{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,19]],"date-time":"2026-10-19T15:57:54Z","timestamp":1792425474826,"version":"4.5.0"},"reference-count":49,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2018,11,28]],"date-time":"2018-11-28T00:00:00Z","timestamp":1543363200000},"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":[[2019,2,16]]},"abstract":"<jats:p>All the extensions of ordinary fuzzy sets with three dimensional membership functions such as intuitionistic fuzzy sets (IFS), intuitionistic fuzzy sets of second type (IFS2), and neutrosophic fuzzy sets (NFS) aim at defining the judgments of decision makers\/ experts with a more detailed description. Introduction of generalized three dimensional spherical fuzzy sets (SFS) including some essential differences from the other fuzzy sets is presented in this paper. The new type of fuzzy sets is based on the spherical fuzzy distances which have been already defined in the literature. Arithmetic operations involving addition, subtraction and multiplication are presented together with their proofs. Aggregation operators, score and accuracy functions are developed. The multi-criteria decision making method TOPSIS is extended to spherical fuzzy TOPSIS and an illustrative example is presented. Additionally, a comparative analysis with intuitionistic fuzzy TOPSIS (IF-TOPSIS) is given.<\/jats:p>","DOI":"10.3233\/jifs-181401","type":"journal-article","created":{"date-parts":[[2018,11,30]],"date-time":"2018-11-30T12:14:51Z","timestamp":1543580091000},"page":"337-352","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":706,"title":["Spherical fuzzy sets and spherical fuzzy TOPSIS method"],"prefix":"10.1177","volume":"36","author":[{"given":"Fatma","family":"Kutlu G\u00fcndo\u011fdu","sequence":"first","affiliation":[{"name":"Department of Industrial Engineering, Istanbul Technical University, Besiktas, Istanbul, Turkey"},{"name":"Department of Industrial Engineering, Istanbul K\u00fclt\u00fcr University, Bakirkoy, Istanbul, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cengiz","family":"Kahraman","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, Istanbul Technical University, Besiktas, Istanbul, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2018,11,28]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/FUZZ-IEEE.2016.7738003"},{"key":"e_1_3_1_3_2","first-page":"1","article-title":"A novel intuitionistic fuzzy DEMATEL - ANP - TOPSIS integrated methodology for freight village location selection","author":"Karajan A.","year":"2017","unstructured":"A.Karajan and C.Kahraman, A novel intuitionistic fuzzy DEMATEL - ANP - TOPSIS integrated methodology for freight village location selection, Journal of Intelligent & Fuzzzy Systems Preprint (2017), 1\u201318.","journal-title":"Journal of Intelligent & Fuzzzy Systems Preprint"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00170-013-5444-5"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-171164"},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.rser.2017.06.095"},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2012.04.033"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1080\/18756891.2015.1046325"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1080\/18756891.2016.1180817"},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2010.08.092"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eij.2014.03.002"},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00244-9"},{"key":"e_1_3_1_13_2","volume-title":"An application of intuitionistic fuzzy set on personnel selection","author":"Boran F.E.","year":"2009","unstructured":"F.E.Boran, An application of intuitionistic fuzzy set on personnel selection, Ankara: Gazi University Institute of Science and Technology (2009)."},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.3390\/mca16020487"},{"key":"e_1_3_1_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2009.03.039"},{"key":"e_1_3_1_16_2","doi-asserted-by":"publisher","DOI":"10.1080\/15567240903047483"},{"key":"e_1_3_1_17_2","first-page":"1","volume-title":"A unifying field in logics neutrosophy: Neutrosophic probability, set and logic","author":"Smarandache F.","year":"1999","unstructured":"F.Smarandache, A unifying field in logics neutrosophy: Neutrosophic probability, set and logic, Rehoboth: American Research Press (1999), 1\u2013141."},{"key":"e_1_3_1_18_2","unstructured":"F.Smarandache Proceedings of the First International Conference on Neutrosophy Neutrosophic Logic Neutrosophic Set Neutrosophic Porbability and Statistics: www.Gallup.Unm.Edu\/~Smarandache\/NeutrosophicProceedings.Pdf. Infinite Study 2003."