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

In neuro-fuzzy (or fuzzy-neural) systems using unconstrained optimization s chemes like backpropagation, it is not possible to guarantee that the resul ting membership functions represent human-interpretable linguistic terms. H owever, one of the most interesting features of fuzzy systems is the insigh t provided on the linguistic relationship between their variables. This wor k is devoted to the study of constraints which when used within an optimiza tion scheme obviate the subjective task of interpreting membership function s. To achieve this, a comprehensive set of semantic properties that members hip functions should have is postulated and discussed. Then a set of constr aints is introduced and shown to be able to fulfil the properties. Implemen tation issues and one example illustrating the importance of the proposed c onstraints are included. (C) 1999 Elsevier Science B.V. All rights reserved .