Some issues on properties of the extended IOWA operators in fuzzy group decision making

Chiclana et al. [Chiclana, F., Herrera-Viedma, E., Herrera, F., Alonso, S. (2007). European Journal of Operational Research 182, 383–399] provided some IOWA operators for aggregating the individual fuzzy preference elations. The aim of this work is further to study their desired properties under group decision making problem with fuzzy preference relations. First, it is proved that the collective preference relations obtained by these cases of IOWA operators verified the reciprocity and the consistency properties. Next, the aggregation of individual judgements (AIJ) and the aggregation of individual priorities (AIP) provide the same priorities of alternatives by utilizing the IOWA operators as aggregation procedure and the row arithmetic mean method (RAMM) as prioritization procedure. Additionally, the Consistency IOWA (C-IOWA) operator guarantees that the group consistency degree is no less than the arithmetic mean of all the individual consistency degree. Finally, two illustrative numerical examples are used to verify the developed approaches.