Publication Details

A Note on One Less Known Class of Generated Residual Implications

HAVLENA Vojtěch and HLINĚNÁ Dana. A Note on One Less Known Class of Generated Residual Implications. In: Proceedings MEMICS 2016. Electronic Proceedings in Theoretical Computer Science, vol. 233. Telč: Faculty of Information Technology BUT, 2016, pp. 13-22. ISSN 2075-2180. Available from: https://arxiv.org/pdf/1612.04979.pdf
Czech title
Poznámka k jedné méně známé třídě generovaných residuálních implikací
Type
conference paper
Language
english
Authors
URL
Keywords

fuzzy logic, integral equations, modeling languages, choquet integral, generated implications, human language, residual implications, t-norm, mathematical operators

Abstract

This paper builds on our contribution [Hl16] which studied modelling of the conjunction in human language. We have discussed three different ways of constructing a conjunction. We have dealt with generated t-norms, generated means and Choquet integral.
In this paper we construct the residual operators based on the above conjunctions. The only operator based on a t-norm is an implication. We show that this implication belongs to the class of g-generated implications which was introduced in [Sm99] and studied in [Hl12]. We study its properties.
Moreover, we investigate this class of generated implications. Some important properties, including relations between some classes of implications, are given.

Published
2016
Pages
13-22
Journal
Electronic Proceedings in Theoretical Computer Science, vol. 233, no. 1, ISSN 2075-2180
Proceedings
Proceedings MEMICS 2016
Series
Electronic Proceedings in Theoretical Computer Science
Conference
MEMICS'16 - 11th Doctoral Workshop on Mathematical and Engineering Methods in Computer Science, Telč, CZ
Publisher
Faculty of Information Technology BUT
Place
Telč, CZ
DOI
UT WoS
000390333200003
EID Scopus
BibTeX
@INPROCEEDINGS{FITPUB12231,
   author = "Vojt\v{e}ch Havlena and Dana Hlin\v{e}n\'{a}",
   title = "A Note on One Less Known Class of Generated Residual Implications",
   pages = "13--22",
   booktitle = "Proceedings MEMICS 2016",
   series = "Electronic Proceedings in Theoretical Computer Science",
   journal = "Electronic Proceedings in Theoretical Computer Science",
   volume = 233,
   number = 1,
   year = 2016,
   location = "Tel\v{c}, CZ",
   publisher = "Faculty of Information Technology BUT",
   ISSN = "2075-2180",
   doi = "10.4204/EPTCS.233.2",
   language = "english",
   url = "https://www.fit.vut.cz/research/publication/12231"
}
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