{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T03:46:11Z","timestamp":1779335171178,"version":"3.51.4"},"reference-count":31,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Fuzzy Sets and Systems"],"published-print":{"date-parts":[[2026,7]]},"DOI":"10.1016\/j.fss.2026.109863","type":"journal-article","created":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T00:11:37Z","timestamp":1774051897000},"page":"109863","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":1,"special_numbering":"C","title":["Conditional imprecise measures, independence, and products of interval probability measures"],"prefix":"10.1016","volume":"535","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9193-900X","authenticated-orcid":false,"given":"Marcello","family":"Basili","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luca","family":"Pratelli","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.fss.2026.109863_bib0001","doi-asserted-by":"crossref","DOI":"10.1016\/j.mathsocsci.2026.102509","article-title":"A new approach for imprecise probabilities","volume":"140","author":"Basili","year":"2026","journal-title":"Math. Soc. Sci."},{"key":"10.1016\/j.fss.2026.109863_bib0002","article-title":"A Treatise On Probability","author":"Keynes","year":"1921"},{"key":"10.1016\/j.fss.2026.109863_bib0003","unstructured":"I. Good, The measure of a non-measurable set, logic, methodology and philosophy of science, Stanford University Press, 1962."},{"issue":"2","key":"10.1016\/j.fss.2026.109863_bib0004","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1214\/aoms\/1177698950","article-title":"Upper and lower probabilities induced by a multivalued mapping","volume":"38","author":"Dempster","year":"1967","journal-title":"Ann. Math. Stat."},{"key":"10.1016\/j.fss.2026.109863_bib0005","series-title":"A Mathematical Theory of Evidence","volume":"1","author":"Shafer","year":"1976"},{"key":"10.1016\/j.fss.2026.109863_bib0006","series-title":"Eleventh International Joint Conference on Artificial Intelligence (IJCAI-89)","first-page":"1161","article-title":"Uncertainty, belief, and probability","author":"Fagin","year":"1989"},{"key":"10.1016\/j.fss.2026.109863_bib0007","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/0167-6377(89)90010-2","article-title":"Linear utility theory for belief functions","volume":"8","author":"Jaffray","year":"1989","journal-title":"Oper. Res. Lett."},{"key":"10.1016\/j.fss.2026.109863_bib0008","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/0304-4068(89)90018-9","article-title":"Maxmin expected utility with non-unique prior","volume":"18","author":"Gilboa","year":"1989","journal-title":"J. Math. Econ."},{"key":"10.1016\/j.fss.2026.109863_bib0009","doi-asserted-by":"crossref","unstructured":"P. Walley, Statistical reasoning with imprecise probabilities, Applied statistics, 1991. 10.2307\/2347427.","DOI":"10.1007\/978-1-4899-3472-7"},{"key":"10.1016\/j.fss.2026.109863_bib0010","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1006\/jeth.1999.2630","article-title":"Maxmin expected utility over savage acts with a set of priors","volume":"92","author":"Casadesus-Masanell","year":"2000","journal-title":"J. Econ. Theory"},{"key":"10.1016\/j.fss.2026.109863_bib0011","first-page":"755","volume":"78","author":"Gilboa","year":"2010","journal-title":"Objective and subjective rationality in a multiple prior model"},{"key":"10.1016\/j.fss.2026.109863_bib0012","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1006\/jeth.1993.1003","article-title":"Updating ambiguous beliefs","volume":"59","author":"Gilboa","year":"1993","journal-title":"J. Econ. Theory"},{"key":"10.1016\/j.fss.2026.109863_bib0013","doi-asserted-by":"crossref","first-page":"1144","DOI":"10.1109\/21.179852","article-title":"Bayesian updating and belief functions","volume":"22","author":"Jaffray","year":"1992","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"10.1016\/j.fss.2026.109863_bib0014","doi-asserted-by":"crossref","first-page":"1328","DOI":"10.1214\/aos\/1176347752","article-title":"Bayes\u2019 theorem for Choquet capacities","volume":"18","author":"Wasserman","year":"1990","journal-title":"Ann. Stat."},{"key":"10.1016\/j.fss.2026.109863_bib0015","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1111\/j.1467-8640.1991.tb00391.x","article-title":"Uncertainty, belief and probability","volume":"7","author":"Fagin","year":"1991","journal-title":"Comput. Intell."},{"key":"10.1016\/j.fss.2026.109863_bib0016","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","article-title":"Intuitionistic fuzzy sets","volume":"20","author":"Atanassov","year":"1986","journal-title":"Fuzzy Sets Syst."