Abstract

ARENAS-DIAZ, Gilberto  and  RAMIREZ-LAMUS, Édgar René. Fuzzy measures and fuzzy integrals. Univ. Sci. [online]. 2013, vol.18, n.1, pp.7-32. ISSN 0122-7483.

This is a study of fuzzy measures and fuzzy integrals; it presents some of the phenomena where they are used. It exposes how the concept of fuzzy measure is introduced and from it, the notion of fuzzy integral is presented. Properties of fuzzy measures are established and they are classified according to additive property and λ-measures, while the probability, plausibility, credibility, possibility and necessity measures are observed as classic examples of the classification completed.The two main fuzzy integrals were analyzed: the Sugeno integral and the Choquet integral, given the application of these integrals is made on finite sets, a comparison between them for the finite case is performed using the concept of equiordered functions. We present two examples in which fuzzy measures and fuzzy integrals are used in the classification of individuals and in quality assessment. It also describes some phenomena where they are applied. Classic measures are used in certain special cases of uncertainty based on randomness. The use in certain contexts of fuzzy measures (non-additive) and fuzzy integrals offer a more flexible and realistic focus in modeling uncertainty.

Keywords : fuzzy measure; λ-measure; Choquet integral; Sugeno integral; equiordering function.

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