A Note on One Less Known Class of Generated Residual Implications

A Note on One Less Known Class of Generated Residual Implications

This paper builds on our contribution [Havlena and Hlinena, 2016] which studied modelling of the conjunction in human language. We have discussed three different ways of constructing conjunction. We have dealt with generated t-norms, generated means and Choquet integral. In this paper we constru...

Full description

Bibliographic Details
Main Authors: Vojtěch Havlena, Dana Hliněná
Format: Article
Language:English
Published: Open Publishing Association 2016-12-01
Series:Electronic Proceedings in Theoretical Computer Science
Online Access:http://arxiv.org/pdf/1612.04979v1
id doaj-020e7d96cac14c5f818ee9c76fedf42f
record_format Article
spelling doaj-020e7d96cac14c5f818ee9c76fedf42f2020-11-25T00:44:02ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802016-12-01233Proc. MEMICS 2016132210.4204/EPTCS.233.2:3A Note on One Less Known Class of Generated Residual ImplicationsVojtěch Havlena0Dana Hliněná1 Brno University of Technology, Czech Republic Brno University of Technology, Czech Republic This paper builds on our contribution [Havlena and Hlinena, 2016] which studied modelling of the conjunction in human language. We have discussed three different ways of constructing 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 generated implications I^g_N which was introduced in [Smutna, 1999] and studied in [Biba and Hlinena, 2012]. We study its properties. More, we investigate this class of generated implications. Some important properties, including relations between some classes of implications, are given.http://arxiv.org/pdf/1612.04979v1
collection DOAJ
language English
format Article
sources DOAJ
author Vojtěch Havlena
Dana Hliněná
spellingShingle Vojtěch Havlena
Dana Hliněná
A Note on One Less Known Class of Generated Residual Implications
Electronic Proceedings in Theoretical Computer Science
author_facet Vojtěch Havlena
Dana Hliněná
author_sort Vojtěch Havlena
title A Note on One Less Known Class of Generated Residual Implications
title_short A Note on One Less Known Class of Generated Residual Implications
title_full A Note on One Less Known Class of Generated Residual Implications
title_fullStr A Note on One Less Known Class of Generated Residual Implications
title_full_unstemmed A Note on One Less Known Class of Generated Residual Implications
title_sort note on one less known class of generated residual implications
publisher Open Publishing Association
series Electronic Proceedings in Theoretical Computer Science
issn 2075-2180
publishDate 2016-12-01
description This paper builds on our contribution [Havlena and Hlinena, 2016] which studied modelling of the conjunction in human language. We have discussed three different ways of constructing 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 generated implications I^g_N which was introduced in [Smutna, 1999] and studied in [Biba and Hlinena, 2012]. We study its properties. More, we investigate this class of generated implications. Some important properties, including relations between some classes of implications, are given.
url http://arxiv.org/pdf/1612.04979v1
work_keys_str_mv AT vojtechhavlena anoteononelessknownclassofgeneratedresidualimplications
AT danahlinena anoteononelessknownclassofgeneratedresidualimplications
AT vojtechhavlena noteononelessknownclassofgeneratedresidualimplications
AT danahlinena noteononelessknownclassofgeneratedresidualimplications
_version_ 1725276893811310592

Similar Items