ON THE APPROXIMATION OF FUZZY PREFERENCES BY EXACT RELATIONS

The generalized Hamming distance is commonly used in determining a clo sest crisp relation to a given fuzzy relation (which, in turn, is cruc ial in studying exact choices originating from fuzzy preferences). Thi s note illustrates a difficulty attached to this practice, and propose s an alternative metric which is intuitively more appropriate in the c ase of fuzzy preferences. Some implications of this new metric on find ing the nearest exact relation to a fuzzy preference ordering and on t he understanding of the max-min transitivity property are also discuss ed.