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In this Section, we briefly describe the interval numbers, the UOWA operator and the POWA operator.
The uncertain OWA (UOWA) operator was introduced by Xu and Da (2002).
An UOWA operator of dimension n is a mapping UOWA: [[OMEGA].sup.n] [right arrow] [OMEGA] that has an associated weighting vector W of dimension n such that [w.sub.j] [member of] [0, 1] and [[summation].sup.n.sub.j=1] [w.sub.j] = 1, then:
Note also that different families of UOWA operators can be studied by choosing a different weighting vector such as the step-UOWA operator, the window-UOWA, the median-UOWA, the olympic-UOWA, the centered-UOWA and the S-UOWA.
Basically, if [beta] = 0, then, we get the probabilistic approach and if [beta] = 1, the UOWA operator.
Note that these properties have to be accomplished for the weighting vector W of the UOWA operator but not necessarily for the weighting vector P of the probabilities.
We have also studied some of its main properties and particular cases including the uncertain probabilistic minimum, the uncertain probabilistic maximum, the UOWA, the UPA, the UAOWA and the UAPA operator.