Aggregation functions and contradictory information

Authors:
Ana Pradera;Gleb Beliakov;Humberto Bustince
Affiliations:
Departamento de Ciencias de la Computación, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain;School of Information Technology, Deakin University, 221 Burwood Hwy, Burwood 3125, Australia;Departamento de Automática y Computación, Universidad Pública de Navarra, Campus Arrosadia s/n, P.O. Box 31006, Pamplona, Spain
Venue:
Fuzzy Sets and Systems
Year:
2012

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Abstract

The aim of this paper is to analyze the behavior of aggregation functions when the inputs are contradictory. This may be a useful criterion helping to choose the most appropriate function for solving a given problem. With that goal, bivariate aggregation functions are classified depending on the output they associate to contradictory couples of the form (x,N(x)), where N is a strong negation. The main properties of the newly defined classes are studied. Examples of functions in each class are provided, paying special attention to the most important families of aggregation functions, such as t-norms, copulas, symmetric sums, uninorms or nullnorms.