Designing and Learning of Adjustable Quasi-Triangular Norms. With Applications to Neuro-Fuzzy Systems.

In this paper, we introduce a new class of operators called quasi-triangular norms. They are denoted by H and parameterized by a parameter ν : H(a₁, a₂, . . . , a_n; ν). From the construction of function H, it follows that it becomes a t-norm for ν = 0 and a dual t-conorm for ν = 1. For ν close to 0, function H resembles a t-norm and for ν close to 1, it resembles a t-conorm. In the paper, we also propose adjustable quasi-implications and a new class of neuro-fuzzy systems. Most neuro-fuzzy systems pro- posed in the past decade employ ‘engineering implications’ defined by a t-norm as the minimum or product. In our proposition, a quasi-implication I(a, b; ν) varies from an ‘engineering implication’ T(a, b) to corresponding S-implication as ν goes from 0 to 1. Consequently, the structure of neuro-fuzzy systems presented in this paper is determined in the process of learning. Learning procedures are derived and simulation examples are presented. [ABSTRACT FROM AUTHOR]