On the duality of aggregation operators and k-negations

Authors:
E. de Amo;M. Díaz Carrillo;J. Fernández-Sánchez
Affiliations:
Departamento de Álgebra y Análisis Matemático, Universidad de Almería, Carretera de Sacramento s/n, 04120 La Caòada de san Urbano, Almería, Spain;Departamento de Análisis Matemático, Universidad de Granada, Campus de Fuentenueva s/n, 18071 Granada, Spain;Grupo de Investigación de Análisis Matemático, Universidad de Almería, Carretera de Sacramento s/n, 04120 La Caòada de san Urbano, Almería, Spain
Venue:
Fuzzy Sets and Systems
Year:
2011

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Abstract

In this paper we study a class of duality functions given by the solution of a system of functional equations related to the De Rham system. With the aid of a generalized dyadic representation system in the unit interval, we study a negation N which is a duality function for pairs of operators satisfying certain boundary conditions. New properties of N are investigated, including its singularity and fractal dimensions for several related sets. As an application we obtain an explicit expression for k-negations.