On weighted P‐quantile aggregation

We consider the problem of aggregating ordinal information with quantitative or qualitative importance based on quantile operations. For a bag 〈x₁, x₂, …, x_n〉 in real or in (finite) ordinal scales, the quantile operations used in this paper are operating based on the floating position index of x_i that is determined by its position on the ordered sequence (x₍₁₎, x₍₂₎, …, x_(n)), where x_(i) is the ith smallest element of the bag 〈x₁, x₂, …, x_n〉. We call this type of quantile aggregation as the floating position index‐based quantile (p‐quantile) aggregation. We study on weighted p‐quantile aggregation in real scales and extend the corresponding techniques to p‐quantile aggregation of ordinal information with quantitative importance. The aggregated result of the latter is represented by a general ordinal proportional 2‐tuple. On basis of the notion of importance transformation (that is modified from Yager), we investigate p‐quantile aggregation of ordinal information with qualitative importance. Then, we use p‐quantile aggregation to define the floating position index‐based ordered weighted averaging (P‐OWA) aggregation of ordinal information with qualitative importance and apply it to the problem of multicriteria decision making. © 2008 Wiley Periodicals, Inc.