{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T07:18:48Z","timestamp":1771658328384,"version":"3.50.1"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2018,3,13]],"date-time":"2018-03-13T00:00:00Z","timestamp":1520899200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Fuzzy Syst."],"published-print":{"date-parts":[[2018,6]]},"DOI":"10.1007\/s40815-018-0469-4","type":"journal-article","created":{"date-parts":[[2018,3,13]],"date-time":"2018-03-13T05:11:58Z","timestamp":1520917918000},"page":"1483-1494","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["The Basis and Coordinates in Intuitionistic Fuzzy Environment"],"prefix":"10.1007","volume":"20","author":[{"given":"Rufei","family":"Ma","sequence":"first","affiliation":[]},{"given":"Shousheng","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Zeshui","family":"Xu","sequence":"additional","affiliation":[]},{"given":"Qian","family":"Lei","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,3,13]]},"reference":[{"key":"469_CR1","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"LA Zadeh","year":"1965","unstructured":"Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338\u2013356 (1965)","journal-title":"Inf. Control"},{"key":"469_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-6123-1","volume-title":"The ordered weighted averaging operators: theory and applications","author":"RR Yager","year":"1997","unstructured":"Yager, R.R., Kacprzyk, J.: The ordered weighted averaging operators: theory and applications. Kluwer, Norwell (1997)"},{"key":"469_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-73723-0","volume-title":"Fuzzy sets and their extensions: representation, aggregation and models","author":"H Bustince","year":"2008","unstructured":"Bustince, H., Herrera, F., Montero, J.: Fuzzy sets and their extensions: representation, aggregation and models. Springer, Berlin (2008)"},{"key":"469_CR4","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.: Intuitionistic fuzzy set. Fuzzy Sets Syst. 20, 87\u201396 (1986)","journal-title":"Fuzzy Sets Syst."},{"key":"469_CR5","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1007\/s10700-010-9090-1","volume":"9","author":"ZS Xu","year":"2010","unstructured":"Xu, Z.S., Cai, X.Q.: Recent advances in intuitionistic fuzzy information aggregation. Fuzzy Optim. Decis. Mak. 9, 359\u2013381 (2010)","journal-title":"Fuzzy Optim. Decis. Mak."},{"key":"469_CR6","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/S0165-0114(98)00271-1","volume":"114","author":"DH Hong","year":"2000","unstructured":"Hong, D.H., Choi, C.H.: Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst. 114, 103\u2013113 (2000)","journal-title":"Fuzzy Sets Syst."},{"key":"469_CR7","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1080\/00207720500382365","volume":"36","author":"K Atanassov","year":"2005","unstructured":"Atanassov, K., Pasi, G., Yager, R.R.: Intuitionistic fuzzy interpretations of multi-criteria multi- person and multi-measurement tool decision making. Int. J. Syst. Sci. 36, 859\u2013868 (2005)","journal-title":"Int. J. Syst. Sci."},{"issue":"2","key":"469_CR8","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/s10700-009-9056-3","volume":"8","author":"ZS Xu","year":"2009","unstructured":"Xu, Z.S., Yager, R.R.: Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optim. Decis. Mak. 8(2), 123\u2013139 (2009)","journal-title":"Fuzzy Optim. Decis. Mak."},{"key":"469_CR9","first-page":"489","volume":"25","author":"ZS Xu","year":"2010","unstructured":"Xu, Z.S., Cai, X.Q.: Nonlinear optimization models for multiple attribute group decision making with intuitionistic fuzzy information. Int. J. Intell. Syst. 25, 489\u2013513 (2010)","journal-title":"Int. J. Intell. Syst."},{"key":"469_CR10","doi-asserted-by":"publisher","first-page":"1603","DOI":"10.1016\/j.patrec.2004.06.006","volume":"25","author":"WL Hung","year":"2004","unstructured":"Hung, W.L., Yang, M.S.: Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance. Pattern Recogn. Lett. 25, 1603\u20131611 (2004)","journal-title":"Pattern Recogn. Lett."},{"key":"469_CR11","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/j.patrec.2006.07.004","volume":"28","author":"KI Vlachos","year":"2007","unstructured":"Vlachos, K.I., Sergiadis, G.D.: Intuitionistic fuzzy information-applications to pattern recognition. Pattern Recogn. Lett. 28, 197\u2013206 (2007)","journal-title":"Pattern Recogn. Lett."},{"issue":"1","key":"469_CR12","first-page":"139","volume":"23","author":"ZS Xu","year":"2007","unstructured":"Xu, Z.S.: On similarity measures of interval-valued intuitionistic fuzzy sets and their application to pattern recognitions. J. Southeast Univ. 23(1), 139\u2013143 (2007)","journal-title":"J. Southeast Univ."