{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:34:29Z","timestamp":1777703669499,"version":"3.51.4"},"reference-count":36,"publisher":"SAGE Publications","issue":"5","license":[{"start":{"date-parts":[[2019,6,27]],"date-time":"2019-06-27T00:00:00Z","timestamp":1561593600000},"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":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2019,11,22]]},"abstract":"<jats:p>\u00a0The measure of the similarity between intuitionistic fuzzy sets (IFSs) is an important topic in IFSs theory. In this paper, we propose two computational formulae for similarity measures on IFSs based on a quaternary function called intuitionistic fuzzy equivalence. We first propose the concept of intuitionistic fuzzy equivalence. Then we give a computational formula for intuitionistic fuzzy equivalencies (i.e., Eq. (1)), which is obtained from combining dissimilarity functions and fuzzy equivalencies. Based on Eq. (1), we obtain two computational formulae for similarity measures on IFSs. The first one is obtained by aggregating Eq. (1). The second one is obtained by respectively aggregating the numerator and the denominator of Eq. (1). We also examine some properties of the proposed similarity measures on IFSs. Finally, we make a comparison between the proposed similarity measures on IFSs and those existing ones in the literature through several counter-intuitive cases.<\/jats:p>","DOI":"10.3233\/jifs-181739","type":"journal-article","created":{"date-parts":[[2019,6,28]],"date-time":"2019-06-28T13:08:16Z","timestamp":1561727296000},"page":"7073-7086","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Two computational formulae for similarity measures on intuitionistic fuzzy sets based on intuitionistic fuzzy equivalencies"],"prefix":"10.1177","volume":"37","author":[{"given":"Xingxing","family":"He","sequence":"first","affiliation":[{"name":"School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, People\u2019s Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingfang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Economics Information Engineering, Southwestern University of Finance and Economics, Chengdu, Sichuan, People\u2019s Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Limin","family":"Du","sequence":"additional","affiliation":[{"name":"Pharmaceutical College, Henan University, Kaifeng, Henan, People\u2019s Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Keyun","family":"Qin","sequence":"additional","affiliation":[{"name":"School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, People\u2019s Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,6,27]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1870-3"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-151805"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2013.08.013"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(96)84611-2"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(95)00154-9"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(02)00214-2"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)00339-9"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/3477.552198"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.07.033"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2016.01.040"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-013-1035-5"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-1648-2"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1109\/21.229476"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0255(98)10083-X"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.patrec.2004.06.006"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2006.10.002"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.20271"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2011.11.029"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(00)00125-1"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)90113-9"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8655(01)00110-6"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.patrec.2006.07.009"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1080\/18756891.2013.780726"},{"key":"e_1_3_2_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2013.03.008"},{"key":"e_1_3_2_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.07.052"},{"key":"e_1_3_2_28_2","first-page":"43","volume-title":"Handbook of Fuzzy Sets Comparison-Theory","author":"Li Y.F.","year":"2016","unstructured":"Y.F.Li, X.X.He and K.Y.Qin, Relationships among several fuzzy measures, in: G.A.Papakostas, A.G.Hatzimichailidis and V.G.Kaburlasos, Handbook of Fuzzy Sets Comparison-Theory, Algorithms and Applications, Science Gate Publishing, 2016, pp. 43\u201378."},{"key":"e_1_3_2_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2015.07.008"},{"key":"e_1_3_2_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8655(03)00111-9"},{"key":"e_1_3_2_31_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(92)90239-Z"},{"key":"e_1_3_2_32_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8655(03)00169-7"},{"key":"e_1_3_2_33_2","volume-title":"Fuzzy Sets and its Applications","author":"Wang P.Z.","year":"1983","unstructured":"P.Z.Wang, Fuzzy Sets and its Applications, Shanghai Science and Technology Press, Shanghai, 1983. 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