The Generalized Hybrid Averaging Operator and its Application in Decision Making // La media generalizada híbrida y su aplicación en la toma de decisiones

José M. Merigó Lindahl, Montserrat Casanovas Ramón

Resumen


We present the generalized hybrid averaging (GHA) operator. It is a new aggregation operator that generalizes the hybrid averaging (HA) operator by using the generalized mean. Thus, we are able to generalize a wide range of mean operators such as the HA, the hybrid geometric averaging (HGA), the hybrid quadratic averaging (HQA), the generalized ordered weighted averaging (GOWA) operator and the weighted generalized mean (WGM). A key feature in this aggregation operator is that it is able to deal with the weighted average and the ordered weighted averaging (OWA) operator in the same formulation. We further generalize the GHA by using quasi-arithmetic means obtaining the quasi-arithmetic hybrid averaging (Quasi-HA) operator. We conclude the paper with an example of the new approach in a financial decision making problem.

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En este artículo se presenta el operador de medias generalizadas híbridas. Es un nuevo operador de agregación que generaliza la media híbrida utilizando la media generalizada. Debido a esto, se puede generalizar una amplia gama de operadores de medias, como la media híbrida, la media geométrica híbrida, la media cuadrática híbrida, la media ponderada ordenada generalizada y la media ponderada generalizada. Un aspecto fundamental en este operador de agregación es la posibilidad de utilizar medias ponderadas y medias ponderadas ordenadas en la misma formulación. A continuación, se presenta una generalización mayor mediante la utilización de medias cuasi-aritméticas, obteniendo así la media cuasi-aritmética híbrida. El trabajo termina con un ejemplo de aplicación del nuevo modelo en un problema de toma de decisiones financieras. 


Palabras clave


Aggregation operator; OWA operator; generalized mean; weighted average; decision making; operador de agregación; operador OWA; media generalizada; media ponderada; toma de decisiones

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