Adaptive robot under fuzzy control

This paper deals with the problem of ranking n fuzzy subsets of the unit interval. A number of methods suggested in the literature is reviewed and tested on a group of selected examples, where the fuzzy sets can be nonnormal and/or nonconvex.The ranking is obtained from: (i) the index of strict preference defined by Watson, (ii) three indexes proposed by Yager, (iii) the algorithm used by Chang, (iv) three versions of the a-preference index suggested by Adamo, (v) the index defined by Baas and Kwakernaak, (vi) three modified versions used by Baldwin and Guild, (vii) the method proposed by Kerre, (viii) three forms of the index suggested by Jain, (ix) the four grades of dominance studied by Dubois and Prade.In simple cases the results are good for all the methods, with some exceptions. In questionable cases, where the decision must be probably modelled in accordance with the context in which it is imbedded, the best indexes seem to be the dominances suggested by Dubois and Prade. These indexes do not force any particular choice, but clearly describe the situation, hence allowing the decision-maker himself to make his ‘best’ choice.