A geometric approach to aggregation

In analogy to the representation of the standard probabilistic average as an expected value of a random variable, a geometric approach to aggregation is proposed. Several properties of such aggregation operators are investigated, and the relationship with distinguished classes of aggregation operators is discussed. Key words. Aggregation operator, fuzzy measure, Choquet integral, triangular norm. In both cases, the surface of the endograph of a non-increasing function hmVf: [O,11 + [O,1] given by h,, (t) = m({f 2 t)) is computed, where m is a (a-additive) measure and f represents the input to be aggregated. We generalize (1) and (2), replacing the aadditivity of the measure by significantly weaker properties. This will lead to a rather general class of geometrical aggregation operators, and many distinguished classes of aggregation operators are special cases thereof.

• Type: Conference
• Year: 2001
• Where: EUSFLAT
• Authors: Erich-Peter Klement, Radko Mesiar, Endre Pap
• Keywords: Aggregation Operators, Distinguished Classes, EUSFLAT 2001, EUSFLAT 2007, Standard Probabilistic Average