{"id":{"repo_id":"catania","oai_identifier":"oai:www.iris.unict.it:20.500.11769/587295"},"canonical_url":"https://search.dev.ndltd.org/etd/catania/oai:www.iris.unict.it:20.500.11769/587295","repository":{"repo_id":"catania","name":"Università degli Studi di Catania","base_url":"https://www.iris.unict.it/oai/request"},"display":{"title":"New non-additive integrals in Multiple Criteria Decision Analysis","abstract":"The proposal and the axiomatization of new fuzzy integrals has a central role in modern Multiple Criteria Decision Analysis. In this thesis we propose some generalizations of well known fuzzy integrals (Choquet, Shilkret and Sugeno). We propose and characterize bipolar fuzzy integrals, which are generalization of the most famous fuzzy integrals to the case of bipolar scale, i.e. those symmetric scale where it is possible for each value to find the opposite. We also deal with the generalization of the concept of universal integral (recently proposed to generalize several fuzzy integrals) to the case of bipolar scales. We also provide the characterization of the bipolar universal integral with respect to a level dependent bi-capacity. Finally, we consider the problem to adapt classical definitions of fuzzy integrals to the case of imprecise interval evaluations. More precisely, standard fuzzy integrals used in MCDA request that the starting evaluations of a choice on various criteria must be expressed in terms of exact-evaluations. We present the robust Choquet, Shilkret and Sugeno integrals, computed with respect to an interval capacity. These are quite natural generalizations of the Choquet, Shilkret and Sugeno integrals, useful to aggregate interval-evaluations of choice alternatives into a single overall evaluation.","abstract_html":"The proposal and the axiomatization of new fuzzy integrals has a central role in modern Multiple Criteria Decision Analysis. In this thesis we propose some generalizations of well known fuzzy integrals (Choquet, Shilkret and Sugeno). We propose and characterize bipolar fuzzy integrals, which are generalization of the most famous fuzzy integrals to the case of bipolar scale, i.e. those symmetric scale where it is possible for each value to find the opposite. We also deal with the generalization of the concept of universal integral (recently proposed to generalize several fuzzy integrals) to the case of bipolar scales. We also provide the characterization of the bipolar universal integral with respect to a level dependent bi-capacity. Finally, we consider the problem to adapt classical definitions of fuzzy integrals to the case of imprecise interval evaluations. More precisely, standard fuzzy integrals used in MCDA request that the starting evaluations of a choice on various criteria must be expressed in terms of exact-evaluations. We present the robust Choquet, Shilkret and Sugeno integrals, computed with respect to an interval capacity. These are quite natural generalizations of the Choquet, Shilkret and Sugeno integrals, useful to aggregate interval-evaluations of choice alternatives into a single overall evaluation.","abstract_has_math":false,"creators":["RINDONE, FABIO"],"institution":"Università degli studi di Catania","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["GRECO, Salvatore","RUSSO, Giovanni"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-12-09","date_published":"2012-12-09","updated_at":"2026-07-24T01:35:22Z","subjects":["Choquet integral, Sugeno integral, bipolar integrals, imprecise evaluations, universal integral"],"languages":["eng"],"rights":["info:eu-repo/semantics/openAccess","license:PUBBLICO - Pubblico con Copyright","license uri:iris.PUB02"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/20.500.11769/587295","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Rindone, Fabio","GRECO, Salvatore","RUSSO, Giovanni"]},{"key":"dc:creator","label":"Author","values":["RINDONE, FABIO"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012-12-09"]},{"key":"dc:publisher","label":"Institution","values":["Università degli studi di Catania","place:Catania"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/doctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Choquet integral, Sugeno integral, bipolar integrals, imprecise evaluations, universal integral"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/openAccess","license:PUBBLICO - Pubblico con Copyright","license uri:iris.PUB02"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/20.500.11769/587295"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The proposal and the axiomatization of new fuzzy integrals has a central role in modern Multiple Criteria Decision Analysis. In this thesis we propose