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Strictly stable families of aggregation operators

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Rojas, Karina and Gómez, Daniel and Montero, Javier and Rodríguez, Juan Tinguaro (2013) Strictly stable families of aggregation operators. Fuzzy Sets and Systems, 228 . pp. 44-63. ISSN 0165-0114

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Official URL: http://www.sciencedirect.com/science/article/pii/S0165011412005271


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Abstract

In this paper we analyze the notion of family of aggregation operators (FAO), also refereed to as extended aggregation functions (EAF), i.e., a set of aggregation operators defined in the unit interval which aggregate several input values into a single output value. In particular, we address the key issue of the relationship that should hold between the operators in a family in order to understand that they properly define a consistent FAO. We focus on the idea of strict stability of a family of aggregation operators in order to propose an operative notion of consistency between operators of such a family. In this way, robustness of the aggregation process can be guaranteed. Some strict stability definitions for FAOs are proposed, leading to a classification of the main aggregation operators in terms of the properties they satisfy. Furthermore, we apply this approach to analyze the stability of some families of aggregation operators based on weights.


Item Type:Article
Uncontrolled Keywords:Aggregation operators; Stability; Consistency; Self-identity; Fuzzy sets
Subjects:Sciences > Mathematics > Mathematical statistics
ID Code:23176
Deposited On:15 Oct 2013 09:03
Last Modified:30 Aug 2018 08:20

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