Results 21 to 30 of about 748 (136)

ϕ ‐δ‐Primary Hyperideals in Krasner Hyperrings

Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022
In this paper, we study commutative Krasner hyperrings with nonzero identity. ϕ‐prime, ϕ‐primary and ϕ‐δ‐primary hyperideals are introduced. The concept of δ‐primary hyperideals is extended to ϕ‐δ‐primary hyperideals. Some characterizations of hyperideals are provided to classify them.
Hao Guan, Elif Kaya, Melis Bolat, Serkan Onar, Bayram Ali Ersoy, Kostaq Hila, Hasan Dinçer   +6 more
wiley   +1 more source

Multicriteria Decision‐Making Problem via Weighted Cosine Similarity Measure and Several Characterizations of Hypergroup and (Weak) Polygroups under the Triplet Single‐Valued Neutrosophic Structure

Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022
Polygroups are an extended form of groups and a subclass of hypergroups that follow group‐type axioms. In this paper, we define a triplet single‐valued neutrosophic set, which is a generalization of fuzzy sets, intuitionistic fuzzy sets, and neutrosophic sets, and we combine this novel concept with hypergroups and polygroups.
M. Shazib Hameed, Zaheer Ahmad, Shahbaz Ali, Augustine Larweh Mahu, Walid F. A Mosa, Dragan Z. Marinkovic   +5 more
wiley   +1 more source

Some Properties of Weak Γ‐Hyperfilters in OrderedΓ‐Semihypergroups

Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022
The main purpose of this paper is to study fundamental properties of weak Γ‐hyperfilters on ordered Γ‐semihypergroups that is a generalization of Γ‐hyperfilters. Also, we investigate the relationship between weak Γ‐hyperfilters and prime Γ‐hyperideals in ordered Γ‐semihypergroups.
Yongsheng Rao, Xiang Chen, Saeed Kosari, Mohammadsadegh Monemrad, Márcio J. Lacerda   +4 more
wiley   +1 more source

Characterizations of Hyperideals and Interior Hyperideals in Ordered Γ‐Semihypergroups

Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022
We give some conditions on ordered Γ‐semihypergroups under which their interior hyperideal is equal to the hyperideal. In this paper, it is shown that in regular (resp., intraregular, semisimple) ordered Γ‐semihypergroups, the hyperideals and the interior hyperideals coincide.
Yongsheng Rao, Qixin Zhou, Ruiqi Cai, Aysha Khan, Zahir Shah   +4 more
wiley   +1 more source

On 1‐Absorbing Prime Hyperideal and Some of Its Generalizations

Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022
In this paper, we introduce the concept of 1‐absorbing prime hyperideals which is an expansion of the prime hyperideals. Several properties of the hyperideals are provided. For example, it is proved that if a strong C‐hyperideal I of R is 1‐absorbing prime that is not prime, then R is a local multiplicative hyperring.
M. Anbarloei, Carmelo Antonio Finocchiaro   +1 more
wiley   +1 more source

[Retracted] Roughness in Hypervector Spaces

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
This paper examines rough sets in hypervector spaces and provides a few examples and results in this regard. We also investigate the congruence relations‐based unification of rough set theory in hypervector spaces. We introduce the concepts of lower and upper approximations in hypervector spaces.
Nabilah Abughazalah, Naveed Yaqoob, Muhammad Usman, Muhammad Gulzar   +3 more
wiley   +1 more source

2‐Prime Hyperideals of Multiplicative Hyperrings

Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022
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, x2⊆I or y2⊆I.
Mahdi Anbarloei, Xiaogang Liu
wiley   +1 more source

Dependence Relations and Grade Fuzzy Set

Symmetry, 2023
With the aim of developing the recent theory of dependence relations, we elaborate a procedure to measure the strength of the influence of an element on another with respect to a given dependence relation on a finite set.
Alessandro Linzi, I. Cristea
semanticscholar   +1 more source

r‐Hyperideals and Generalizations of r‐Hyperideals in Krasner Hyperrings

Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022
This paper deals with Krasner hyperrings as an important class of algebraic hyperstructures. We investigate some properties of r‐hyperideals in commutative Krasner hyperrings. Some properties of pr‐hyperideals are also studied. The relation between prime hyperideals and r‐hyperideals is investigated. We show that the image and the inverse image of an r‐
Peng Xu, Melis Bolat, Elif Kaya, Serkan Onar, Bayram Ali Ersoy, Kostaq Hila, Kamal Kumar   +6 more
wiley   +1 more source

DIFFERENTIAL MULTIPLICATIVE HYPERRINGS [PDF]

Journal of Algebraic Systems, 2014
There are several kinds of hyperrings, for example, Krasnerhyperrings, multiplicative hyperring, general hyperrings and$H_v$-rings. In a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation.
L. Kamali Ardekani, Bijan Davvaz
doaj   +1 more source