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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
A Graded Approach to Cardinal Theory of Finite Fuzzy Sets, Part II: Fuzzy Cardinality Measures and Their Relationship to Graded Equipollence
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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