Modern approaches in fuzzy sets, intuitionistic fuzzy sets, generalized nets and related topics. Volume I: Foundations * Α-properties of fuzzy relations and aggregation procedure

De Tré, Guy; Bentkowska, Urszula

Modern approaches in fuzzy sets, intuitionistic fuzzy sets, generalized nets and related topics. Volume I: Foundations * Α-properties of fuzzy relations and aggregation procedure

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Title: Modern approaches in fuzzy sets, intuitionistic fuzzy sets, generalized nets and related topics. Volume I: Foundations * Α-properties of fuzzy relations and aggregation procedure

Abstract:

In the paper the problem of preservation of properties of fuzzy relations during aggregation process is considered. It means that properties of fuzzy relations R1, . . . ,Rn on a set X are compared with properties of the aggregated fuzzy relation RF = F(R1, . . . ,Rn), where F is a function of the type F : [0, 1]n → [0, 1]. There are discussed α-properties (which may be called graded properties) as reflexivity, irreflexivity, symmetry, asymmetry, antisymmetry, connectedness and transitivity, where α ∈ [0, 1]. Fuzzy relations with a given graded property are considered (there may be diverse grades of the same property) and the obtained grade of the aggregated fuzzy relation is provided. There is also discussed the ,,converse” problem. Namely, relation RF = F(R1, . . . ,Rn) is assumed to have a graded property and the properties of relations R1, . . . ,Rn are examined (possibly with some assumptions on F).

Relation:

Książka = Book

Detailed Resource Type:

Książka

Resource Identifier:

oai:rcin.org.pl:198429

Source:

KS-2014-02-T1P04

Language:

eng

Language of abstract:

eng

Rights:

Licencja Creative Commons Uznanie autorstwa 4.0

Terms of use:

Zasób chroniony prawem autorskim. [CC BY 4.0 Międzynarodowe] Korzystanie dozwolone zgodnie z licencją Creative Commons Uznanie autorstwa 4.0, której pełne postanowienia dostępne są pod adresem: ; -

Digitizing institution:

Instytut Badań Systemowych Polskiej Akademii Nauk

Original in:

Biblioteka Instytutu Badań Systemowych PAN

Projects co-financed by:

Program Operacyjny Polska Cyfrowa, lata 2014-2020, Działanie 2.3 : Cyfrowa dostępność i użyteczność sektora publicznego; środki z Europejskiego Funduszu Rozwoju Regionalnego oraz współfinansowania krajowego z budżetu państwa

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Last modified:

Oct 15, 2021

In our library since:

Jul 19, 2021

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https://rcin.org.pl./publication/234753

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Ksiazki

Edition name	Date
KS-2014-02-T1P04 : De Tré Guy, Bentkowska Urszula : Modern approaches in fuzzy sets, intuitionistic fuzzy sets, generalized nets and related topics. Volume I: Foundations * Α-properties of fuzzy relations and aggregation procedure	Oct 15, 2021