{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T16:12:20Z","timestamp":1778688740229,"version":"3.51.4"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2017,9,7]],"date-time":"2017-09-07T00:00:00Z","timestamp":1504742400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71471172"],"award-info":[{"award-number":["71471172"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Mach. Learn. & Cyber."],"published-print":{"date-parts":[[2019,2]]},"DOI":"10.1007\/s13042-017-0719-z","type":"journal-article","created":{"date-parts":[[2017,9,11]],"date-time":"2017-09-11T16:36:36Z","timestamp":1505147796000},"page":"347-355","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":73,"title":["Some distances, similarity and entropy measures for interval-valued neutrosophic sets and their relationship"],"prefix":"10.1007","volume":"10","author":[{"given":"Jun","family":"Ye","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shigui","family":"Du","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,9,7]]},"reference":[{"key":"719_CR1","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","volume":"20","author":"K Atanassov","year":"1986","unstructured":"Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87\u201396","journal-title":"Fuzzy Sets Syst"},{"key":"719_CR2","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1016\/0165-0114(89)90205-4","volume":"31","author":"K Atanassov","year":"1989","unstructured":"Atanassov K, Gargov G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31:343\u2013349","journal-title":"Fuzzy Sets Syst"},{"key":"719_CR3","first-page":"47","volume":"9","author":"A Aydo\u011fdu","year":"2015","unstructured":"Aydo\u011fdu A (2015) On entropy and similarity measure of interval valued neutrosophic sets. Neutrosophic Sets Syst 9:47\u201349","journal-title":"Neutrosophic Sets Syst"},{"key":"719_CR4","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1016\/0165-0114(96)84610-0","volume":"78","author":"H Bustince","year":"1996","unstructured":"Bustince H, Burillo P (1996) Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst 78:305\u2013316","journal-title":"Fuzzy Sets Syst"},{"key":"719_CR5","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1016\/S0019-9958(72)90199-4","volume":"20","author":"AS Luca De","year":"1972","unstructured":"De Luca AS, Termini S (1972) A definition of nonprobabilistic entropy in the setting of fuzzy set theory. Inf Control 20:301\u2013312","journal-title":"Inf Control"},{"key":"719_CR6","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-016-2436-z","author":"P Ji","year":"2016","unstructured":"Ji P, Zhang HY, Wang JQ (2016) A projection-based TODIM method under multi-valued neutrosophic environments and its application in personnel selection. Neural Comput Appl. doi: 10.1007\/s00521-016-2436-z","journal-title":"Neural Comput Appl"},{"issue":"3","key":"719_CR7","doi-asserted-by":"crossref","first-page":"1245","DOI":"10.3233\/IFS-130810","volume":"26","author":"P Majumder","year":"2014","unstructured":"Majumder P, Samanta SK (2014) On similarity and entropy of neutrosophic sets. J Intell Fuzzy Syst 26(3):1245\u20131252","journal-title":"J Intell Fuzzy Syst"},{"key":"719_CR8","doi-asserted-by":"publisher","first-page":"336","DOI":"10.1016\/j.asoc.2014.08.070","volume":"25","author":"JJ Peng","year":"2014","unstructured":"Peng JJ, Wang JQ, Zhang HY, Chen XH (2014) An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets. Appl Soft Comput 25:336\u2013346","journal-title":"Appl Soft Comput"},{"issue":"10","key":"719_CR9","doi-asserted-by":"publisher","first-page":"2342","DOI":"10.1080\/00207721.2014.994050","volume":"47","author":"JJ Peng","year":"2016","unstructured":"Peng JJ, Wang JQ, Wang J, Zhang HY, Chen XH (2016) Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems. Int J Syst Sci 47(10):2342\u20132358","journal-title":"Int J Syst Sci"},{"key":"719_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-016-2411-8","author":"JJ Peng","year":"2016","unstructured":"Peng JJ, Wang J, Wu XH (2016) An extension of the ELECTRE approach with multi-valued neutrosophic information. Neural Comput Appl. doi: 10.1007\/s00521-016-2411-8","journal-title":"Neural Comput Appl"},{"key":"719_CR11","volume-title":"The mathematical theory of communications","author":"CE Shannon","year":"1947","unstructured":"Shannon CE, Weaver W (1947) The mathematical theory of communications. The University of Illinois Press, Urbana"},{"key":"719_CR12","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","volume":"27","author":"CE Shannon","year":"1948","unstructured":"Shannon CE (1948) A mathematical