THE INVERSE PROBLEM OF THE AGGREGATION OF FUZZY SETS

The inverse problem of the aggregation of fuzzy sets is addressed: the result of the aggregation of several fuzzy sets being known, the aim is to determine the initial sets. The case of the aggregation of two premises is studied first and a rule-based method is proposed to determine exactly all the widest solution sets of the problem. A recurrent algorithm is then proposed to solve the problem in the case of any number of fuzzy sets. The relevance of the proposed criteria enables to cope with the exponential complexity of the problem, and to define the widest solution sets only. Examples are provided to illustrate how the solving algorithms can practically be applied.