Abstract
This chapter discusses various representations of set functions with a view toward practical applications of fuzzy measures. This includes Möbius and interaction representations, as well as vector representations that allow various calculations to be performed systematically and efficiently using software. Fuzzy measure transformations between the different representations in matrix-vector form are specified, which are also convenient for computer implementation. Lastly we address the marginal contributions representation and express various quantities with its help.
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Beliakov, G., James, S., Wu, JZ. (2020). Representations. In: Discrete Fuzzy Measures. Studies in Fuzziness and Soft Computing, vol 382. Springer, Cham. https://doi.org/10.1007/978-3-030-15305-2_4
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DOI: https://doi.org/10.1007/978-3-030-15305-2_4
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