The Symmetric Sugeno Integral

Michel Grabisch

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Abstract: We propose an extension of the Sugeno integral for negative numbers, in the spirit of the symmetric extension of Choquet integral, also called \Sipos\ integral. Our framework is purely ordinal, since the Sugeno integral has its interest when the underlying structure is ordinal. We begin by defining negative numbers on a linearly ordered set, and we endow this new structure with a suitable algebra, very close to the ring of real numbers. In a second step, we introduce the Möbius transform on this new structure. Lastly, we define the symmetric Sugeno integral, and show its similarity with the symmetric Choquet integral.

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Date: 2003
Note: View the original document on HAL open archive server: https://hal.science/hal-00272084
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Published in Fuzzy Sets and Systems, 2003, 139 (3), pp.473-490

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00272084

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