Applications of rough soft sets to Krasner (m,n)-hyperrings and corresponding decision making methods

Ma, Xueling; Zhan, Jianming; Davvaz, Bijan

doi:10.2298/fil1819599m

Cited by 9 publications

(9 citation statements)

References 34 publications

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“…Later on, Crombez and Timm [5,6] defined the notion of the (m, n)-rings and their quotient structures. Mirvakili and Davvaz [20] defined (m, n)-hyperrings and obtained several results in this respect. In [10], they introduced a generalization of the notion of a hypergroup in the sense of Marty and a generalization of an n-ary group, which is called n-ary hypergroup.…”

Section: Introductionmentioning

confidence: 99%

$J$-hyperideals and their expansions in a Krasner $(m,n)$-hyperring

Anbarloei

2023

Hacettepe Journal of Mathematics and Statistics

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Over the years, different types of hyperideals have been introduced in order to let us fully realize the structures of hyperrings in general. ‎ ‎The aim of this research work is to define and characterize a new class of hyperideals in a Krasner ‎$‎(m,n)‎$‎-hyperring that we call ‎n-ary ‎‎$‎J‎$‎-hyperideals. A proper hyperideal ‎$‎Q‎$ o‎f a ‎Krasner ‎$‎(m,n)‎$‎-hyperring with the scalar identity ‎$‎1_R‎$ ‎is said to be an n-ary ‎$J‎$‎-hyperideal ‎‎‎‎if whenever $x_1^n \in R$ such that ‎$‎g(x_1^n) ‎\in ‎Q‎$ ‎and ‎‎$‎x_i \notin J_{(m,n)}(R)$, then ‎$‎g(x_1^{i-1},1_R,x_{i+1}^n) \in Q‎$‎. Also, we study the concept of n-ary ‎$‎\delta‎$‎-‎$‎J‎$‎-hyperideals as an expansion of n-ary $‎J‎$‎-hyperideals. Finally, we extend the notion of n-ary $‎\delta‎$‎-‎$‎J‎$‎-hyperideals to ‎$‎(k,n)‎$‎-absorbing ‎$‎\delta‎$‎-‎$‎J‎$-hyperideals.‎ ‎Let $\delta$ be a hyperideal expansion of a Krasner $(m,n)$-hyperring $R$ and $k$ be a positive integer‎. ‎A proper hyperideal $Q$ of $R$ is called $(k,n)$-absorbing $\delta‎$‎-‎$‎J‎$‎-hyperideal if for $x_1^{kn-k+1} \in R$‎, ‎$g(x_1^{kn-k+1}) \in Q$ implies that $g(x_1^{(k-1)n-k+2}) \in J_{(m,n)}(R)$ or a $g$-product of $(k-1)n-k+2$ of $x_i^,$ s except $g(x_1^{(k-1)n-k+2})$ is in $\delta(Q)$‎.

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Section: Introductionmentioning

confidence: 99%

$J$-hyperideals and their expansions in a Krasner $(m,n)$-hyperring

Anbarloei

2023

Hacettepe Journal of Mathematics and Statistics

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“…In [12], they introduced and illustrated a generalization of the notion of a hypergroup in the sense of Marty and a generalization of an n-ary group, which is called n-ary hypergroup. The n-ary structures has been studied in [19,20,21,22,29]. Mirvakili and Davvaz [26] defined (m, n)-hyperrings and obtained several results in this respect.…”

Section: Introductionmentioning

confidence: 99%

Extensions of $n$-ary prime hyperideals via an $n$-ary multiplicative subset in a Krasner $(m,n)$-hyperring

Anbarloei¹

2022

Preprint

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Let R be a Krasner (m, n)-hyperring and S be an n-ary multiplicative subset of R. The purpose of this paper is to introduce the notion of n-ary S-prime hyperideals as a new expansion of n-ary prime hyperideals. A hyperideal I of R disjoint with S is said to be an n-ary S-prime hyperideal if there exists s ∈ S such that whenever g(x n 1 ) ∈ I for all x n 1 ∈ R, then g(s, x i , 1 (n−2) ) ∈ I for some 1 ≤ i ≤ n. Several properties and characterizations concerning n-ary S-prime hyperideals are presented. The stability of this new concept with respect to various hyperring-theoretic constructions are studied. Furthermore, we extend this concept to n-ary S-primary hyperideals. We obtained some specific results explaining the structure.2010 Mathematics Subject Classification. 16Y99. Key words and phrases.n-ary J-hyperideal, n-ary δ-J-hyperideal, (k, n)-absorbing δ-Jhyperideal.

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“…Later on, Crombez and Timm [5,6] defined the notion of the (m, n)-rings and their quotient structures. The n-ary hyperstructures have been studied in [17,18,19,22,28]. In [10], Davvaz and Vougiouklis introduced a generalization of the notion of a hypergroup in the sense of Marty and a generalization of an n-ary group, which is called n-ary hypergroup.…”

Section: Introductionmentioning

confidence: 99%

Classes of F-hyperideals of a Krasner F^{(m,n)}-hyperring

Anbarloei¹

2022

Preprint

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Krasner F (m,n) -hyperrings were introduced and investigated by Farshi and Davvaz. In this paper, our purpose is to define and characterize three particular classes of F -hyperideals in a Krasner F (m,n) -hyperring, namely prime F -hyperideals, maximal F -hyperideals and primary F -hyperideals, which extend similar concepts of ring context. Furthermore, we examine the relations between these structures. Then a number of major conclusions are given to explain the general framework of these structures.Key words and phrases. prime F -hyperideal, maximal F -hyperideal, primary F -hyperideal, Krasner F (m,n) -hyperring. * ) be the set of all fuzzy subsets of G.the following conditions are satisfied: (1) (a•b)•c = a•(b•c) for all a, b, c ∈ G, (2) there exists e ∈ G with a ∈ supp(a•e∩e•a), for all a ∈ G, (3) for each a ∈ G, there exists a unique element afor all a, b, c ∈ G. Indeed, a fuzzy hyperoperation assigns to each pair of elements of G a non-zero fuzzy subset of G, while a hyperoperation assigns to each pair of elements of G a non-empty subset of G. The concepts of Krasner F (m,n) -hyperrings and F -hyperideals were defined in [14] by Farshi and Davvaz. In this paper, we continue the study of F -hyperideals of a Krasner F (m,n) -hyperring, initiated in [14]. We define and analyze there particular types of F -hyperideals in a Krasner F (m,n) -hyperring, maximal F -hyperideals and primary F -hyperideals. We investigate the connections between them. Moreover, we introduce the concepts of F -radical, quotient Krasner F (m,n) -hyperring and Jacobson radical. The overall framework of these structures is then explained. It is shown (Theorem 4.6) that if Q is an primary F -hyperideal of a Krasner F (m,n)hyperring (R, f, g), then √ Q F is a prime F -hyperideal of R. PreliminariesIn this section we recall some basic terms and definitions from [14] which we need to develop our paper.

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Applications of rough soft sets to Krasner (m,n)-hyperrings and corresponding decision making methods

Cited by 9 publications

References 34 publications

$J$-hyperideals and their expansions in a Krasner $(m,n)$-hyperring

$J$-hyperideals and their expansions in a Krasner $(m,n)$-hyperring

Extensions of $n$-ary prime hyperideals via an $n$-ary multiplicative subset in a Krasner $(m,n)$-hyperring

Classes of F-hyperideals of a Krasner F^{(m,n)}-hyperring

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