On derivations of quantales

Xiao, Qimei; Liu, Wenjun

doi:10.1515/math-2016-0030

Cited by 5 publications

(3 citation statements)

References 15 publications

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“…Derivation is helpful to the research of structure and property in algebraic system. Derivations in quantale was studied by Xiao and Liu [29]. Quantale module developed on quantale as a structure was studied by Abramsky and Vickers [30].…”

Section: Introductionmentioning

confidence: 99%

Rough Substructures Based on Overlaps of Successor in Quantales Under Serial Fuzzy Relations

Qurashi,

Almutairi,

Kanwal

et al. 2023

IEEE Access

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In this research article, a new connection between serial fuzzy relations and an extended version of rough sets in an algebraic structure quantale is established. The extended notion of rough sets consists of successor class and an overlap of the successor class of an element of a quantale. Thus a new approximation space based on serial fuzzy relations via the overlaps of successor in quantales, are introduced. The main purpose of this study is to provide basic algebraic structures based on serial fuzzy-relations. In this way, the new approximation space acquires certain appealing algebraic properties. Compatible fuzzy relations in quantale are being applied to introduce the notions of rough multiplicative set, rough m-system and further rough substructures of quantales. Following that, various quantale substructures are described in terms of successor overlaps under serial fuzzy relations, leading to the development of some key theorems. Moreover, several results including quantale homomorphism between rough substructures and their homomorphic images are provided. It is concluded that this new study is significantly easy and superior to various types of approximations in various types of algebraic structures. Furthermore, different examples are given to show the effectiveness of the developed approach and a comparative study of the investigated approach with some existing methods are expressed broadly which show that the investigated approach are more effective and easy than the existing approaches. INDEX TERMSQuantale, rough ideal, SFrelations, TCFR, rough multiplicative set, rough m-system.

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Section: Introductionmentioning

confidence: 99%

Rough Substructures Based on Overlaps of Successor in Quantales Under Serial Fuzzy Relations

Qurashi,

Almutairi,

Kanwal

et al. 2023

IEEE Access

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“…The notion of (∧, ∨)-derivation on a lattice is witnessing increased attention. It studies, among others, in partially ordered sets [1,31], in distributive lattices [30], in semilattices [29], in bounded hyperlattices [24], in quantales and residuated lattices [10,25] and in several kinds of algebras [14,17,19]. Furthermore, it used in the definition of congruences and ideals in a distributive lattice [20].…”

Section: Introductionmentioning

confidence: 99%

(F,G)-Derivations on a Lattice

AMROUNE¹,

ZEDAM²,

YETTOU³

2022

KgJMat

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In the present paper, we introduce the notion of (F,G)-derivation on a lattice as a generalization of the notion of (∧,∨)-derivation. This newly notion is based on two arbitrary binary operations F and G instead of the meet (∧) and the join (∨) operations. Also, we investigate properties of (F,G)-derivation on a lattice in details. Furthermore, we deﬁne and study the notion of principal (F,G)-derivations as a particular class of (F,G)-derivations. As applications, we provide two representations of a given lattice in terms of its principal (F,G)-derivations.

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“…In particular, the nonlinear density-dependent mortality term, a(t)x(t) b(t)+x(t) is referred to as population mortality, β j (t)x(th j (t))e -γ j (t)x(t-g j (t)) designates the time-dependent birth function with maturation delay h j (t) and incubation delay g j (t), and gets the maximum reproduces rate 1 γ j (t) , and j ∈ I. For the past decade or so, for the special case of (1.2) with h j ≡ g j (j ∈ I), not only the dynamic behaviors of time-delay Nicholson's blowflies models, such as existence, persistence, oscillation, periodicity and stability, but also the variants of the models have aroused current research interest, and some useful results have been obtained in the existing papers; for example, see [7][8][9][10][11][12][13][14][15]. In addition, it is proved that more than one delay involved in the identical nonlinear function F j can cause chaotic oscillations in [1], and an example is given to represent that two delays, rather than one delay, can produce a continuous oscillation.…”

Section: Introductionmentioning

confidence: 99%

Global asymptotic stability for a nonlinear density-dependent mortality Nicholson’s blowflies system involving multiple pairs of time-varying delays

Cao

2020

Adv Differ Equ

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In our article, a nonlinear density-dependent mortality Nicholson's blowflies system with patch structure has been investigated, in which the delays are time-varying and multiple pairs. Based upon the fluctuation lemma and differential inequality techniques, some sufficient conditions are found to ensure the global asymptotic stability of the addressed model. Moreover, a numerical example is provided to illustrate the feasibility and effectiveness of the obtained findings, and our consequences are new even when the considered model degenerates to the scalar Nicholson's blowflies equation.

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On derivations of quantales

Cited by 5 publications

References 15 publications

Rough Substructures Based on Overlaps of Successor in Quantales Under Serial Fuzzy Relations

Rough Substructures Based on Overlaps of Successor in Quantales Under Serial Fuzzy Relations

(F,G)-Derivations on a Lattice

Global asymptotic stability for a nonlinear density-dependent mortality Nicholson’s blowflies system involving multiple pairs of time-varying delays

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