On Fuzzy Sheffer Stroke Operation
The generalization of the classical logical connectives to the fuzzy logic framework has been one of the main research lines since the introduction of fuzzy logic. Although many classical logical connectives have been already generalized, the Sheffer stroke operation has received scant attention. This operator can be used by itself, without any other logical operator, to define a logical formal system in classical logic. Therefore, the goal of this article is to present some initial ideas on the fuzzy Sheffer stroke operation in fuzzy logic. A definition of this operation in the fuzzy logic framework is proposed. Then, a characterization theorem in terms of a fuzzy conjunction and a fuzzy negation is presented. Finally, we show when we can obtain other fuzzy connectives from fuzzy Sheffer stroke operation.
KeywordsSheffer stroke Fuzzy implication Fuzzy negation t-norm t-conorm
M. Baczyński and W. Niemyska were supported by the National Science Centre, Poland, under Grant No. 2015/19/B/ST6/03259. P. Helbin has been supported from statutory activity of the Institute of Mathematics, University of Silesia in Katowice. P. Berruezo, S. Massanet and D. Ruiz-Aguilera acknowledge the partial support by the Spanish Grant TIN2016-75404-P, AEI/FEDER, UE.