Regularity of Intuitionistic Fuzzy Relations on Hypergroupoids

Cristea, Irina

doi:10.2478/auom-2014-0009

Cited by 10 publications

(8 citation statements)

References 17 publications

(18 reference statements)

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“…The links between binary (or n-ary) relations or fuzzy relations and algebraic hyperstructures represent currently an important line of research, developed both from a theoretical point of view [24][25][26][27] and also for the applications in social science [28], code theory [29], graph theory [30], automata theory [22,31], etc. In this article, motivated by the special interdependencies existing between the variables used for the weather forecasting, we introduced a new type of relation, called dependence relations, and started the study of their algebraic properties.…”

Section: Discussionmentioning

confidence: 99%

Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures

2019

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The aim of this paper is to study, from an algebraic point of view, the properties of interdependencies between sets of elements (i.e., pieces of secrets, atmospheric variables, etc.) that appear in various natural models, by using the algebraic hyperstructure theory. Starting from specific examples, we first define the relation of dependence and study its properties, and then, we construct various hyperoperations based on this relation. We prove that two of the associated hypergroupoids are H v -groups, while the other two are, in some particular cases, only partial hypergroupoids. Besides, the extensivity and idempotence property are studied and related to the cyclicity. The second goal of our paper is to provide a new interpretation of the dependence relation by using elements of the theory of algebraic hyperstructures.

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Section: Discussionmentioning

confidence: 99%

Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures

2019

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“…He defined the hypergroups as a generalization of groups in 1934. Since then, algebraic hyperstructures have been investigated by many researchers with numerous applications in both pure and applied sciences [11,12,13,14,15,18,27,31,37]. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set.…”

Section: Introductionmentioning

confidence: 99%

2-Prime Hyperideals

Anbarloei

2021

Preprint

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Multiplicative hyperrings are an important class of algebraic hyperstructures which generalize rings further to allow multiple output values for the multiplication operation. Let R be a commutative multiplicative hyperring. A proper hyperideal I of R is called 2-prime if x • y ⊆ I for some x, y ∈ R, then x 2 ⊆ I or y 2 ⊆ I. The 2-prime hyperideals are a generalization of prime hyperideals. In this paper, we aim to study 2-prime hyperideals and give some results. Moreover, we investigate δ-2-primary hyperideals which are an expansion of 2-prime hyperideals.2010 Mathematics Subject Classification. 20N20.

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“…The hyperstructure theory was introduced by Marty in 1934, at the 8th Congress of Scandinavian Mathematicians [25], when he defined the hypergroups and began to investigate their properties with applications to groups, algebraic functions and rational fractions. Later on, many researchers have worked on this new field of modern algebra and developed it [11,12,36,13,14,16,24,27,29]. In a classical algebraic structure, the composition of two elements is an element, but in an algebraic hyperstructure, the composition of two elements is a set.…”

Section: Introductionmentioning

confidence: 99%

On 1-absorbing prime hyperideal and some of its generalizations

Anbarloei¹

2021

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Let R be a multiplicative hyperring. In this paper, we define the concept of 1-absorbing prime hyperideals which is a generalization of the prime hyperideals. A proper hyperideal I of R is called a 1-absorbing prime hyperideal if for nonunit elements x, y, z ∈ R, x•y •z ⊆ I , then either x•y ⊆ I or z ∈ I. Several properties of the hyperideals are provided. Moreover, we introduce the notions of 1-absorbing primary hyperideals, strongly 1-absorbing primary hyperideals and weakly 1-absorbing primary hyperideals which are generalizations of the 1-absorbing prime hyperideals and then we will show some properties of them.

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Regularity of Intuitionistic Fuzzy Relations on Hypergroupoids

Abstract: In this paper we introduce the notions of regular and strongly regular intuitionistic fuzzy relations on hypergroupoids, studying some related properties and connections with the classical case. Then we investigate the lattice structure of these kinds of intuitionistic fuzzy equivalences.

Cited by 10 publications

References 17 publications

Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures

Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures

2-Prime Hyperideals

On 1-absorbing prime hyperideal and some of its generalizations

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