},{"key":"e_1_3_1_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2010.03.013"},{"key":"e_1_3_1_20_2","doi-asserted-by":"publisher","DOI":"10.1080\/18756891.2016.1204119"},{"key":"e_1_3_1_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2013.03.002"},{"key":"e_1_3_1_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2016.07.047"},{"key":"e_1_3_1_23_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19760220120"},{"issue":"1","key":"e_1_3_1_24_2","first-page":"29","article-title":"On a new geometrical interpretation of the intu-itionistic fuzzy sets","volume":"1","author":"Antonov I.","year":"1995","unstructured":"I.Antonov, On a new geometrical interpretation of the intu-itionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets 1(1) (1995), 29\u201331.","journal-title":"Notes on Intuitionistic Fuzzy Sets"},{"key":"e_1_3_1_25_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2006.889755"},{"key":"e_1_3_1_26_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2016.2646749"},{"key":"e_1_3_1_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"issue":"1","key":"e_1_3_1_28_2","first-page":"27","article-title":"Geometrical interpretation of the elements of the intuitionistic fuzzy objects, Preprint IM-MFAIS, 189, Sofia.","volume":"20","author":"Atanassov K.","year":"2016","unstructured":"K.Atanassov, Geometrical interpretation of the elements of the intuitionistic fuzzy objects, Preprint IM-MFAIS, 189, Sofia. Reprinted: Int. J. Bioautomation 20 (S1) (2016), 27\u201342, 1989.","journal-title":"Reprinted: Int. J. Bioautomation"},{"key":"e_1_3_1_29_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1870-3"},{"key":"e_1_3_1_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"e_1_3_1_31_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(75)90036-5"},{"key":"e_1_3_1_32_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.autcon.2013.12.009"},{"key":"e_1_3_1_33_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-015-1891-2"},{"key":"e_1_3_1_34_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2015.12.020"},{"key":"e_1_3_1_35_2","volume-title":"Application al'aide au Diagnostic en Pathologie Thyroidienne","author":"Sambuc R.","year":"1975","unstructured":"R.Sambuc, Function \u00d6-Flous, Application al'aide au Diagnostic en Pathologie Thyroidienne. University of Marseille (1975)."},{"key":"e_1_3_1_36_2","doi-asserted-by":"publisher","DOI":"10.1080\/03081078608934952"},{"key":"e_1_3_1_37_2","first-page":"263","article-title":"Multicriteria Evaluation of Cloud Service Providers Using Pythagorean Fuzzy TOPSIS.","author":"Cevik Onar S.","year":"2018","unstructured":"S.Cevik Onar, B.Oztaysi, C.Kahraman,Multicriteria Evaluation of Cloud Service Providers Using Pythagorean Fuzzy TOPSIS. Journal of Multiple-Valued Logic & Soft Computing (2018), 263\u2013283.","journal-title":"Journal of Multiple-Valued Logic & Soft Computing"},{"key":"e_1_3_1_38_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2011.09.074"},{"key":"e_1_3_1_39_2","first-page":"57","volume":"26","author":"Chen T.Y.","year":"2015","unstructured":"T.Y.Chen, The inclusion-based TOPSIS method with interval-valued intuitionistic fuzzy sets for multiple criteria group decision making Applied Soft Computing 26 (2015), 57\u201373.","journal-title":"The inclusion-based TOPSIS method with interval-valued intuitionistic fuzzy sets for multiple criteria group decision making Applied Soft Computing"},{"issue":"6","key":"e_1_3_1_40_2","first-page":"529","article-title":"Hesitant fuzzy sets","volume":"25","author":"Torra V.","year":"2010","unstructured":"V.Torra, Hesitant fuzzy sets, International Journal of Intelligent Systems 25(6) (2010), 529\u2013539.","journal-title":"International Journal of Intelligent Systems"},{"key":"e_1_3_1_41_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.21788"},{"key":"e_1_3_1_42_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2014.08.073"},{"key":"e_1_3_1_43_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.21676"},{"key":"e_1_3_1_44_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.01.029"},{"key":"e_1_3_1_45_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.20342"},{"key":"e_1_3_1_46_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2016.12.014"},{"key":"e_1_3_1_47_2","doi-asserted-by":"publisher","DOI":"10.3846\/20294913.2016.1181684"},{"key":"e_1_3_1_48_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2011.06.022"},{"key":"e_1_3_1_49_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.02.013"},{"key":"e_1_3_1_50_2","doi-asserted-by":"publisher","DOI":"10.1057\/s41274-016-0171-6"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-181401","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-181401","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-181401","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:41:56Z","timestamp":1777455716000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-181401"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,28]]},"references-count":49,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,2,16]]}},"alternative-id":["10.3233\/JIFS-181401"],"URL":"https:\/\/doi.org\/10.3233\/jifs-181401","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,28]]}}}