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For the Choquet integral defined with respect to the following fuzzy measure: v({1,2,3})=1 v({1,2})=1,v({1,3})=0.7,v({2,3})=0.4 v({1})=0.5,v({2})=0.2,v({3})=0.2 v()=0 Options: x 1 and x 2 contribute to the

For the Choquet integral defined with respect to the following fuzzy measure:

v({1,2,3})=1

v({1,2})=1,v({1,3})=0.7,v({2,3})=0.4

v({1})=0.5,v({2})=0.2,v({3})=0.2

v()=0

Options:

  • x1andx2contribute to the output in a complimentary way.When both inputs are high, they affect the output more than the sum of their individual contributions when only one or the other is high.

  • x1andx2are somewhat redundant in their contribution to the output.If one input is already high, then the other input being high does not add much more to the output, especially when compared to its contribution when the other is low.

  • x1andx2are additive.The inputs contribute to the output to the same degree whether or not the other input is high.

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