{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T21:04:45Z","timestamp":1777064685321,"version":"3.51.4"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2022,8,3]],"date-time":"2022-08-03T00:00:00Z","timestamp":1659484800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,8,3]],"date-time":"2022-08-03T00:00:00Z","timestamp":1659484800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61973332"],"award-info":[{"award-number":["61973332"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Intell"],"published-print":{"date-parts":[[2023,4]]},"DOI":"10.1007\/s10489-022-03877-7","type":"journal-article","created":{"date-parts":[[2022,8,3]],"date-time":"2022-08-03T06:02:30Z","timestamp":1659506550000},"page":"8799-8808","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Quantum algorithm of Dempster rule of combination"],"prefix":"10.1007","volume":"53","author":[{"given":"Lipeng","family":"Pan","sequence":"first","affiliation":[]},{"given":"Xiaozhuan","family":"Gao","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9286-2123","authenticated-orcid":false,"given":"Yong","family":"Deng","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,8,3]]},"reference":[{"key":"3877_CR1","doi-asserted-by":"crossref","unstructured":"Dempster AP (1966) Upper and lower probabilities induced by a multivalued mapping(upper and lower probabilities induced by multivalued mapping)","DOI":"10.1214\/aoms\/1177698950"},{"key":"3877_CR2","doi-asserted-by":"crossref","unstructured":"Shafer G (1976) A mathematical theory of evidence, vol 42. Princeton University Press","DOI":"10.1515\/9780691214696"},{"issue":"6","key":"3877_CR3","first-page":"3983","volume":"15","author":"Y Deng","year":"2020","unstructured":"Deng Y (2020) Information volume of mass function. Int J Computs Commun Control 15(6):3983","journal-title":"Int J Computs Commun Control"},{"key":"3877_CR4","doi-asserted-by":"publisher","first-page":"358","DOI":"10.1016\/j.knosys.2018.08.037","volume":"163","author":"M Zhou","year":"2019","unstructured":"Zhou M, Liu X-B, Yang J-B, Chen Y-W, Wu J (2019) Evidential reasoning approach with multiple kinds of attributes and entropy-based weight assignment. Knowl-Based Syst 163:358\u2013375","journal-title":"Knowl-Based Syst"},{"issue":"8","key":"3877_CR5","doi-asserted-by":"publisher","first-page":"4895","DOI":"10.1109\/TSMC.2019.2944640","volume":"51","author":"S-W Tang","year":"2019","unstructured":"Tang S-W, Zhou Z-J, Hu C-H, Yang J-B, Cao Y (2019) Perturbation analysis of evidential reasoning rule. IEEE Trans Syst Man Cybern: Syst 51(8):4895\u20134910","journal-title":"IEEE Trans Syst Man Cybern: Syst"},{"issue":"2","key":"3877_CR6","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/0004-3702(94)90026-4","volume":"66","author":"P Smets","year":"1994","unstructured":"Smets P, Kennes R (1994) The transferable belief model. Artif Intell 66(2):191\u2013234","journal-title":"Artif Intell"},{"issue":"1","key":"3877_CR7","doi-asserted-by":"publisher","first-page":"4542","DOI":"10.15837\/ijccc.2022.1.4542","volume":"17","author":"Y Deng","year":"2022","unstructured":"Deng Y (2022) Random permutation set. Int J Comput Commun Control 17(1):4542","journal-title":"Int J Comput Commun Control"},{"issue":"10","key":"3877_CR8","doi-asserted-by":"publisher","first-page":"3266","DOI":"10.1007\/s10489-019-01617-y","volume":"50","author":"F Xiao","year":"2019","unstructured":"Xiao F (2019) Generalization of Dempster\u2013Shafer theory: a complex mass function. Appl Intell 50(10):3266\u20133275","journal-title":"Appl Intell"},{"key":"3877_CR9","doi-asserted-by":"publisher","unstructured":"Gao X, Pan L, Deng Y (2021) Quantum pythagorean fuzzy evidence theory (qpfet): a negation of