theory of communications. Bell Syst Tech J 27:379\u2013423","journal-title":"Bell Syst Tech J"},{"key":"719_CR13","volume-title":"Neutrosophy. Neutrosophic probability, set, and logic","author":"F Smarandache","year":"1998","unstructured":"Smarandache F (1998) Neutrosophy. Neutrosophic probability, set, and logic. American Research Press, Rehoboth"},{"key":"719_CR14","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1016\/S0165-0114(98)00402-3","volume":"118","author":"E Szmidt","year":"2001","unstructured":"Szmidt E, Kacprzyk J (2001) Entropy on intuitionistic fuzzy sets. Fuzzy Sets Syst 118:467\u2013477","journal-title":"Fuzzy Sets Syst"},{"key":"719_CR15","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/0165-0114(86)90077-1","volume":"20","author":"I Turksen","year":"1986","unstructured":"Turksen I (1986) Interval valued fuzzy sets based on normal forms. Fuzzy Sets Syst 20:191\u2013210","journal-title":"Fuzzy Sets Syst"},{"issue":"15","key":"719_CR16","doi-asserted-by":"publisher","first-page":"3598","DOI":"10.1080\/00207721.2015.1102359","volume":"47","author":"ZP Tian","year":"2016","unstructured":"Tian ZP, Zhang HY, Wang J, Wang JQ, Chen XH (2016) Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets. Int J Syst Sci 47(15):3598\u20133608","journal-title":"Int J Syst Sci"},{"key":"719_CR17","doi-asserted-by":"publisher","DOI":"10.1007\/s13042-016-0552-9","author":"ZP Tian","year":"2016","unstructured":"Tian ZP, Wang J, Zhang HY, Wang JQ (2016) Multi-criteria decision-making based on generalized prioritized aggregation operators under simplified neutrosophic uncertain linguistic environment. Int J Mach Learn Cybern. doi: 10.1007\/s13042-016-0552-9","journal-title":"Int J Mach Learn Cybern"},{"key":"719_CR18","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/j.patrec.2006.07.004","volume":"28","author":"IK Valchos","year":"2007","unstructured":"Valchos IK, Sergiadis GD (2007) Intuitionistic fuzzy information\u2014a pattern recognition. Pattern Recognit Lett 28:197\u2013206","journal-title":"Pattern Recognit Lett"},{"key":"719_CR19","volume-title":"Interval neutrosophic sets and logic: theory and applications in computing","author":"H Wang","year":"2005","unstructured":"Wang H, Smarandache F, Zhang YQ, Sunderraman R (2005) Interval neutrosophic sets and logic: theory and applications in computing. Hexis, Phoenix, USA"},{"key":"719_CR20","first-page":"410","volume":"4","author":"H Wang","year":"2010","unstructured":"Wang H, Smarandache F, Zhang YQ, Sunderraman R (2010) Single valued neutrosophic sets. Multisp Multistruct 4:410\u2013413","journal-title":"Multisp Multistruct"},{"key":"719_CR21","doi-asserted-by":"publisher","first-page":"4273","DOI":"10.1016\/j.ins.2011.06.001","volume":"181","author":"CP Wei","year":"2011","unstructured":"Wei CP, Wang P, Zhang YZ (2011) Entropy, similarity measure of interval valued intuitionistic sets and their applications. Inf Sci 181:4273\u20134286","journal-title":"Inf Sci"},{"key":"719_CR22","doi-asserted-by":"publisher","DOI":"10.1007\/s40815-016-0180-2","author":"XH Wu","year":"2016","unstructured":"Wu XH, Wang J, Peng JJ, Chen XH (2016) Cross-entropy and prioritized aggregation operator with simplified neutrosophic sets and their application in multi-criteria decision-making problems. Int J Fuzzy Syst. doi: 10.1007\/s40815-016-0180-2","journal-title":"Int J Fuzzy Syst"},{"issue":"1\u20132","key":"719_CR23","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1007\/s00607-009-0075-2","volume":"87","author":"J Ye","year":"2010","unstructured":"Ye J (2010) Two effective measures of intuitionistic fuzzy entropy. Computing 87(1\u20132):55\u201362","journal-title":"Computing"},{"key":"719_CR24","doi-asserted-by":"publisher","first-page":"3864","DOI":"10.1016\/j.apm.2010.03.025","volume":"34","author":"J Ye","year":"2010","unstructured":"Ye J (2010) Multicriteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval-valued intuitionistic fuzzy sets. Appl Math Model 34:3864\u20133870","journal-title":"Appl Math Model"},{"issue":"4","key":"719_CR25","doi-asserted-by":"publisher","first-page":"386","DOI":"10.1080\/03081079.2012.761609","volume":"42","author":"J Ye","year":"2013","unstructured":"Ye J (2013) Multicriteria decision-making method using the correlation coefficient under single-value neutrosophic environment. Int J Gen Syst 42(4):386\u2013394","journal-title":"Int J Gen Syst"},{"issue":"5","key":"719_CR26","doi-asserted-by":"crossref","first-page":"2459","DOI":"10.3233\/IFS-130916","volume":"26","author":"J Ye","year":"2014","unstructured":"Ye J (2014) A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets. J