http://hdl.handle.net/20.500.12128/13982
Title: | Fuzzy implications: alpha migrativity and generalised laws of importation |
Authors: | Baczyński, Michał Jayaram, Balasubramaniam Mesiar, Radko |
Keywords: | Fuzzy connectives; T-norm; Fuzzy implication; Law of importation; Alpha-migrativity |
Issue Date: | 2020 |
Citation: | "Information Sciences" Vol. 531, (2020), s. 87-96 |
Abstract: | In this work, we discuss the law of α-migrativity as applied to fuzzy implication functions in a meaningful way. A generalisation of this law leads us to Pexider-type functional equations connected with the law of importation, viz., the generalised law of importation I(C(x,α),y)=I(x,J(α,y)) (GLI) and the generalised cross-law of importation I(C(x,α),y)=J(x,I(α,y)) (CLI), where C is a generalised conjunction. In this article we investigate only (GLI). We begin by showing that the satisfaction of law of importation by the pairs (C, I) and/or (C, J) does not necessarily lead to the satisfaction of (GLI). Hence, we study the conditions under which these three laws are related. |
URI: | http://hdl.handle.net/20.500.12128/13982 |
DOI: | 10.1016/j.ins.2020.04.033 |
ISSN: | 0020-0255 1872-6291 |
Appears in Collections: | Artykuły (WNŚiT) |
File | Description | Size | Format | |
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Baczynski_Fuzzy_implications_alpha_migrativity.pdf | 613,56 kB | Adobe PDF | View/Open |
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