Semantic constraints for membership function optimization

The optimization of fuzzy systems using bio-inspired strategics, such as ne ural network learning rules or evolutionary optimization techniques, is bec oming more and more popular. In general, fuzzy systems optimized in such a way cannot provide a linguistic interpretation, preventing us from using on e of their most interesting and useful features. This work addresses this d ifficulty and points out a set of constraints that when used within an opti mization scheme obviate the subjective task of interpreting membership func tions. To achieve this a comprehensive set of semantic properties that memb ership functions should have is postulated and discussed. These properties are translated in terms of nonlinear constraints that are coded within a gi ven optimization scheme, such as backpropogation. Implementation issues and one example illustrating the importance of the proposed constraints are in cluded.