2016/12/15 by Vojtěch Havlena, Dana Hliněná
Mathematics · #math.LO
paper · pdf · doi:10.4204/eptcs.233.2
published as EPTCS 233, 2016, pp. 13-22 · In Proceedings MEMICS 2016, arXiv:1612.04037
arxiv created 2016/12/15 · arxiv updated 2016/12/16
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 IgN 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.