Towards true linguistic modelling through optimal numerical solutions

This paper is concerned with both the problems of quantitative and qualitative modelling of complex systems by using fuzzy techniques. A unified approach for the identification and subsequent extraction of linguistic knowledge of systems using fuzzy relational models is addressed. This approach deals with the identification problem by means of optimal numerical solutions based on weighted least squares and quadratic programming formulations. The linguistic knowledge is extracted in the form of consistent fuzzy rules that describe linguistically the behaviour of the identified system. A new methodology for the simplification of the extracted rules is derived by using a pruning criterion based on the representability matrix concept introduced in previous work. Several numerical aspects concerning the proposed optimization schemes and a covering discussion about the linguistic interpretation of the resulting models are also included together with illustrative examples in the contexts of pattern classification and dynamic systems identification. The paper also provides an overview of fuzzy modelling techniques that intends to situate the relational models among other fuzzy model architectures typically adopted in the literature, highlighting their main advantages and drawbacks.