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 children's social environment is the main influence to consider in achieving sound child development, affecting throughout school life. For this reason, the development of child's 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 child's 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.
In this work, we extend these consistency notions defined on previous works. Particularly, this paper focuses on aggregation processes in which the information has a prioritized hierarchical structure, the different levels of the structure being related through a linear order. In this sense, we will first define the notion of hierarchical aggregation family, which is composed by an unstructured FAO and a FAO that aggregates data with a linear structure. Then, we will define some stability properties for this kind of structured families. In practical terms, this paper focuses on the construction issues that allow the development of indexes with an improved ability to represent our knowledge of a social reality. In this sense, a method to develop indexes of child’s home environment with prioritized information is proposed. The information involved in home environment has been represented by means of fuzzy sets, where the membership functions, as well as the priority relationships between the variables, were defined through expert’s judgments. The developed indexes have been generated by means of a stable family of prioritized aggregation operators, based on both the prioritized operators defined by Yager and the stability properties of a hierarchical structure proposed in this paper. This method was applied in the context of a population of Chilean children on a vulnerable condition, where the qualitative information of its home environment was generated in 2008 through the codification of the semi-structured interviews of a longitudinal research made by the National Board of Kindergartens (JUNJI) of Chile government
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