Fuzzified weighted OWA (FWOWA) operator

In practice, it is often necessary to combine information from different sources. For this task, one of aggregation operators can be used. Probably the best-known of them are the weighted average and the OWA (ordered weighted average) operator. The weighted average makes it possible to assign importances to the individual information sources. On the other hand, with the OWA operator, the importances are assigned to the aggregated values according to their order. In cases when we need to combine these two approaches, the weighted OWA (WOWA) operator can be used. The situation when the aggregated values are not known precisely is very common in the practice. That is why fuzzified versions of various aggregation operators begun to emerge. In this paper, a fuzzified WOWA operator, which can aggregate values expressed by fuzzy numbers, will be presented. The version studied in this paper is based on Zadeh’s extension principle. The behavior of the presented fuzzified WOWA operator will be demonstrated on an illustrative example and it will be compared to a different approach to the fuzzification of the WOWA and to another aggregation operator generalizing the fuzzy weighted average and the fuzzy OWA operator. Finally, a software tool for the fuzzified WOWA calculation will be mentioned.