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27 octobre 2021
- handle: 10670/1.581345
- halshs: halshs-03483960
- doi: 10.1007/978-3-030-87756-9_21
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info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-030-87756-9_21
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Binary alternatives Sugeno integral model Interaction indices 2-maxitive capacity Binary alternativesCiter ce document
Paul Alain Kaldjob Kaldjob et al., « Necessary and Possible Interaction in a 2-Maxitive Sugeno Integral Model », HAL-SHS : économie et finance, ID : 10.1007/978-3-030-87756-9_21
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This paper proposes and studies the notion of interaction between two criteria in a 2-maxitive Sugeno integral model. Within the framework of binary alternatives, we give a necessary and sufficient condition for preferential information on binary alternatives to be representable by a 2-maxitive Sugeno integral model. Using this condition, we show that it is always possible to choose a numerical representation, for which all the interaction indices are strictly positive. Outside the framework of binary alternatives, by introducing binary variables, we propose a MILP allowing to test whether an ordinal preference information is representable by a 2-maxitive Sugeno integral model and whether the interpretation of the interaction indices is ambiguous or not. We illustrate our results with examples.