Towards neuro-linguistic modeling: Constraints for optimization of membership functions

In neuro-fuzzy (or fuzzy-neural) systems using unconstrained optimization schemes like backpropagation, it is not possible to guarantee that the resulting membership functions represent human-interpretable linguistic terms. However, one of the most interesting features of fuzzy systems is the insight provided on the linguistic relationship between their variables. This work is devoted to the study of constraints which when used within an optimization scheme obviate the subjective task of interpreting membership functions. To achieve this, a comprehensive set of semantic properties that membership functions should have is postulated and discussed. Then a set of constraints is introduced and shown to be able to fulfil the properties. Implementation issues and one example illustrating the importance of the proposed constraints are included. (C) 1999 Elsevier Science B.V. All rights reserved.