Publication Date




Published in Bulletin for Studies and Exchanges on Fuzziness and its AppLications (BUSEFAL), Vol. 78, Spring 1999, pp. 12-16.


Originally, fuzzy logic was proposed to describe human reasoning. Lately, it turned out that fuzzy logic is also a convenient approximation tool, and that moreover, sometimes a better approximation can be obtained if we use real values outside the interval [0,1]; it is therefore necessary to describe possible extension of t-norms and t-conorms to such new values. It is reasonable to require that this extension be associative, i.e., that the set of truth value with the corresponding operation form a semigroup. Semigroups have been extensively studied in mathematics. In this short paper, we describe several results from semigroup theory which we believe to be relevant for the proposed extension of t-norms and t-conorms.