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Idempotence

About: Idempotence is a research topic. Over the lifetime, 1860 publications have been published within this topic receiving 19976 citations. The topic is also known as: idempotent.


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Journal ArticleDOI
TL;DR: The aim of this paper is to present a generating set for the class of intermediate (or, equivalently, idempotent) aggregation functions, which consists of lattice operations and certain ternary idem Potent aggregation functions.

10 citations

Journal ArticleDOI
TL;DR: In this paper, the authors characterize the paramedial, comedial, and coparamedial pairs of quasigroup operations and characterize the algebras with a unit element and an idempotent regular element.
Abstract: In this paper we characterize the paramedial, comedial, and coparamedial pairs of quasigroup operations and paramedial, comedial, and coparamedial algebras with the quasigroup operations. Then we characterize paramedial, comedial, and coparamedial algebras with a unit element and an idempotent regular element.

10 citations

Journal ArticleDOI
TL;DR: In this article, the spectral radius of linear combinations of two projections in C*-algebras was studied. And the commutator of the two projections was investigated.
Abstract: In this note, we study the spectrum and give estimations for the spectral radius of linear combinations of two projections in C*-algebras. We also study the commutator of two projections.

10 citations

Proceedings ArticleDOI
18 Jul 2010
TL;DR: It is proved that the most usual algebraic and morphological properties are preserved, such as, duality, monotonicity, interaction with union and intersection, invariance under translating and scaling, local knowledge property, extensitivity, idempotence, and many others.
Abstract: In this paper, a new approach to fuzzy mathematical morphology based on discrete t-norms is studied. It is proved that the most usual algebraic and morphological properties are preserved, such as, duality, monotonicity, interaction with union and intersection, invariance under translating and scaling, local knowledge property, extensitivity, idempotence, and many others. In fact, all properties satisfied by the approach based on nilpotent t-norms hold in the discrete case. This is quite important since in practice we only work with discrete objects. Experimental results for some discrete t-norms are included. They are compared with classical morphological algorithms based on the Łukasiewicz t-norm and the umbra approach, and with the fuzzy approach based on idempotent uninorms, proving that they are suitable to be used in edge detection.

10 citations

Posted Content
TL;DR: In this paper, the authors propose uniform idempotent right quasigroups and emergent algebras as an alternative to differentiable algebraes, inspired from research subjects in sub-riemannian geometry and metric geometry.
Abstract: Inspired from research subjects in sub-riemannian geometry and metric geometry, we propose uniform idempotent right quasigroups and emergent algebras as an alternative to differentiable algebras Idempotent right quasigroups (irqs) are related with racks and quandles, which appear in knot theory (the axioms of a irq correspond to the first two Reidemeister moves) To any uniform idempotent right quasigroup can be associated an approximate differential calculus, with Pansu differential calculus in sub-riemannian geometry as an example An emergent algebra A over a uniform idempotent right quasigroup X is a collection of operations such that each operation emerges from X, meaning that it can be realized as a combination of the operations of the uniform irq X, possibly by taking limits which are uniform with respect to a set of parameters Two applications are considered: we prove a bijection between contractible groups and distributive uniform irqs (uniform quandles) and that some symmetric spaces in the sense of Loos may be seen as uniform quasigroups with a distributivity property

10 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023106
2022263
202184
2020100
201991
201892