On a Graded Notion of t-Norm and Dominance

Abstract—The paper studies graded properties of MTL valued binary connectives, focusing on conjunctive connectives such as t-norms, uninorms, aggregation operators, or quasicopulas. The graded properties studied include monotony, a generalized Lipschitz property, unit and null elements, commutativity, associativity, and idempotence. Finally, a graded notion of dominance is investigated and applied to transmission of graded properties of fuzzy relations. The framework of Fuzzy Class Theory (or higher-order fuzzy logic) is employed as a tool for easy derivation of graded theorems on the connectives.

• Type: Conference
• Year: 2010
• Where: ISMVL
• Authors: Libor Behounek, Petr Cintula, Ulrich Bodenhofer, Susanne Saminger-Platz, Peter Sarkoci
• Keywords: Artificial Intelligence, Conjunctive Connectives, Graded, ISMVL 2010, Studies Graded Properties