},{"key":"10.1016\/j.fss.2026.109863_bib0017","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/0165-0114(89)90205-4","article-title":"Interval valued intuitionistic fuzzy sets","volume":"31","author":"Atanassov","year":"1989","journal-title":"Fuzzy Sets Syst."},{"key":"10.1016\/j.fss.2026.109863_bib0018","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/0165-0114(89)90215-7","article-title":"More on intuitionistic fuzzy sets","volume":"33","author":"Atanassov","year":"1989","journal-title":"Fuzzy Sets Syst."},{"key":"10.1016\/j.fss.2026.109863_bib0019","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.fss.2004.02.015","article-title":"Trapeziodal approximation of fuzzy number","volume":"153","author":"Grzegorzewski","year":"2005","journal-title":"Fuzzy Sets Syst."},{"key":"10.1016\/j.fss.2026.109863_bib0020","doi-asserted-by":"crossref","first-page":"1464","DOI":"10.1016\/j.eswa.2010.07.055","article-title":"Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets","volume":"38","author":"Nayagam","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"10.1016\/j.fss.2026.109863_bib0021","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/s00500-018-3592-0","article-title":"Pythagorean hesitant fuzzy Choquet integral aggregation operators and their application to multi-attribute decision-making","volume":"23","author":"Khan","year":"2019","journal-title":"Soft Comput."},{"key":"10.1016\/j.fss.2026.109863_bib0022","doi-asserted-by":"crossref","DOI":"10.1016\/j.asoc.2023.110579","article-title":"Continuous intuitionistic fuzzy sets (CINFUS) and their AHP&TOPSIS extension: research proposals evaluation for grant funding","volume":"145","author":"Alkan","year":"2023","journal-title":"Appl. Soft Comput."},{"key":"10.1016\/j.fss.2026.109863_bib0023","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1080\/03081078208934833","article-title":"A class of fuzzy measures based on triangular norms","volume":"8","author":"Dubois","year":"1982","journal-title":"Int. J. Gen. Syst."},{"key":"10.1016\/j.fss.2026.109863_bib0024","article-title":"Possibility Theory: An Approach to the Computerized Processing of Uncertainty","author":"Dubois","year":"1988"},{"key":"10.1016\/j.fss.2026.109863_bib0025","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-017-2434-0","article-title":"Non-Additive Measure and Integral","author":"Denneberg","year":"1994"},{"key":"10.1016\/j.fss.2026.109863_bib0026","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1111\/j.2517-6161.1968.tb00722.x","article-title":"A generalization of Bayesian inference","volume":"30","author":"Dempster","year":"1968","journal-title":"J. R. Stat. Soc. Ser. B (Methodol.)"},{"key":"10.1016\/j.fss.2026.109863_bib0027","first-page":"141","article-title":"Multilinear fuzzy measures and their products","volume":"73","author":"Koshevoy","year":"1995","journal-title":"Fuzzy Sets Syst."},{"key":"10.1016\/j.fss.2026.109863_bib0028","first-page":"183","article-title":"On product of non-additive measures (capacities)","volume":"89","author":"Koshevoy","year":"1997","journal-title":"Fuzzy Sets Syst."},{"key":"10.1016\/j.fss.2026.109863_bib0029","first-page":"123","article-title":"Additive and nonadditive integration theory and applications to expected utility","volume":"14","author":"Marinacci","year":"1999","journal-title":"Econ. Theory"},{"key":"10.1016\/j.fss.2026.109863_bib0030","first-page":"1261","article-title":"Unique product measures for nonadditive probabilities","volume":"28","author":"Marinacci","year":"2000","journal-title":"Ann. Probab."},{"key":"10.1016\/j.fss.2026.109863_bib0031","series-title":"Set Functions, Games and Capacities in Decision Making","author":"Grabisch","year":"2016"}],"container-title":["Fuzzy Sets and Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0165011426001016?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0165011426001016?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T12:40:32Z","timestamp":1777725632000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0165011426001016"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7]]},"references-count":31,"alternative-id":["S0165011426001016"],"URL":"https:\/\/doi.org\/10.1016\/j.fss.2026.109863","relation":{},"ISSN":["0165-0114"],"issn-type":[{"value":"0165-0114","type":"print"}],"subject":[],"published":{"date-parts":[[2026,7]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Conditional imprecise measures, independence, and products of interval probability measures","name":"articletitle","label":"Article Title"},{"value":"Fuzzy Sets and Systems","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.fss.2026.109863","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"109863"}}