CALCULATION AND APPLICATION OF A MINIMUM FUZZY RELATIONAL MATRIX

This paper compares the maximum and minimum inverse formulations for f uzzy identification of a relational matrix given a series of non-norma l input-output data. Baboshin and Naryshkin (1990) showed, for the cas e of normal input data, that identification of the relational matrix u sing an estimate of the minimum inverse resulted in a smaller Hamming distance, between actual and predicted output values, than the Mamdani identification method. This paper extends their work to include unres tricted or non-normal input data and confirms that the estimate of the minimum inverse for this case is again better than Mamdani's method. It is then proven that the relative rank of identification algorithms for minimization of the Hamming distance between the actual and predic ted output values is: the maximum inverse calculation of Sanchez (1976 ); the minimum inverse formulation, initial formulation by Sanchez (19 77), and extended to a series of input-output data by Sessa (1984); th e estimate of the minimum inverse; and then the Mamdani method. Howeve r, this ranking applies only in the fuzzy domain and not to the discre te or defuzzified domain relevant to many practical applications.