Identification algorithms for fuzzy relational matrices. I: Non-optimizing algorithms (Q1971887)

The paper reviews and evaluates several identification algorithms for fuzzy relational matrices. It deals with the algorithms which do not involve the optimization of a performance index and compares them using the same (standardized) input-output data, membership functions and defuzzification procedure. The relational matrices, learned for each algorithm from the Box-Jenkins gas furnace data (a benchmark for fuzzy identification), are compared from the viewpoint of effectiveness of the output prediction. The shape of the reference fuzzy sets is chosen as isoscele triangles and the first order fuzzy state space relational model with time delay is used in the comparison. A new on-line identification algorithm, guaranteeing completeness of the relational matrix, is proposed and ranked the best in the class under consideration. The conclusions of the paper apply to the conditions assumed for the comparison of the algorithms.