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Meet-distributive lattices have the intersection property [PDF]
Mathematica Bohemica, 2023 This paper is an erratum of H. Mühle: Distributive lattices have the intersection property, Math. Bohem. (2021). Meet-distributive lattices form an intriguing class of lattices, because they are precisely the lattices obtainable from a closure operator ...
Henri Mühle
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On Dualization over Distributive Lattices [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 Given a partially order set (poset) $P$, and a pair of families of ideals $\mathcal{I}$ and filters $\mathcal{F}$ in $P$ such that each pair $(I,F)\in \mathcal{I}\times\mathcal{F}$ has a non-empty intersection, the dualization problem over $P$ is to ...
Khaled Elbassioni
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On α-Multiplier on Almost Distributive Lattices [PDF]
Journal of Mathematics, 2021 In this paper, we initiate the concept of α-multiplier on almost distributive lattices. We prove some useful results by using the notion of α-multiplier and generalize the idea of multiplier on almost distributive lattices.
Ying Wang +5 more
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Boolean Lifting Properties for Bounded Distributive Lattices [PDF]
Scientific Annals of Computer Science, 2015 In this paper, we introduce the lifting properties for the Boolean elements of bounded distributive lattices with respect to the congruences, filters and ideals, we establish how they relate to each other and to significant algebraic properties, and we ...
D. Cheptea, G. Georgescu, C. Mureșan
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“Complete-simple” distributive lattices [PDF]
Proceedings of the American Mathematical Society, 1993 It is well known that the only simple distributive lattice is the two-element chain. We can generalize the concept of a simple lattice to complete lattices as follows: a complete lattice is complete-simple if it has only the two trivial complete congruences.
Grätzer, G., Schmidt, E. T.
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Rough sets based on fuzzy ideals in distributive lattices [PDF]
Open Mathematics, 2020 In this paper, we present a rough set model based on fuzzy ideals of distributive lattices. In fact, we consider a distributive lattice as a universal set and we apply the concept of a fuzzy ideal for definitions of the lower and upper approximations in ...
Yang Yongwei, Zhu Kuanyun, Xin Xiaolong
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Quantifiers on distributive lattices [PDF]
Discrete Mathematics, 1991 The author studies (bounded) distributive lattices equipped with (the non-Boolean analogue of) a quantifier in the sense of \textit{P. R. Halmos} [Compos. Math. 12, 217--249 (1956; Zbl 0087.24505)], that is a closure operator \(\nabla\) which preserves finite joins (including 0) and satisfies the identity \(\nabla(a\land \nabla b)=\nabla a\land \nabla ...
Cignoli, Roberto
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Belief functions on distributive lattices
Artificial Intelligence, 2013 The Dempster-Shafer theory of belief functions is an important approach to deal with uncertainty in AI.In the theory, belief functions are defined on Boolean algebras of events. In many applications of belief functions in real world problems, however, the objects that we manipulateis no more a Boolean algebra but a distributive ...
Chunlai Zhou
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A decomposition of distributive lattices [PDF]
Discrete Mathematics, 1985 The author works out the concept of a split decomposition of a distributive lattice fitting into the general decomposition theory of Cunningham and Edmonds. He clarifies the amount of uniqueness valid for repeated decompositions, the structure of the building stones, and the reconstruction process.
Fujishige, Satoru
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Distributive lattices have the intersection property [PDF]
Mathematica Bohemica, 2021 Distributive lattices form an important, well-behaved class of lattices. They are instances of two larger classes of lattices: congruence-uniform and semidistributive lattices.
Henri Mühle
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