Approximating infinite solution sets by discretization of the scales of truth degrees

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Approximating infinite solution sets by discretization of the scales of truth degrees

Popis výsledku v původním jazyce

The present paper discusses the problem of approximating possibly infinite sets of solutions by finite sets of solutions via discretization of scales of truth degrees. Infinite sets of solutions we have in mind in this paper typically appear in constraint-based problems such as ``find all collections in a given finite universe satisfying constraint C''. In crisp setting, i.e. when collections are conceived as crisp sets, the set of all such collections is finite and often computationally tractable. In fuzzy setting, i.e. when collections are conceived as fuzzy sets, the set of all such collections may be infinite and, ipso facto, computationally intractable when one uses the unit interval [0,1] as the scale of membership degrees. A natural solution tothis problem is to uses, instead of [0,1], a finite subset K of [0,1] which approximates [0,1] to a satisfactory degree. This idea is pursued in the present paper. To be sufficiently specific, we illustrate the idea on a particular method

Název v anglickém jazyce

Approximating infinite solution sets by discretization of the scales of truth degrees

Popis výsledku anglicky

The present paper discusses the problem of approximating possibly infinite sets of solutions by finite sets of solutions via discretization of scales of truth degrees. Infinite sets of solutions we have in mind in this paper typically appear in constraint-based problems such as ``find all collections in a given finite universe satisfying constraint C''. In crisp setting, i.e. when collections are conceived as crisp sets, the set of all such collections is finite and often computationally tractable. In fuzzy setting, i.e. when collections are conceived as fuzzy sets, the set of all such collections may be infinite and, ipso facto, computationally intractable when one uses the unit interval [0,1] as the scale of membership degrees. A natural solution tothis problem is to uses, instead of [0,1], a finite subset K of [0,1] which approximates [0,1] to a satisfactory degree. This idea is pursued in the present paper. To be sufficiently specific, we illustrate the idea on a particular method

Druh

D - Stať ve sborníku

CEP obor

BD - Teorie informace

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2007

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Proceedings of North American Fuzzy Information Processing Society 2007

ISBN

978-1-4244-1213-6

ISSN

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e-ISSN

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Počet stran výsledku

6

Strana od-do

325-330

Název nakladatele

IEEE Computer Society Press

Místo vydání

New York

Místo konání akce

San Diego

Datum konání akce

15. 7. 2007

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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