The Duality of Preference: Reconciling A Priori and A Posteriori Attitudes in Induced OWA Operator
摘要
The Ordered Weighted Averaging (OWA) and its variant, the Induced Ordered Weighted Averaging (IOWA), are two significant aggregation operators that assist decision-makers (DMs) in their decision-making processes. The characteristic of OWA operator is its “orness" metric measures its intrinsic optimism or pessimism level. However, the IOWA operator introduces a significant additional notion. The order of the inputs is not fixed in advance. Instead, it is decided by external elements, known as inducing variables. These variables guide how the inputs are arranged before aggregation stage. This paper shows that a lone, static measure of ‘attitudinal character’ is not enough for IOWA operators. We therefore introduce two complementary ideas. The first is ‘intrinsic attitude’, which represents the operator’s built-in attitudinal bias, similar to the concept of orness (attitudinal character) in OWA operators. The second is ‘realized attitude’, which describes the actual behavior observed when the operator is applied to the input values. This realized attitude follows from the interaction between the inducing variables and the input values. This dual understanding helps in creating and understanding IOWA-based decision systems better. It makes them clearer and reduces unintentional biases in decision making.