Consistency and stability in aggregation operators: An application to missing data problems

Abstract

In this work we analyze the key issue of the relationship that should hold between the operators in a family {A n } of aggregation operators in order to understand they properly define a consistent whole. Here we extend some of the ideas about stability of a family of aggregation operators into a more general framework, formally defining the notions of i − L and j − R strict stability for families of aggregation operators. The notion of strict stability of order k is introduced as well. Finally, we also present an application of the strict stability conditions to deal with missing data problems in an information aggregation process. For this analysis, we have focused in the weighted mean family and the quasi-arithmetic weighted means families.

A novel ordered weighted averaging weight determination based on ordinal dispersion

“…For the levels under analysis, ∈ α {0.3, 0.5, 0.6} it is clear that motorbike P 1 , achieving the highest score on its best two criteria, ranks on the first position at all exigence levels. Motorbike P 7 ranks at better positions for higher values as T A B L E 7 MEOWA, MOOWA, and MINOOWA weights for three different level of orness 0.45 (6) 0.35 (4) 0.45 (6) 0.5 (5)(6) 0.26 (6) 0.3 (7) 0.38 (7) the weights associated to this exigence levels concentrate on the first scores. When taking into account P 7 worst score, the motorbike loses position in the ranking.…”

An axiomatic approach to finite means

“…A typical situation, encountered in the study of aggregation operators in fuzzy set theory, appears when J = [0, 1] (see e.g. [36,35]).…”

“…Among classical operators in this theory we may consider triangular norms, triangular conorms and copulas (see e.g. [32,43,2,37,36,51,35]).…”

“…dropping the anonymity-neutrality conditions, concepts as left-recursivity and right-recursivity have been defined and analyzed (see e.g. [22,3,12,35]). These conditions would agree with iterativity under anonymity-neutrality.…”

“…[40,41,23]) as well as from a miscellaneous wide set of interdisciplinary applications (e.g. : aggregation of individual preferences into a social one, in Mathematical Social Choice, see [20,15,17,29,14], or the study of aggregation operators in Fuzzy Set Theory, see [26,46,22,3,12,35]).…”