Parametric classes of generalized conjunction and disjunction operations for fuzzy modeling

It is argued that inference procedures of fuzzy models do not always require commutativity and associativity of the operations used. This raises the possibility of considering nonassociative and noncommutative conjunction and disjunction operations. Such operations are investigated in this paper and different methods for their generation are proposed. A number of new types of conjunction operations that are simpler than the known parametric classes of T-norms are given and, as an application example, the approximation of a function by a fuzzy inference system is considered.