On the Sheffer stroke operation in fuzzy logic

Abstract

From the beginnings of fuzzy logic, the Sheffer stroke operation has been overlooked and the efforts of the researchers have been devoted to other logical connectives. In this paper, the Sheffer stroke operation is introduced in fuzzy logic generalizing the classical operation when the truth values are restricted to {0, 1}(2). Similar to what happens in Boolean logic, the fuzzy Sheffer stroke is functionally complete and it can be used to generate any other fuzzy logical connective by combinations of itself. Two construction methods are presented and the close connection of this operation with a pair of fuzzy conjunction and negation is analysed.