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The aim of this paper is to introduce a new and rigorous methodology based on the concept of a fuzzy extension of a transformation function for the design of environmental quality indexes. A fuzzy extension is a generalisation of a classical function extended to the field of the fuzzy sets defined in R. Transformation functions are used to convert the values taken by the environmental indicators on the site into the values that represent their contributions to the environmental quality index. For the design of the index, a set of attributes is defined, which should include all the significant factors of the environmental quality under consideration. In addition, an environmental indicator is selected to quantify each attribute, together with its range of values. Next, a fuzzy extension is defined for each environmental indicator and subsequently, a pair-wise comparison matrix of the relative importance of the attributes is calculated, and a standardized priority vector is determined. The values taken by the environmental indicators on the site are described in fuzzy terms. The fuzzy contribution to the environmental quality index is the image of the indicator’s value through the fuzzy extension of the transformation function. The fuzzy value of the environmental quality index is the result of adding the fuzzy contributions according to their relative importance. Finally, punctual and interval classic estimators of the environmental quality index are calculated by the defuzzification of the fuzzy value of the environmental quality index.

Nueva metodología para el diseño de índices de calidad ambiental basada en extensiones difusas de funciones de transformación