quantum mass function view. IEEE Trans Fuzzy Syst. https:\/\/doi.org\/10.1109\/TFUZZ.2021.3057993https:\/\/doi.org\/10.1109\/TFUZZ.2021.3057993","DOI":"10.1109\/TFUZZ.2021.3057993 10.1109\/TFUZZ.2021.3057993"},{"key":"3877_CR10","doi-asserted-by":"publisher","unstructured":"Xiao F (2021) CEQD: a complex mass function to predict interference effects. IEEE Trans Cybern. https:\/\/doi.org\/10.1109\/TCYB.2020.3040770https:\/\/doi.org\/10.1109\/TCYB.2020.3040770","DOI":"10.1109\/TCYB.2020.3040770 10.1109\/TCYB.2020.3040770"},{"key":"3877_CR11","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.fss.2018.11.006","volume":"366","author":"A Trabelsi","year":"2019","unstructured":"Trabelsi A, Elouedi Z, Lefevre E (2019) Decision tree classifiers for evidential attribute values and class labels. Fuzzy Sets Syst 366:46\u201362","journal-title":"Fuzzy Sets Syst"},{"issue":"5","key":"3877_CR12","doi-asserted-by":"publisher","first-page":"2015","DOI":"10.1109\/TNNLS.2020.2995862","volume":"32","author":"Z-G Liu","year":"2020","unstructured":"Liu Z-G, Huang L-Q, Zhou K, Denoeux T (2020) Combination of transferable classification with multisource domain adaptation based on evidential reasoning. IEEE Trans Neural Networ Learn Syst 32(5):2015\u20132029","journal-title":"IEEE Trans Neural Networ Learn Syst"},{"key":"3877_CR13","doi-asserted-by":"crossref","unstructured":"Irhoumah M, Pusca R, Lef\u00e8vre E, Mercier D, Romary R (2019) Information fusion with correlation coefficient for detecting inter-turn short circuit faults in asynchronous machines. In: 2019 IEEE 12th International symposium on diagnostics for electrical machines, power electronics and drives (SDEMPED). IEEE, pp 232\u2013237","DOI":"10.1109\/DEMPED.2019.8864854"},{"issue":"3","key":"3877_CR14","doi-asserted-by":"publisher","first-page":"920","DOI":"10.1002\/qre.2773","volume":"37","author":"Y Hu","year":"2021","unstructured":"Hu Y, Gou L, Deng X, Jiang W (2021) Failure mode and effect analysis using multi-linguistic terms and dempster\u2013shafer evidence theory. Qual Reliab Eng Int 37(3):920\u2013934","journal-title":"Qual Reliab Eng Int"},{"issue":"8","key":"3877_CR15","doi-asserted-by":"publisher","first-page":"2150263","DOI":"10.1142\/S0218348X21502637","volume":"29","author":"Q Gao","year":"2021","unstructured":"Gao Q, Wen T, Deng Y (2021) Information volume fractal dimension. Fractals 29(8):2150263","journal-title":"Fractals"},{"key":"3877_CR16","doi-asserted-by":"publisher","unstructured":"Song X, Xiao F (2022) Combining time-series evidence: a complex network model based on a visibility graph and belief entropy. Appl Intell. https:\/\/doi.org\/10.1007\/s10489-021-02956-5","DOI":"10.1007\/s10489-021-02956-5"},{"key":"3877_CR17","doi-asserted-by":"crossref","unstructured":"Martin A (2019) Conflict management in information fusion with belief functions. In: Information quality in information fusion and decision making. Springer, pp 79\u201397","DOI":"10.1007\/978-3-030-03643-0_4"},{"key":"3877_CR18","doi-asserted-by":"publisher","unstructured":"Xiao F (2021) CaFtR: a fuzzy complex event processing method. International Journal of Fuzzy Systems. https:\/\/doi.org\/10.1007\/s40815-021-01118-6","DOI":"10.1007\/s40815-021-01118-6"},{"issue":"3","key":"3877_CR19","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1016\/S1566-2535(02)00076-3","volume":"3","author":"R Haenni","year":"2002","unstructured":"Haenni R (2002) Are alternatives to dempster\u2019s rule of combination real alternatives?: Comments on \u201cabout the belief function combination and the conflict management problem\u201d\u2014-lefevre et al Inform Fus 3 (3):237\u2013239","journal-title":"Inform Fus"},{"key":"3877_CR20","unstructured":"Irhoumah