Quantifiers Induced by Subjective Expected Value of Sample Information

The ordered weighted averaging (OWA) operator provides a unified framework for multiattribute decision making (MADM) under uncertainty. In this paper, we attempt to tackle some issues arising from the quantifier guided aggregation using OWA operators. This allows us to consider a more general case involving the generation of quantifier targeted at the specified decision maker (DM) by using sample information. In order to do that, we first develop a repeatable interactive procedure in which with the given sample values, and the expected values the DM involved provides with personal preferences, we build nonlinear optimal models to extract from the DM information about his/her decision attitude in an OWA weighting vector form. After that, with the obtained attitudinal weighting vectors we suggest a suitable quantifier just for this DM by means of the piecewise linear interpolations. This obtained quantifier is totally derived from the behavior of the DM involved and thus inherently characterized by his/her own attitudinal character. Owing to the nature of this type of quantifier, we call it the subjective expected value of sample information-induced quantifier. We show some properties of the developed quantifier. We also prove the consistency of OWA aggregation guided by this type of quantifier. In contrast with parameterized quantifiers, our developed quantifiers are oriented toward the specified DMs with proper consideration of their decision attitudes or behavior characteristics, thus bringing about more intuitively appealing and convincing results in the quantifier guided OWA aggregation.