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Maximum entropy ordered weighted averaging in the binomial decomposition framework
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DOI：10.1002/int.22083.png)
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摘要
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We consider the maximum entropy constrained optimization problem associated with ordered weighted averaging (OWA) in the binomial decomposition framework. We begin by reviewing the analytic solution of the maximum entropy method proposed by Filev and Yager in 1995, and later by Fuller and Majlender in 2001. Next, we briefly review the binomial decomposition framework, which allows for an alternative parametric description of the OWA functions. The values of the binomial coefficients alpha j,j=1, horizontal ellipsis ,n are uniquely determined by the weighting structure of the OWA function. We observe that for low orness values omega is an element of[0,0.5], the optimal weights are decreasing, whereas they are increasing for high orness values omega is an element of[0.5,1]. Moreover, we notice that the optimal values of the first and last weights have a wide range in [0,1], whereas the values of the other weights have more restricted ranges. As for the optimal alpha j,j=1, horizontal ellipsis ,n coefficients, we find that their behavior with respect to orness values omega is an element of[0,1] is very different for low/high orness. We illustrate graphically the optimal alpha j,j=1, horizontal ellipsis ,n coefficients in two parts, first for low orness values omega is an element of[0,0.5] and then for high orness values omega is an element of[0.5,1]. We observe that the optimal alpha j,j=1, horizontal ellipsis ,n for low orness values omega is an element of[0,0.5] are all nonnegative and take values in the unit interval, independently of the dimension n. On the contrary, the optimal values of the alpha j,j=1, horizontal ellipsis ,n coefficients for high orness values omega is an element of[0.5,1] depend strongly on the dimension n, both in the complexity of their distribution and in the amplitude of their scale.
Keyword:
OWA functions
orness
maximum entropy method
binomial decomposition
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