Generators of fuzzy logical operations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F20%3A00340266" target="_blank" >RIV/68407700:21230/20:00340266 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/978-3-030-38565-1_8" target="_blank" >https://doi.org/10.1007/978-3-030-38565-1_8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-38565-1_8" target="_blank" >10.1007/978-3-030-38565-1_8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Generators of fuzzy logical operations

Popis výsledku v původním jazyce

We deal with fuzzy logical operations with values in the real unit interval. Many of them can be considered equivalent up to an isomorphism (i.e., increasing bijection) of the set of values. This is the case of all involutive fuzzy negations; an elegant proof was given by Nguyen and Walker (A first course in fuzzy logic, 2nd edn. Chapman & Hall/CRC, Boca Raton, 2000 [23]) . The situation is more tricky for binary operations, triangular norms, triangular conorms, and fuzzy implications. For the most common classes of these operations, the existence of their (additive or multiplicative) generators is known; however, their computation can be often unfeasible. We proved that a rather general subclass allows computing the generators from partial derivatives. Here we summarize preceding results in this direction (mostly with simplified proofs) and add several new ones.

Název v anglickém jazyce

Generators of fuzzy logical operations

Popis výsledku anglicky

We deal with fuzzy logical operations with values in the real unit interval. Many of them can be considered equivalent up to an isomorphism (i.e., increasing bijection) of the set of values. This is the case of all involutive fuzzy negations; an elegant proof was given by Nguyen and Walker (A first course in fuzzy logic, 2nd edn. Chapman & Hall/CRC, Boca Raton, 2000 [23]) . The situation is more tricky for binary operations, triangular norms, triangular conorms, and fuzzy implications. For the most common classes of these operations, the existence of their (additive or multiplicative) generators is known; however, their computation can be often unfeasible. We proved that a rather general subclass allows computing the generators from partial derivatives. Here we summarize preceding results in this direction (mostly with simplified proofs) and add several new ones.

Druh

C - Kapitola v odborné knize

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Centrum pokročilých aplikovaných přírodních věd</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název knihy nebo sborníku

Algebraic Techniques and Their Use in Describing and Processing Uncertainty

ISBN

978-3-030-38565-1

Počet stran výsledku

24

Strana od-do

89-112

Počet stran knihy

170

Název nakladatele

Springer

Místo vydání

Cham

Kód UT WoS kapitoly

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