ORDER NORMS ON BOUNDED PARTIALLY ORDERED SETSG

In this paper, we extend the domains of affirmation and negation operators, and more important, of triangular (semi)norms and (semi)conorms from the unit interval to bounded partially ordered sets. The fundamental properties of the original operators are proven to be conserved under this extension. This clearly shows that they are essentially based upon order-theoretic notions. Consequently, a rather general ordertheoretic invariance study of these operators is undertaken. Also, in a brief algebraic excursion, the notion of weak invertibility of these operators is introduced, and the relation with the order-theoretic concept of residuals is studied. The importance of these results for fuzzy set theory and possibility theory is briefly discussed.