},{"key":"469_CR13","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1016\/S0165-0114(98)00235-8","volume":"117","author":"SK De","year":"2001","unstructured":"De, S.K., Biswas, R., Roy, A.R.: An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets Syst. 117, 209\u2013213 (2001)","journal-title":"Fuzzy Sets Syst."},{"key":"469_CR14","doi-asserted-by":"crossref","unstructured":"Szmidt, E., Kacprzyk, J.: A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning. In: Lecture Notes in Artificial Intelligence, 2004, vol. 3070, pp. 388\u2013393","DOI":"10.1007\/978-3-540-24844-6_56"},{"key":"469_CR15","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1080\/03081070600574353","volume":"35","author":"ZS Xu","year":"2006","unstructured":"Xu, Z.S., Yager, R.R.: Some geometric aggregation operators based on intuitionistic fuzzy sets. Int. J. Gen. Syst. 35, 417\u2013433 (2006)","journal-title":"Int. J. Gen. Syst."},{"key":"469_CR16","doi-asserted-by":"publisher","first-page":"1179","DOI":"10.1109\/TFUZZ.2006.890678","volume":"15","author":"ZS Xu","year":"2007","unstructured":"Xu, Z.S.: Intuitionistic fuzzy aggregation operations. IEEE Trans. Fuzzy Syst. 15, 1179\u20131187 (2007)","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"469_CR17","doi-asserted-by":"publisher","first-page":"468","DOI":"10.1002\/int.21696","volume":"30","author":"Q Lei","year":"2015","unstructured":"Lei, Q., Xu, Z.S.: Derivative and differential operations of intuitionistic fuzzy numbers. Int. J. Intell. Syst. 30, 468\u2013498 (2015)","journal-title":"Int. J. Intell. Syst."},{"key":"469_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.knosys.2014.11.019","volume":"76","author":"Q Lei","year":"2015","unstructured":"Lei, Q., Xu, Z.S.: Fundamental properties of intuitionistic fuzzy calculus. Knowl. Based Syst. 76, 1\u201316 (2015)","journal-title":"Knowl. Based Syst."},{"key":"469_CR19","doi-asserted-by":"publisher","first-page":"1519","DOI":"10.1109\/TFUZZ.2014.2362559","volume":"23","author":"Q Lei","year":"2015","unstructured":"Lei, Q., Xu, Z.S., Bustince, H., Burusco, A.: Definite integrals of Atanassov\u2019s intuitionistic fuzzy information. IEEE Trans. Fuzzy Syst. 23, 1519\u20131533 (2015)","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"469_CR20","doi-asserted-by":"publisher","DOI":"10.1109\/tfuzz.2016.2593498","author":"Q Lei","year":"2016","unstructured":"Lei, Q., Xu, Z.S.: A unification of intuitionistic fuzzy calculus theories based on subtraction derivatives and division derivatives. IEEE Trans. Fuzzy Syst. (2016). \n                    https:\/\/doi.org\/10.1109\/tfuzz.2016.2593498","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"469_CR21","doi-asserted-by":"publisher","first-page":"1410","DOI":"10.1109\/TFUZZ.2016.2516583","volume":"24","author":"Q Lei","year":"2016","unstructured":"Lei, Q., Xu, Z.S.: Relationship between two types of intuitionistic fuzzy definite integrals. IEEE Trans. Fuzzy Syst. 24, 1410\u20131425 (2016)","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"469_CR22","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1016\/j.ins.2015.08.005","volume":"327","author":"Q Lei","year":"2016","unstructured":"Lei, Q., Xu, Z.S., Bustince, H., Fernandez, J.: Intuitionistic fuzzy integrals based on Archimedean t-conorms and t-norms. Inf. Sci. 327, 57\u201370 (2016)","journal-title":"Inf. Sci."}],"container-title":["International Journal of Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s40815-018-0469-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40815-018-0469-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40815-018-0469-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,12]],"date-time":"2019-03-12T20:56:29Z","timestamp":1552424189000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s40815-018-0469-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,13]]},"references-count":22,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2018,6]]}},"alternative-id":["469"],"URL":"https:\/\/doi.org\/10.1007\/s40815-018-0469-4","relation":{},"ISSN":["1562-2479","2199-3211"],"issn-type":[{"value":"1562-2479","type":"print"},{"value":"2199-3211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,13]]},"assertion":[{"value":"22 June 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 November 2017","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 February 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 March 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}