{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T04:40:06Z","timestamp":1777696806418,"version":"3.51.4"},"reference-count":100,"publisher":"SAGE Publications","issue":"5","license":[{"start":{"date-parts":[[2025,4,28]],"date-time":"2025-04-28T00:00:00Z","timestamp":1745798400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Intelligent Data Analysis: An International Journal"],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:p>Probabilistic dual hesitant fuzzy set (PDHFS), as an extension of dual hesitant fuzzy set (DHFS) and probabilistic hesitant fuzzy set (PHS), can better describe the uncertainty and fuzziness in the real world through membership degree (MD) and non-membership degree (NMD) and their respective probability information. Therefore, it can collect more comprehensive fuzzy information in decision-making issues, which makes PDHFS has a wide range of applications in practice. The distance, similarity and entropy measures (EMs) of PDHFSs were studied. Due to the particularity of PDHFS, the length of MD and NMD of two probabilistic dual hesitation fuzzy elements (PDHFEs) are often different. To define the distance measure more expediently, many current studies need to add fresh elements to ensure that the length of corresponding elements in MD and NMD are the same, which will destroy the original information of the elements. In order to overcome this disadvantage, this paper defined some novel PDHF distance measures without adding elements. Some novel PDHF similarity measures were defined through the complementary relationship between distance and similarity measures based on the newly proposed PDHF distance measures. The fuzziness of a given PDHFS can be measured by the similarity measure between it and its complement. Based on the property, some novel PDHF EMs were proposed. Finally, three numerical examples are given to illustrate the effectiveness and rationality of these novel information measures.<\/jats:p>","DOI":"10.1177\/1088467x241308761","type":"journal-article","created":{"date-parts":[[2025,4,29]],"date-time":"2025-04-29T02:48:27Z","timestamp":1745894907000},"page":"1153-1186","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Some novel probabilistic dual hesitant fuzzy information measures and their applications to multi-attribute decision-making"],"prefix":"10.1177","volume":"29","author":[{"given":"Baoquan","family":"Ning","sequence":"first","affiliation":[{"name":"Mathematics and Statistics, Liupanshui Normal University, 553004, Liupanshui, P.R. China"},{"name":"School of Mathematical Sciences, Sichuan Normal University, Chengdu, 610101, P.R. China"}]},{"given":"Cun","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Management, Xihua University, Chengdu, 610039, P.R. China"}]},{"given":"Guiwu","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Sichuan Normal University, Chengdu, 610101, P.R. China"},{"name":"School of Business, Sichuan Normal University, Chengdu, 610101, P.R. China"}]}],"member":"179","published-online":{"date-parts":[[2025,4,28]]},"reference":[{"key":"e_1_3_2_2_2","first-page":"149","article-title":"An innovative approach to evaluation of the quality of websites in the tourism industry: a novel mcdm approach based on bipolar neutrosophic numbers and the hamming distance","volume":"18","author":"Stanujkic D","year":"2019","unstructured":"Stanujkic D, Karabasevic D, Smarandache F, et al. An innovative approach to evaluation of the quality of websites in the tourism industry: a novel mcdm approach based on bipolar neutrosophic numbers and the hamming distance. Transformations in Business & Economics 2019; 18: 149\u2013162.","journal-title":"Transformations in Business & Economics"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.3846\/transport.2019.7442"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-202839"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-210313"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10489-019-01608-z"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10489-021-02200-0"},{"key":"e_1_3_2_8_2","first-page":"3226","article-title":"A new efficient decision making algorithm based on interval-valued fuzzy soft set","volume":"51","author":"Ma XQ","year":"2021","unstructured":"Ma XQ, Fei QH, Qin HW, et al. A new efficient decision making algorithm based on interval-valued fuzzy soft set. Appl. Intell 2021; 51: 3226\u20133240.","journal-title":"Appl. Intell"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10489-021-02216-6"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10489-020-01879-x"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10489-021-02354-x"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-202954"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40815-021-01138-2"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.3846\/tede.2021.15038"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10489-017-0960-x"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.3390\/en14133891"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2021.04.105"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.autcon.2021.103761"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.inffus.2017.01.007"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2020.2994997"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1080\/07373937.2021.1933514"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.3846\/tede.2021.15044"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(89)90205-4"},{"key":"e_1_3_2_26_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-021-05713-5"},{"key":"e_1_3_2_27_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-210918"},{"key":"e_1_3_2_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2021.107187"},{"key":"e_1_3_2_29_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-211461"},{"key":"e_1_3_2_30_2","doi-asserted-by":"publisher","DOI":"10.3390\/e23060688"},{"key":"e_1_3_2_31_2","first-page":"529","article-title":"Hesitant fuzzy sets","volume":"25","author":"Torra V","year":"2010","unstructured":"Torra V. Hesitant fuzzy sets. International Journal of Intelligent Systems 2010; 25: 529\u2013539.","journal-title":"International Journal of Intelligent Systems"},{"key":"e_1_3_2_32_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.inffus.2017.08.005"},{"key":"e_1_3_2_33_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-019-04250-6"},{"key":"e_1_3_2_34_2","doi-asserted-by":"publisher","DOI":"10.1007\/s13042-020-01102-w"},{"key":"e_1_3_2_35_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-179435"},{"key":"e_1_3_2_36_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10489-021-02372-9"},{"key":"e_1_3_2_37_2","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/879629"},{"key":"e_1_3_2_38_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2018.03.019"},{"key":"e_1_3_2_39_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-210025"},{"key":"e_1_3_2_40_2","first-page":"15483","article-title":"A new concept of Cosine similarity measures based on dual hesitant fuzzy sets and its possible applications","volume":"22","author":"Zhang YT","year":"2019","unstructured":"Zhang YT, Wang L, Yu XH, et al. A new concept of Cosine similarity measures based on dual hesitant fuzzy sets and its possible applications. Cluster Computing-the Journal of Networks Software Tools and Applications 2019; 22: 15483\u201315492.","journal-title":"Cluster Computing-the Journal of Networks Software Tools and Applications"},{"key":"e_1_3_2_41_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2017.02.033"},{"key":"e_1_3_2_42_2","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2019.2931405"},{"key":"e_1_3_2_43_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-019-04362-y"},{"key":"e_1_3_2_44_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2019.106211"},{"key":"e_1_3_2_45_2","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2020.3035906"},{"key":"e_1_3_2_46_2","doi-asserted-by":"publisher","DOI":"10.1007\/s13042-020-01230-3"},{"key":"e_1_3_2_47_2","doi-asserted-by":"publisher","DOI":"10.1111\/exsy.13015"},{"key":"e_1_3_2_48_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2022.117419"},{"key":"e_1_3_2_49_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10489-021-02821-5"},{"key":"e_1_3_2_50_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00347-9"},{"key":"e_1_3_2_51_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(92)90239-Z"},{"key":"e_1_3_2_52_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.patrec.2004.06.006"},{"key":"e_1_3_2_53_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-200364"},{"key":"e_1_3_2_54_2","first-page":"159","article-title":"New distance and similarity measures for hesitant fuzzy soft sets","volume":"16","author":"Rezaei K","year":"2019","unstructured":"Rezaei K, Rezaei H. New distance and similarity measures for hesitant fuzzy soft sets. Iranian Journal of Fuzzy Systems 2019; 16: 159\u2013176.","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"e_1_3_2_55_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-141511"},{"key":"e_1_3_2_56_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2011.01.028"},{"key":"e_1_3_2_57_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.22898"},{"key":"e_1_3_2_58_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-220999"},{"key":"e_1_3_2_59_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10462-022-10244-y"},{"key":"e_1_3_2_60_2","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2022.3215232"},{"key":"e_1_3_2_61_2","doi-asserted-by":"publisher","DOI":"10.3390\/sym14020242"},{"key":"e_1_3_2_62_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40314-020-1111-2"},{"key":"e_1_3_2_63_2","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2019.2963484"},{"key":"e_1_3_2_64_2","doi-asserted-by":"crossref","unstructured":"Ren ZL Xu ZS Wang H. Ieee An Extended TODIM Method Under Probabilistic Dual Hesitant Fuzzy Information and its Application on Enterprise Strategic Assessment in: IEEE International Conference on Industrial Engineering and Engineering Management (IEEE IEEM) Singapore SINGAPORE 2017: 1464\u20131468.","DOI":"10.1109\/IEEM.2017.8290136"},{"key":"e_1_3_2_65_2","doi-asserted-by":"publisher","DOI":"10.3390\/math6120280"},{"key":"e_1_3_2_66_2","doi-asserted-by":"publisher","DOI":"10.1007\/s13042-022-01631-6"},{"key":"e_1_3_2_67_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40815-022-01350-8"},{"key":"e_1_3_2_68_2","first-page":"192","article-title":"Similarity