Skip navigation

Please use this identifier to cite or link to this item:
Title: On a generalization of multiplicative Sincov's equation for fuzzy implication functions
Authors: Baczyński, Michał Krzysztof
Fechner, Włodzimierz
Massanet, Sebastia
Keywords: Fuzzy implications; t-norms; Generators; Power based implications; Powers of t-norms; Multiplicative Sincov’s equation
Issue Date: 2022
Citation: Fuzzy Sets and Systems, (2022)
Abstract: Characterizations of families of fuzzy implication functions are a necessary step to fully understand the behaviour of the members of the family, their potential applicability and their relations with other families. These characterizations are based on additional algebraical properties that completely define the family. Recently, the class of power based implications was characterized through, among others, the property I(x, y) ·I(y, z) =I(x, z)in a concrete sub-domain. This property, called in the literature also as multiplicative Sincov’s equation, was uncommon to other families, and it was studied in-depth in a previous article. This equality is generalized in this paper by understanding the internal product as the product t-norm and changing it to a general arbitrary continuous Archimedean t-norm. This additional property is analyzed jointly with the weak ordering property or the ordering property, leading to a characterization of those fuzzy implication functions satisfying both additional properties.
DOI: 10.1016/j.fss.2022.07.004
ISSN: 1872-6801
Appears in Collections:Artykuły (WNŚiT)

Files in This Item:
File Description SizeFormat 
Baczynski_On_a_generalization.pdf844,27 kBAdobe PDFView/Open
Show full item record

Uznanie Autorstwa 3.0 Polska Creative Commons License Creative Commons