this paper, the notions of pseudo-BL algebras and pseudo-MV algesias are introduced, which are generalizations of derivations of a BL-algebra.
Abstract: Pseudo-BL algebras are a natural generalization of BL-algebras and of pseudo-MV algebras.In this paper the notions of five different types of derivations on a pbl as generalizations of derivations of a BL-algebra are introduced. Moreover, as an extension of derivations of a pbl , the notions of $(varphi , psi)$-derivations are defined on these types. Finally, several related properties are discussed.
TL;DR: In this paper , the concept of near Krasner hyperrings was introduced and investigated on a nearness approximation space. And the concepts of near subhyperring, near hyperideal, near homomorphism and near homomorphic hyperring were defined.
Abstract: Krasner hyperrings are a generalization of rings. Indeed, in a Krasner hyperring the addition is a hyperoperation, while the multiplication is an ordinary operation. On the other hand, a generalization of rough set theory is the near set theory. Now, in this paper we are interested in combining these concepts. We study and investigate the notion of near Krasner hyperrings on a nearness approximation space. Also, we define near subhyperring, near hyperideal, near homomorphism and prove some results and present several examples in this respect
TL;DR: In this article , the generalized centroid C of a semiprime hyperring R is shown to be a regular hyperring, and if C is a hyperfield, then R is a prime hyperring.
Abstract: Abstract In this paper, the notion of generalized centroid is applied to hyperrings. We show that the generalized centroid C of a semiprime hyperring R is a regular hyperring. Also, we show that if C is a hyperfield, then R is a prime hyperring.
TL;DR: This paper studies constacyclic codes over Krasner hyper-lds in which they are characterized by their generating polynomial, and studies the dual of these codes by studying their parity check polynomials.
Abstract: . The class of constacyclic codes plays an important role in the theory or error-correcting codes. They are considered as a remarkable generalization of cyclic codes. In this paper, we study constacyclic codes over finite Krasner hyperfields in which we characterize them by their generating polynomial. Moreover, we study the dual of these codes by finding their parity check polynomial.
TL;DR: In this article , the concept of a near edge Cayley graph was introduced, which is an extended study of rough approximations in Cayley graphs by using more than one equivalence relations.
Abstract: In this paper, we study near approximations in Cayley graphs, which are an extended study of rough approximations in Cayley graphs by using more than one equivalence relations. Furthermore, we introduce the notion of a near edge Cayley graphs, expanded to the near vertex pseudo-Cayley graphs and near pseudo-Cayley graphs. Some theorems dealing with the properties discussed are derived. We illustrate some examples especially in cyclic groups for simplification in graphs visualization.