A Graded Approach to Cardinal Theory of Finite Fuzzy Sets, Part II: Fuzzy Cardinality Measures and Their Relationship to Graded Equipollence

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F20%3AA2101N3H" target="_blank" >RIV/61988987:17610/20:A2101N3H - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0165011418308303" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011418308303</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2018.10.023" target="_blank" >10.1016/j.fss.2018.10.023</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A Graded Approach to Cardinal Theory of Finite Fuzzy Sets, Part II: Fuzzy Cardinality Measures and Their Relationship to Graded Equipollence

Popis výsledku v původním jazyce

In this article, we propose an axiomatic system for fuzzy 'cardinality' measures (referred to as fuzzy c-measures for short) assigning to each finite fuzzy set a generalized cardinal that expresses the number of elements that the fuzzy set contains. The system generalizes an axiomatic system introduced by J. Casasnovas and J. Torrens (2003). We show that each fuzzy c-measure is determined by two appropriate homomorphisms between the reducts of residuated-dually residuated (rdr-)lattices. For linearly ordered rdr-lattices, we prove that each fuzzy c-measure is a product of a non-decreasing and a non-increasing fuzzy c-measure, which indicates that there is a close relation between fuzzy c-measures and FGCount, FLCount and FECount provided by L.A. Zadeh (1983) and generalized by M. Wygralak (2001). Finally, the relationship of fuzzy c-measures to graded equipollence introduced in the first part of this contribution is analyzed.

Název v anglickém jazyce

A Graded Approach to Cardinal Theory of Finite Fuzzy Sets, Part II: Fuzzy Cardinality Measures and Their Relationship to Graded Equipollence

Popis výsledku anglicky

In this article, we propose an axiomatic system for fuzzy 'cardinality' measures (referred to as fuzzy c-measures for short) assigning to each finite fuzzy set a generalized cardinal that expresses the number of elements that the fuzzy set contains. The system generalizes an axiomatic system introduced by J. Casasnovas and J. Torrens (2003). We show that each fuzzy c-measure is determined by two appropriate homomorphisms between the reducts of residuated-dually residuated (rdr-)lattices. For linearly ordered rdr-lattices, we prove that each fuzzy c-measure is a product of a non-decreasing and a non-increasing fuzzy c-measure, which indicates that there is a close relation between fuzzy c-measures and FGCount, FLCount and FECount provided by L.A. Zadeh (1983) and generalized by M. Wygralak (2001). Finally, the relationship of fuzzy c-measures to graded equipollence introduced in the first part of this contribution is analyzed.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

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)

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

FUZZY SET SYST

ISSN

0165-0114

e-ISSN

—

Svazek periodika

380

Číslo periodika v rámci svazku

February

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

40

Strana od-do

64-103

Kód UT WoS článku

000497961200004

EID výsledku v databázi Scopus

2-s2.0-85055990190