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
Havlena Vojtěch, Ing., Ph.D. (DITS FIT BUT)
Hliněná Dana, doc. RNDr., Ph.D. (DMAT FEEC BUT)
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
10.4204/EPTCS.233.2
UT WoS
000390333200003
EID Scopus
2-s2.0-85018658170
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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