Project «The Data-Based Fuzzy Modeling of Engineering Systems» supported by Grant of Russian Foundation for Basic Research (06-08-00248)

1. The technique for fuzzy model identification is offered.

2. Within the framework of the offered technique (stage «expert evaluation») the algorithms of fuzzy inference based on formal logical reasoning approach and Mamdani's approximation are developed.

3. The algorithms and programs for fuzzy rules base formation based on fuzzy clustering method and subjective division of the data (stage «structural identification») are developed.

4. The algorithms for parametrical identification based on gradient descent technique, Kalman filter, evolutionary methods and ant colony are developed.

5. The hybrid algorithms based on classical (derivative-based) and meta-heuristical methods (not derivative-based) are developed.

6. The program systems realizing all above mentioned algorithms are developed.

7. The experiments with fuzzy systems such as 2ISO are executed. Types of models (singleton, Mamdani's), algorithms for identification, a kind of membership functions (triangular, trapezoid, parabolic, Gaussian) and degree of their fuzzifility (alfa-cut), way of the task of the t-operator (Zadeh, Probabilistic, Lukasiewicz, Schweizer- Sklar), way of the task of the most fuzzy inference (formal logical reasoning approach and Mamdani'sapproximation), number of terms in sets here changed.

8. Methodical recommendations.

8.1. Fuzzy rules and the membership functions should cover all universum, on which they are determined. The transition from one membership function to another should not contain breaks, differently surface of a conclusion will contain also breaks.

8.2. For singleton-type fuzzy systems the best inferences is received for hybrid algorithms.

8.3. For Mamdani's-type fuzzy systems and test data described by linear function, the best inferences are received for formal logical reasoning approach, center-of-gravity defuzzification method, with triangular membership functions, at the task of t-normal Lukasiewicz's function and t-conormal Probabilistic function. However property of a duality of  t-norms and t-conormal concerning fuzzy negation here is not observed.