Intell Fuzzy Syst 26(5):2459\u20132466","journal-title":"J Intell Fuzzy Syst"},{"issue":"3","key":"719_CR27","doi-asserted-by":"publisher","first-page":"1170","DOI":"10.1016\/j.apm.2013.07.020","volume":"38","author":"J Ye","year":"2014","unstructured":"Ye J (2014) Single valued neutrosophic cross-entropy for multicriteria decision making problems. Appl Math Model 38(3):1170\u20131175","journal-title":"Appl Math Model"},{"issue":"1","key":"719_CR28","doi-asserted-by":"crossref","first-page":"165","DOI":"10.3233\/IFS-120724","volume":"26","author":"J Ye","year":"2014","unstructured":"Ye J (2014) Similarity measures between interval neutrosophic sets and their applications in multicriteria decision making. J Intell Fuzzy Syst 26(1):165\u2013172","journal-title":"J Intell Fuzzy Syst"},{"issue":"5","key":"719_CR29","doi-asserted-by":"crossref","first-page":"2231","DOI":"10.3233\/IFS-141187","volume":"27","author":"J Ye","year":"2014","unstructured":"Ye J (2014) Some aggregation operators of interval neutrosophic linguistic numbers for multiple attribute decision making. J Intell Fuzzy Syst 27(5):2231\u20132241","journal-title":"J Intell Fuzzy Syst"},{"issue":"3","key":"719_CR30","doi-asserted-by":"publisher","first-page":"837","DOI":"10.1007\/s13042-015-0382-1","volume":"8","author":"J Ye","year":"2017","unstructured":"Ye J (2017) Multiple attribute group decision making based on interval neutrosophic uncertain linguistic variables. Int J Mach Learn Cybern 8(3):837\u2013848","journal-title":"Int J Mach Learn Cybern"},{"key":"719_CR31","first-page":"2937","volume-title":"Fuzzy sets and systems","author":"LA Zadeh","year":"1965","unstructured":"Zadeh LA (1965) Fuzzy sets and systems. In: Proceedings of the symposium on systems. Theory Polytechnic Institute of Brooklyn, New York, pp\u00a029\u201337"},{"key":"719_CR32","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"L Zadeh","year":"1965","unstructured":"Zadeh L (1965) Fuzzy sets. Inf Control 8:338\u2013353","journal-title":"Inf Control"},{"key":"719_CR33","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/j.ins.2014.06.012","volume":"283","author":"QS Zhang","year":"2014","unstructured":"Zhang QS, Xing HY, Liu FC, Ye J, Tang P (2014) Some new entropy measures for interval-valued intuitionistic fuzzy sets based on distances and their relationships with similarity and inclusion measures. Inf Sci 283:55\u201369","journal-title":"Inf Sci"},{"key":"719_CR34","doi-asserted-by":"crossref","unstructured":"Zhang HY, Wang JQ, Chen XH (2014) Interval neutrosophic sets and their application in multicriteria decision making problems. Sci World J 2014 (ID 645953, 15 pages)","DOI":"10.1155\/2014\/645953"},{"issue":"6","key":"719_CR35","doi-asserted-by":"publisher","first-page":"1027","DOI":"10.1080\/18756891.2015.1099917","volume":"8","author":"HY Zhang","year":"2015","unstructured":"Zhang HY, Ji P, Wang JQ, Chen XH (2015) Improved weighted correlation coefficient based on integrated weight for interval neutrosophic sets and its application in multi-criteria decision making problems. Int J Comput Intell Syst 8(6):1027\u20131043","journal-title":"Int J Comput Intell Syst"},{"issue":"3","key":"719_CR36","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1007\/s00521-015-1882-3","volume":"27","author":"HY Zhang","year":"2016","unstructured":"Zhang HY, Wang JQ, Chen XH (2016) An outranking approach for multi-criteria decision-making problems with interval-valued neutrosophic sets. Neural Comput Appl 27(3):615\u2013627","journal-title":"Neural Comput Appl"}],"container-title":["International Journal of Machine Learning and Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s13042-017-0719-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-017-0719-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-017-0719-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,17]],"date-time":"2020-10-17T11:44:36Z","timestamp":1602935076000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s13042-017-0719-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,7]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,2]]}},"alternative-id":["719"],"URL":"https:\/\/doi.org\/10.1007\/s13042-017-0719-z","relation":{},"ISSN":["1868-8071","1868-808X"],"issn-type":[{"value":"1868-8071","type":"print"},{"value":"1868-808X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,7]]},"assertion":[{"value":"16 August 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 August 2017","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 September 2017","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}