measures for fuzzy sets","volume":"8","author":"Beg I","year":"2009","unstructured":"Beg I, Ashraf S. Similarity measures for fuzzy sets. Applied and Computational Mathematics 2009; 8: 192\u2013202.","journal-title":"Applied and Computational Mathematics"},{"key":"e_1_3_2_69_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-141492"},{"key":"e_1_3_2_70_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488504003235"},{"key":"e_1_3_2_71_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488512500225"},{"key":"e_1_3_2_72_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-021-05707-2"},{"key":"e_1_3_2_73_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2019.09.027"},{"key":"e_1_3_2_74_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2008.10.028"},{"key":"e_1_3_2_75_2","doi-asserted-by":"publisher","DOI":"10.1002\/cae.21642"},{"key":"e_1_3_2_76_2","first-page":"1","article-title":"A fuzzy similarity measure of intuitionistic fuzzy sets for color image retrieval systems","volume":"22","author":"Afsari F","year":"2014","unstructured":"Afsari F, Eslami E, Woo PY. A fuzzy similarity measure of intuitionistic fuzzy sets for color image retrieval systems. Journal of Multiple-Valued Logic and Soft Computing 2014; 22: 1\u201320.","journal-title":"Journal of Multiple-Valued Logic and Soft Computing"},{"key":"e_1_3_2_77_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-2012-0527"},{"key":"e_1_3_2_78_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218001413500213"},{"key":"e_1_3_2_79_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-013-1035-5"},{"key":"e_1_3_2_80_2","doi-asserted-by":"publisher","DOI":"10.3390\/math7050437"},{"key":"e_1_3_2_81_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2016.04.037"},{"key":"e_1_3_2_82_2","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2019.2942766"},{"key":"e_1_3_2_83_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-191723"},{"key":"e_1_3_2_84_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40747-018-0084-x"},{"key":"e_1_3_2_85_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-202212"},{"key":"e_1_3_2_86_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.21965"},{"key":"e_1_3_2_87_2","first-page":"87","article-title":"Interval-Valued intuitionistic fuzzy sets and similarity measure","volume":"14","author":"Pekala B","year":"2017","unstructured":"Pekala B, Balicki K. Interval-Valued intuitionistic fuzzy sets and similarity measure. Iranian Journal of Fuzzy Systems 2017; 14: 87\u201398.","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"e_1_3_2_88_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-131024"},{"key":"e_1_3_2_89_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2011.06.001"},{"key":"e_1_3_2_90_2","doi-asserted-by":"publisher","DOI":"10.1111\/itor.12477"},{"key":"e_1_3_2_91_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40314-015-0219-2"},{"key":"e_1_3_2_92_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-141474"},{"key":"e_1_3_2_93_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40747-020-00224-6"},{"key":"e_1_3_2_94_2","article-title":"Cold chain vulnerability assessment through two-stage grey comprehensive measurement of intuitionistic fuzzy entropy","author":"Xu L","year":"2021","unstructured":"Xu L, Tang Q. Cold chain vulnerability assessment through two-stage grey comprehensive measurement of intuitionistic fuzzy entropy. Kybernetes 2021. https:\/\/doi.org\/10.1108\/K-1102-2021-0161","journal-title":"Kybernetes"},{"key":"e_1_3_2_95_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40815-020-00877-y"},{"key":"e_1_3_2_96_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-182540"},{"key":"e_1_3_2_97_2","doi-asserted-by":"publisher","DOI":"10.3390\/s20030913"},{"key":"e_1_3_2_98_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-016-9257-5"},{"key":"e_1_3_2_99_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00402-3"},{"key":"e_1_3_2_100_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(72)90199-4"},{"key":"e_1_3_2_101_2","doi-asserted-by":"publisher","DOI":"10.1080\/03081077908547452"}],"updated-by":[{"DOI":"10.1177\/1088467x251351750","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T00:00:00Z","timestamp":1750809600000}}],"container-title":["Intelligent Data Analysis: An International Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1088467X241308761","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/1088467X241308761","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1088467X241308761","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:21:01Z","timestamp":1777454461000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/1088467X241308761"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,28]]},"references-count":100,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["10.1177\/1088467X241308761"],"URL":"https:\/\/doi.org\/10.1177\/1088467x241308761","relation":{},"ISSN":["1088-467X","1571-4128"],"issn-type":[{"value":"1088-467X","type":"print"},{"value":"1571-4128","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,28]]}}}