M, Pusca R, Lef\u00e8vre E, Mercier D, Romary R (1981) Computational methods for a mathematical theory of evidence. In: Proceedings of the seventh international conference on artificial intelligence, pp 868\u2013875"},{"key":"3877_CR21","doi-asserted-by":"publisher","first-page":"104584","DOI":"10.1016\/j.engappai.2021.104584","volume":"108","author":"X Gao","year":"2022","unstructured":"Gao X, Pan L, Deng Y (2022) A generalized divergence of information volume and its applications. Eng Appl Artif Intell 108:104584","journal-title":"Eng Appl Artif Intell"},{"key":"3877_CR22","doi-asserted-by":"publisher","unstructured":"Xiao F, Wen J, Pedrycz W (2022) Generalized divergence-based decision making method with an application to pattern classification. IEEE Trans Knowl Data Eng. https:\/\/doi.org\/10.1109\/TKDE.2022.3177896https:\/\/doi.org\/10.1109\/TKDE.2022.3177896","DOI":"10.1109\/TKDE.2022.3177896 10.1109\/TKDE.2022.3177896"},{"key":"3877_CR23","doi-asserted-by":"crossref","unstructured":"Barnett J A (2008) Computational methods for a mathematical theory of evidence. In: Classic works of the Dempster-Shafer theory of belief functions. Springer, pp 197\u2013216","DOI":"10.1007\/978-3-540-44792-4_8"},{"issue":"3","key":"3877_CR24","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1016\/0004-3702(85)90064-5","volume":"26","author":"J Gordon","year":"1985","unstructured":"Gordon J, Shortliffe E H (1985) A method for managing evidential reasoning in a hierarchical hypothesis space. Artif Intell 26(3):323\u2013357","journal-title":"Artif Intell"},{"issue":"4","key":"3877_CR25","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1016\/0888-613X(87)90024-7","volume":"1","author":"G Shafer","year":"1987","unstructured":"Shafer G, Shenoy P P, Mellouli K (1987) Propagating belief functions in qualitative Markov trees. Int J Approx Reason 1(4):349\u2013400","journal-title":"Int J Approx Reason"},{"issue":"3","key":"3877_CR26","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1109\/MEX.1986.4306979","volume":"1","author":"PP Shenoy","year":"1986","unstructured":"Shenoy P P, Shafer G (1986) Propagating belief functions with local computations. IEEE Expert 1(3):43\u201352","journal-title":"IEEE Expert"},{"issue":"2","key":"3877_CR27","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1016\/0004-3702(93)90072-J","volume":"61","author":"B Tessem","year":"1993","unstructured":"Tessem B, et al. (1993) Approximations for efficient computation in the theory of evidence. Artif Intell 61(2):315\u2013329","journal-title":"Artif Intell"},{"key":"3877_CR28","doi-asserted-by":"crossref","unstructured":"Lowrance J D, Garvey T D, Strat T M (2008) A framework for evidential-reasoning systems. In: Classic works of the Dempster-Shafer theory of belief functions. Springer, pp 419\u2013434","DOI":"10.1007\/978-3-540-44792-4_16"},{"key":"3877_CR29","doi-asserted-by":"crossref","unstructured":"Wilson N (1991) A Monte-Carlo algorithm for Dempster-Shafer belief. In: Uncertainty proceedings 1991. Elsevier, pp 414\u2013417","DOI":"10.1016\/B978-1-55860-203-8.50058-9"},{"key":"3877_CR30","doi-asserted-by":"publisher","first-page":"101283","DOI":"10.1016\/j.jocs.2020.101283","volume":"50","author":"M Benalla","year":"2021","unstructured":"Benalla M, Achchab B, Hrimech H (2021) On the computational complexity of dempster\u2019s rule of combination, a parallel computing approach. J Comput Sci 50:101283","journal-title":"J Comput Sci"},{"key":"3877_CR31","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1016\/j.ins.2020.10.060","volume":"555","author":"M Chaveroche","year":"2021","unstructured":"Chaveroche M, Davoine F, Cherfaoui V (2021) Focal points and their implications for M\u00f6bius