Karina Rojas

Some Properties of Consistency in the Families of Aggregation Operators

Properties related with aggregation operators functions have been widely studied in literature. Nevertheless, few efforts have been dedicated to analyze those properties related with the family of operators in a global way. What should be the relationship among the members of a family of aggregation operators? Is it possible to build the aggregation of n data with aggregation operators of lower dimension? Should it exist some consistency in the family of aggregation operators? In this work, we analyze two properties of consistency in a family of aggregation operators: Stability and Structural Relevance. The stability property for a family of aggregation operators tries to force a family to have a stable/continuous definition in the sense that the aggregation of n items should be similar to the aggregation of n + 1 items if the last item is the aggregation of the previous n items. Following this idea some definitions and results are given. The second concept presented in this work is related with the construction of the aggregation operator when the data that have to be aggregated has an inherent structure. The Structural Relevance property tries to give some ideas about the construction of the aggregation operator when the items are related by means of a graph.

Development of child's home environment indexes based on consistent families of aggregation operators with prioritized hierarchical information

The interventions aimed at the early childhood are of a main interest in educational policy, since it is in this period when it is possible to produce a major impact in the subsequent human development. The quality of childrens social environment is the main influence to consider in achieving sound child development, affecting throughout school life. For this reason, the development of childs environment indexes appears in a natural way in the evaluation of all kind of educational policy research and social programs. However, crisp measures and indexes, based on usual linear techniques, do not ensure an adequate representation of social reality, since this last has a fuzzy nature and a nonlinear behavior. The development of indexes can be seen as an aggregation problem. In this paper, we extend the notions of consistency and strict stability of a family of aggregation operators (FAO), proposed in a previous work of the authors for the case of an aggregation process in which the data have no particular structure, to the case in which the information has a prioritized hierarchical structure. This extended notion of strict stability is then used to address the construction of indexes. Particularly, we apply this approach to develop a construction method of childs home environment indexes in which a stable family of prioritized aggregation operators is used in order to ensure robustness of the aggregation process when the information has a lineal structure. These indexes are built using fuzzy data that fit into a hierarchical structure by means of a stable family of prioritized aggregation operators based on the prioritized operator formulated by Yager, where the order relationship over fuzzy information was defined by experts on child development.

Stability in Aggregation Operators

Aggregation functions have been widely studied in literature. Nevertheless, few efforts have been dedicated to analyze those properties related with the family of operators in a global way. In this work, we analyze the stability in a family of aggregation operators The stability property for a family of aggregation operators tries to force a family to have a stable/continuous definition in the sense that the aggregation of n − 1 items should be similar to the aggregation of n items if the last item is the aggregation of the previous n − 1 items. Following this idea some definitions and results are given.

On Stability of Families for Improper Aggregation Operators

This work extends the notion of consistency in terms of stability for Families of Aggregation Operators (FAO), as defined in previous works. The notion of stability proposed in this work, not only extends the previous one, but it can be applied to a wider set of FAOs, particularly, to those that we name here as Family of Improper Aggregation Operators (FIAO), or improper FAOs. When the aggregated value cannot be considered as a new item from the input, the present definition of consistency cannot be applied. This is usual in several areas, namely in the development of social, economic and political indexes, as far as the aggregation process typically yield a new and different concept from the input elements.

Consistency and stability in aggregation operators with data structure

In this work, we continue with a previous work in which we analyzed and defined notions of consistency, stability and continuity of a family of aggregation operators (FAO) when the data is unstructured. Here we use these concepts to tackle with aggregation problem for those situations in which the information or data that has to be aggregated has an inherent structure. In particular, we will focus on two structures that has received an important attention during last decades due to it application is different fields as Muticriteria Decision Analysis: The linear order structures and the hierarchical structures from a prioritized point of view.