some generalizations of well known fuzzy integrals (Choquet, Shilkret and Sugeno). We propose and characterize bipolar fuzzy integrals, which are generalization of the most famous fuzzy integrals to the case of bipolar scale, i.e. those symmetric scale where it is possible for each value to find the opposite. We also deal with the generalization of the concept of universal integral (recently proposed to generalize several fuzzy integrals) to the case of bipolar scales. We also provide the characterization of the bipolar universal integral with respect to a level dependent bi-capacity. Finally, we consider the problem to adapt classical definitions of fuzzy integrals to the case of imprecise interval evaluations. More precisely, standard fuzzy integrals used in MCDA request that the starting evaluations of a choice on various criteria must be expressed in terms of exact-evaluations. We present the robust Choquet, Shilkret and Sugeno integrals, computed with respect to an interval capacity. These are quite natural generalizations of the Choquet, Shilkret and Sugeno integrals, useful to aggregate interval-evaluations of choice alternatives into a single overall evaluation.","La proposta e la caratterizzazione di nuovi integrali fuzzy ha un ruolo centrale nel campo delle decisioni ulticriteriali. In questa tesi verranno vengono presentate alcune interessanti generalizzazioni dei più conosciuti integrali fuzzy nella letteratura, cioè l'integrale di Choquet, Sugeno e Shilkret. Presenteremo e caratterizzeremo alcuni integrali bipolari, che sono generalizzazioni dei più noti integrali fuzzy anel caso di una scala bipolare. Presenteremo la generalizzazione del concetto di integrale universale al caso di scale bipolari simmetriche. Infine adatteremo le definizioni di integrale di Choquet, Shilkret e Sugeno al caso di valutazioni intervallari."]},{"key":"dc:title","label":"Title","values":["New non-additive integrals in Multiple Criteria Decision Analysis"]}]}],"canonical_facts":{"dc:contributor":["Rindone, Fabio","GRECO, Salvatore","RUSSO, Giovanni"],"dc:creator":["RINDONE, FABIO"],"dc:date":["2012-12-09"],"dc:description":["The proposal and the axiomatization of new fuzzy integrals has a central role in modern Multiple Criteria Decision Analysis. In this thesis we propose some generalizations of well known fuzzy integrals (Choquet, Shilkret and Sugeno). We propose and characterize bipolar fuzzy integrals, which are generalization of the most famous fuzzy integrals to the case of bipolar scale, i.e. those symmetric scale where it is possible for each value to find the opposite. We also deal with the generalization of the concept of universal integral (recently proposed to generalize several fuzzy integrals) to the case of bipolar scales. We also provide the characterization of the bipolar universal integral with respect to a level dependent bi-capacity. Finally, we consider the problem to adapt classical definitions of fuzzy integrals to the case of imprecise interval evaluations. More precisely, standard fuzzy integrals used in MCDA request that the starting evaluations of a choice on various criteria must be expressed in terms of exact-evaluations. We present the robust Choquet, Shilkret and Sugeno integrals, computed with respect to an interval capacity. These are quite natural generalizations of the Choquet, Shilkret and Sugeno integrals, useful to aggregate interval-evaluations of choice alternatives into a single overall evaluation.","La proposta e la caratterizzazione di nuovi integrali fuzzy ha un ruolo centrale nel campo delle decisioni ulticriteriali. In questa tesi verranno vengono presentate alcune interessanti generalizzazioni dei più conosciuti integrali fuzzy nella letteratura, cioè l'integrale di Choquet, Sugeno e Shilkret. Presenteremo e caratterizzeremo alcuni integrali bipolari, che sono generalizzazioni dei più noti integrali fuzzy anel caso di una scala bipolare. Presenteremo la generalizzazione del concetto di integrale universale al caso di scale bipolari simmetriche. Infine adatteremo le definizioni di integrale di Choquet, Shilkret e Sugeno al caso di valutazioni intervallari."],"dc:identifier":["https://hdl.handle.net/20.500.11769/587295"],"dc:language":["eng"],"dc:publisher":["Università degli studi di Catania","place:Catania"],"dc:rights":["info:eu-repo/semantics/openAccess","license:PUBBLICO - Pubblico con Copyright","license uri:iris.PUB02"],"dc:subject":["Choquet integral, Sugeno integral, bipolar integrals, imprecise evaluations, universal integral"],"dc:title":["New non-additive integrals in Multiple Criteria Decision Analysis"],"dc:type":["info:eu-repo/semantics/doctoralThesis"]},"updated_at":"2026-07-24T01:35:22Z"}