New triangular operator generators for fuzzy systems

Triangular operators (t-operators) form an integral part in the design and analysis of fuzzy systems. Simple monotonic, continuous, nonconditional functions are used in an operator generator to generate t-operators. Depending on the operator generator and the function that it uses, it becomes easier to characterize and classify the families of t-operators. In this paper, the author proposes two operator generators that will extend the domain of triangular operators in the realm of fuzzy set theory. The conventional operator generators generate a t-norm and a t-conorm by using a decreasing function and an increasing function, respectively. In contrast, in this study, increasing functions generate t-norms, while decreasing functions generate t-conorms, respectively.