Structured fuzzy models

The paper deals with a problem of modeling of fuzzy systems in random environments. A model is proposed that is capable of handling two distinct forms of imprecision, viz. randomness and fuzziness. The model is required to cope with both of them while modeling a variety of problems in management, medical diagnosis, and unsupervised pattern recognition. The models proposed in the paper are constructed and evaluated in a formal framework established by fuzzy relation equations. Randomness is introduced as additional constraints imposed on the structure of the fuzzy relation equation (hence: structured fuzzy models). The forecasting (prediction) problem is studied in detail.