{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/choquet-integral-in-decision-analysis-lessons","title":"Choquet integral in decision analysis - lessons from the axiomatization","arxiv_id":"1611.09926","date":"2016-11-29","proceeding":null,"authors":["Mikhail Timonin"],"abstract":"The Choquet integral is a powerful aggregation operator which lists many\nwell-known models as its special cases. We look at these special cases and\nprovide their axiomatic analysis. In cases where an axiomatization has been\npreviously given in the literature, we connect the existing results with the\nframework that we have developed. Next we turn to the question of learning,\nwhich is especially important for the practical applications of the model. So\nfar, learning of the Choquet integral has been mostly confined to the learning\nof the capacity. Such an approach requires making a powerful assumption that\nall dimensions (e.g. criteria) are evaluated on the same scale, which is rarely\njustified in practice. Too often categorical data is given arbitrary numerical\nlabels (e.g. AHP), and numerical data is considered cardinally and ordinally\ncommensurate, sometimes after a simple normalization. Such approaches clearly\nlack scientific rigour, and yet they are commonly seen in all kinds of\napplications. We discuss the pros and cons of making such an assumption and\nlook at the consequences which axiomatization uniqueness results have for the\nlearning problems. Finally, we review some of the applications of the Choquet\nintegral in decision analysis. Apart from MCDA, which is the main area of\ninterest for our results, we also discuss how the model can be interpreted in\nthe social choice context. We look in detail at the state-dependent utility,\nand show how comonotonicity, central to the previous axiomatizations, actually\nimplies state-independency in the Choquet integral model. We also discuss the\nconditions required to have a meaningful state-dependent utility representation\nand show the novelty of our results compared to the previous methods of\nbuilding state-dependent models.","url_abs":"http://arxiv.org/abs/1611.09926v1","url_pdf":"http://arxiv.org/pdf/1611.09926v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[],"tasks":[],"methods":[{"method_slug":"mff","method_name":"MFF"}],"datasets_introduced":[],"methods_introduced":[{"slug":"mff","name":"MFF","full_name":"Multimodal Fuzzy Fusion Framework"}],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}