A Note on One Less Known Class of Generated Residual Implications

Vojtěch Havlena
(Brno University of Technology, Czech Republic)
Dana Hliněná
(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.

In Jan Bouda, Lukáš Holík, Jan Kofroň, Jan Strejček and Adam Rambousek: Proceedings 11th Doctoral Workshop on Mathematical and Engineering Methods in Computer Science (MEMICS 2016), Telč, Czech Republic, 21st-23rd October 2016, Electronic Proceedings in Theoretical Computer Science 233, pp. 13–22.
Published: 13th December 2016.

ArXived at: https://dx.doi.org/10.4204/EPTCS.233.2 bibtex PDF
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