Results 31 to 40 of about 242,644 (80)
A class of hyperrings and hyperfields
International Journal of Mathematics and Mathematical Sciences, 1983 Hyperring is a structure generalizing that of a ring, but where the addition is not a composition, but a hypercomposition, i.e., the sum x+y of two elements, x,y, of a hyperring H is, in general, not an element but a subset of H.
Marc Krasner
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On Fuzzy Ordered Hyperideals in Ordered Semihyperrings
Advances in Fuzzy Systems, Volume 2019, Issue 1, 2019., 2019 In this paper, we introduce the concept of fuzzy ordered hyperideals of ordered semihyperrings, which is a generalization of the concept of fuzzy hyperideals of semihyperrings to ordered semihyperring theory, and we investigate its related properties. We show that every fuzzy ordered quasi‐hyperideal is a fuzzy ordered bi‐hyperideal, and, in a regular ...
O. Kazancı +3 more
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δ‐Primary Hyperideals on Commutative Hyperrings
International Journal of Mathematics and Mathematical Sciences, Volume 2017, Issue 1, 2017., 2017 The purpose of this paper is to define the hyperideal expansion. Hyperideal expansion is associated with prime hyperideals and primary hyperideals. Then, we define some of their properties. Prime and primary hyperideals’ numerous results can be extended into expansions.
Elif Ozel Ay +3 more
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Some Generalized Forms of Fuzzy Interval Valued Hyperideals in a Hyperring
Journal of Applied Mathematics, Volume 2014, Issue 1, 2014., 2014 Some generalized forms of the hyperideals of a hyperring in the paper of Zhan et al. (2008) will be given. As a generalization of the interval valued (α, β)‐fuzzy hyperideals of a hyperring with α, β ∈ {∈, q, ∈∧q, ∈∨q} and α ≠ ∈∧q, the notion of generalized interval valued (α, β)‐fuzzy hyperideals of a hyperring is also introduced. Special attention is
Hongjie Li +3 more
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Fuzzy Γ‐Hyperideals in Γ‐Hypersemirings by Using Triangular Norms
The Scientific World Journal, Volume 2014, Issue 1, 2014., 2014 The concept of Γ‐semihyperrings was introduced by Dehkordi and Davvaz as a generalization of semirings, semihyperrings, and Γ‐semiring. In this paper, by using the notion of triangular norms, we define the concept of triangular fuzzy sub‐Γ‐semihyperrings as well as triangular fuzzy Γ‐hyperideals of a Γ‐semihyperring, and we study a few results in this ...
B. A. Ersoy +4 more
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Associate, Hyperdomainlike, and Presimplifiable Hyperrings
Journal of Mathematics, Volume 2014, Issue 1, 2014., 2014 Based on the works of Axtell et al., Anderson et al., and Ghanem on associate, domainlike, and presimplifiable rings, we introduce new hyperrings called associate, hyperdomainlike, and presimplifiable hyperrings. Some elementary properties of these new hyperrings and their relationships are presented.
Agboola Adesina Abdul Akeem +2 more
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Applications of Soft Union Sets in the Ring Theory
Journal of Applied Mathematics, Volume 2013, Issue 1, 2013., 2013 The aim of the paper is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of (λ, μ)‐soft union rings which is a generalization of that of soft union rings is proposed.
Yongwei Yang +3 more
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Structure of Intuitionistic Fuzzy Sets in Γ‐Semihyperrings
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 As we know, intuitionistic fuzzy sets are extensions of the standard fuzzy sets. Now, in this paper, the basic definitions and properties of intuitionistic fuzzy Γ‐hyperideals of a Γ‐semihyperring are introduced. A few examples are presented. In particular, some characterizations of Artinian and Noetherian Γ‐semihyperring are given.
Bayram Ali Ersoy +2 more
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Ordered Left Almost ⋇‐Semihypergroups Based on Fuzzy Sets
Journal of Mathematics, Volume 2024, Issue 1, 2024.The concept of an involution or anti‐involution is a self‐inverse linear mapping that plays a prominent role in the theory of algebraic structures, particularly rings, hyperrings, ordered semigroups, and ordered semihypergroups. Nowadays, the study of involutions in ordered hyperstructures is a particular area of research in the field of hyperstructure
Nabilah Abughazalah +2 more
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On Rough Hyperideals in Hyperlattices
Journal of Applied Mathematics, Volume 2013, Issue 1, 2013., 2013 We introduce and study rough hyperideals in hyperlattices. First, we give some interesting examples of hyperlattices and introduce hyperideals of hyperlattices. Then, applying the notion of rough sets to hyperlattices, we introduce rough hyperideals in hyperlattices, which are extended notions of hyperideals of hyperlattices.
Pengfei He +3 more
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