Abstract
Ordered Weighted Aggregation operators (OWA) are widely analyzed and applied to real world problems, given their appealing characteristic to reflect human reasoning, but are enable in the basic definition to include importance weights for the criteria. To obviate, some extensions were introduced, but we show how none of them can satisfy completely a set of required properties. Thus we introduce a new proposal, the Standard Deviation OWA (SDOWA) which conversely satisfy all the listed properties and seems to be more convincing then other ones.
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Notes
- 1.
Values in between zero and one. In many cases, the normalization of the original data is obtained normally by a values function, see [7].
- 2.
Both OWA and WOWA are particular cases of NAM, see [12], 1citeTorra-3.
- 3.
- 4.
A linguistic term-set as “it exists”, “most”, “for all” etc. can be represented by a RIM, see [19].
- 5.
- 6.
Clearly, the orness index is defined by \(1-\textit{andness}\).
- 7.
Other properties are introduces by some Authors, as homogeneity and symmetry, but they are with minor significance for our purpose, see [8].
- 8.
In [8] these properties are implicitly used in the discussion of WOWA operators, see point 1. and 2. at page 386 of the quoted reference.
- 9.
- 10.
Two sets of weights can be sufficient for a WOWA too, but an interpolation algorithm is required, see [12].
- 11.
A part other drawback, WOWA sometimes returns counterintuitive results [8].
- 12.
With \(\alpha =0.5\) the Author claims that the two sets of weights receive the same importance, but as just commented above, it is unclear the real meaning of such a choice.
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Cardin, M., Giove, S. (2021). SDOWA: A New OWA Operator for Decision Making. In: Esposito, A., Faundez-Zanuy, M., Morabito, F., Pasero, E. (eds) Progresses in Artificial Intelligence and Neural Systems. Smart Innovation, Systems and Technologies, vol 184. Springer, Singapore. https://doi.org/10.1007/978-981-15-5093-5_28
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