Designing and learning of adjustable quasi-triangular norms with applications to neuro-fuzzy systems. - Rutkowski, L. (IEEE Transactions on fuzzy systems)
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,...,an;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 proposed 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 work is determined in the process of learning. Learning procedures are derived and simulation examples are presented.