na Br.nrapcxera aKa,n;eMlrn na HaYKMTe Comptes rendus de l' Academic bulgare des Sciences Tome 61, No 5, 2008 MATHEMATIQUES Sous-ensemble flous FUZZY CRITERIA IMPORTANCE DEPENDING ON MEMBERSHIP DEGREES OF FUZZY RELATIONS Vania Peneva, Ivan Popchev (Submitted on March 12, 2008) Abstract The problem is connected with the weighted aggregation of fuzzy relations given by criteria that evaluate a finite set of alternatives. The weights of these criteria are quadratic weighting functions depending on the membership degrees of the fuzzy relations. Transformed membership degrees computed by the help of these weighting functions are used in aggregation procedures. The properties of these relations required to decide the problems of choice, ranking or clustering of the alternatives' set are proved. Key words: fuzzy multicriteria decision making, fuzzy relations, aggre- gation operators, fuzzy relations' properties, weighting functions 2000 Mathematics Subject Classification: 03E72 1. Introduction. The following multicriteria decision making problem is considered. A finite number of alternatives is evaluated by several independent fuzzy criteria comparing each couple of the alternatives by assigning fuzzy re- lations with membership degrees values in the unit interval. The importance of each criterion is quadratic weighting function with values in unit interval as well. Aggregation operators, uniting the membership degrees by all relations, taking into account the respective weighting functions in order to compute the multicri- teria score of the fuzzy relations are used. The purpose is the obtained aggregated fuzzy relation to possess some properties giving a possibility to decide some mul- ticriteria decision making problems. This work is supported by the Bulgarian Academy of Sciences under grant 010077. 2 579