Encyclopedia of Distances

Deza, Elena; Deza, Michel

doi:10.1007/978-3-642-00234-2

Cited by 781 publications

(75 citation statements)

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“…Let m be a positive integer and X a set with at least m+2 elements. A function d : X m+1 → R is called m-hemi-metric if (see, also [1,2,5]):…”

Section: Hemi-metrics and Super-metricsmentioning

confidence: 99%

If d is super-metric, then d/(1+d) is super-metric

Warrens¹

2017

imf

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Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. AbstractIf a function d is metric, a well-known result is that d/(1 + d) is also metric. We consider m-ary analogs of the binary notion of semimetric, called hemi-metrics and super-metrics. The metrics are totally symmetric maps from X m+1 into R ≥0 . It is shown that, if d is supermetric, then d/(1 + d) is also super-metric.Mathematics Subject Classification: 51Fxx, 54E35

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“…Let m be a positive integer and X a set with at least m+2 elements. A function d : X m+1 → R is called m-hemi-metric if (see, also [1,2,5]):…”

Section: Hemi-metrics and Super-metricsmentioning

confidence: 99%

If d is super-metric, then d/(1+d) is super-metric

Warrens¹

2017

imf

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“…The algorithm stated in [34] is applied on the optimal Advances in Operations Research location of the office of the delivery service in the subway of the city Novosibirsk, Russia. In this paper, the British Rail metric [35] which assumes that any path between two points includes the central point (origin) was considered.…”

Section: Preliminariesmentioning

confidence: 99%

“…In case of Strategy 4, the distance function for the working part of the manipulator can be described by British Rail metric (flower shop metric) [35], with considering an axis of rotation as the origin. Distance function in Strategy 3 corresponds to the French metro metric with polar coordinates.…”

Section: Strategymentioning

confidence: 99%

Algorithms for Location Problems Based on Angular Distances

Kazakovtsev

Stanimirović

Osinuga

et al. 2014

Advances in Operations Research

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This paper describes four mathematical models for the single-facility location problems based on four special distance metrics and algorithms for solving such problems. In this study, algorithms of solving Weber problems using four distance predicting functions (DPFs) are proposed in accordance with four strategies for manipulator control. A numerical example is presented in this proposal as an analytical proof of the optimality of their results.

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“…First part of this section is devoted to the theoretical basis for notions of distance, similarity and metrics [25]. Further we define distance and similarity based on IBA.…”

Section: Similarity Based On Ibamentioning

confidence: 99%

A Consensus Model in Group Decision Making Based on Interpolative Boolean Algebra

Poledica¹,

Milošević²,

Dragović³

et al. 2013

Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology

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The aim of this paper is to propose a soft consensus model based on interpolative Boolean algebra for group decision making problems. Consensus degrees are calculated on three levels (on pairs of alternatives, alternatives, collective level) by means of pseudo-logical aggregation. The relation of equivalence is employed as a similarity measure among experts' opinions. In fact real-valued realization of equivalence is used as a generalized Boolean polynomial.In the illustrative example of sustainable development problem, we have shown that the proposed model is appropriate to determine the level of agreement among experts.

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Encyclopedia of Distances

Cited by 781 publications

References 0 publications

If d is super-metric, then d/(1+d) is super-metric

If d is super-metric, then d/(1+d) is super-metric

Algorithms for Location Problems Based on Angular Distances

A Consensus Model in Group Decision Making Based on Interpolative Boolean Algebra

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