transforms and Dempster-Shafer theory. Inf Sci 555:215\u2013235","journal-title":"Inf Sci"},{"key":"3877_CR32","doi-asserted-by":"crossref","unstructured":"Chelikowsky J R, Louie S G (1996) Quantum theory of real materials, vol 348. Springer Science & Business Media","DOI":"10.1007\/978-1-4613-0461-6"},{"issue":"5","key":"3877_CR33","doi-asserted-by":"publisher","first-page":"893","DOI":"10.1021\/cr00005a013","volume":"91","author":"RichardFW Bader","year":"1991","unstructured":"Bader Richard FW (1991) A quantum theory of molecular structure and its applications. Chem Rev 91(5):893\u2013928","journal-title":"Chem Rev"},{"issue":"1","key":"3877_CR34","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1038\/nphys2474","volume":"9","author":"N Lambert","year":"2013","unstructured":"Lambert N, Chen Y-N, Cheng Y-C, Li C-M, Chen G-Y, Nori F (2013) Quantum biology. Nat Phys 9(1):10\u201318","journal-title":"Nat Phys"},{"key":"3877_CR35","doi-asserted-by":"crossref","unstructured":"Nielsen M A, Chuang I (2002) Quantum computation and quantum information. American Association of Physics Teachers","DOI":"10.1119\/1.1463744"},{"key":"3877_CR36","doi-asserted-by":"crossref","unstructured":"Deng X, Jiang W (2021) Quantum representation of basic probability assignments based on mixed quantum states. In: 2021 IEEE 24th International conference on information fusion (FUSION). IEEE, pp 1\u20136","DOI":"10.23919\/FUSION49465.2021.9626984"},{"key":"3877_CR37","doi-asserted-by":"publisher","unstructured":"Xiao F, Pedrycz W (2022) Negation of the quantum mass function for multisource quantum information fusion with its application to pattern classification. IEEE Trans Pattern Anal Mach Intell. https:\/\/doi.org\/10.1109\/TPAMI.2022.3167045","DOI":"10.1109\/TPAMI.2022.3167045"},{"key":"3877_CR38","unstructured":"Rechenberg H (2001) The historical development of quantum theory, vol 1. Springer Science & Business Media"},{"issue":"27","key":"3877_CR39","doi-asserted-by":"publisher","first-page":"1259","DOI":"10.1142\/S0217984901003093","volume":"15","author":"M Andrecut","year":"2001","unstructured":"Andrecut M, Ali MK (2001) Efficient algorithm for initializing amplitude distribution of a quantum register. Mod Phys Lett B 15(27):1259\u20131264","journal-title":"Mod Phys Lett B"},{"issue":"1","key":"3877_CR40","doi-asserted-by":"publisher","first-page":"014303","DOI":"10.1103\/PhysRevA.64.014303","volume":"64","author":"G-L Long","year":"2001","unstructured":"Long G-L, Sun Y (2001) Efficient scheme for initializing a quantum register with an arbitrary superposed state. Phys Rev A 64(1):014303","journal-title":"Phys Rev A"}],"container-title":["Applied Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-022-03877-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10489-022-03877-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-022-03877-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,30]],"date-time":"2023-04-30T09:16:52Z","timestamp":1682846212000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10489-022-03877-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,3]]},"references-count":40,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2023,4]]}},"alternative-id":["3877"],"URL":"https:\/\/doi.org\/10.1007\/s10489-022-03877-7","relation":{},"ISSN":["0924-669X","1573-7497"],"issn-type":[{"value":"0924-669X","type":"print"},{"value":"1573-7497","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,3]]},"assertion":[{"value":"9 June 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 August 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that there is no conflict of interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Conflict of Interests"}}]}}