On reciprocity indexes in the aggregation of fuzzy preference relations using the OWA operator

Chiclana, Herrera and Herrera-Viedma studied conditions under which the reciprocity property is maintained in the aggregation of reciprocal fuzzy preference relations using the OWA operator guided by a relative linguistic quantifier. In this note, we focus on the reciprocity in the aggregation of fuzzy preference relations (that is, the additive reciprocity is not assumed) using the OWA operator. By defining a reciprocity index for measuring the non-reciprocity degree of fuzzy preference relations, we show that a sufficient (but not necessary) condition under which a "collective" fuzzy preference relation, obtained by aggregating a set of "individual" fuzzy preference relations using an OWA operator guided by a linguistic quantifier with parameter a and b, has a reciprocity index no greater than the largest of the corresponding "individual" reciprocity indexes. Our result is helpful to complete Chiclana et al.'s decision model [F. Chiclana, F. Herrera, E. Herrera-Viedma, Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations, Fuzzy Sets and Systems 97 (1998) 33-48].