{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T13:41:49Z","timestamp":1783950109619,"version":"3.55.0"},"reference-count":49,"publisher":"Wiley","license":[{"start":{"date-parts":[[2022,7,27]],"date-time":"2022-07-27T00:00:00Z","timestamp":1658880000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006261","name":"Taif University","doi-asserted-by":"publisher","award":["TURSP-2020\/36"],"award-info":[{"award-number":["TURSP-2020\/36"]}],"id":[{"id":"10.13039\/501100006261","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Sensors"],"published-print":{"date-parts":[[2022,7,27]]},"abstract":"<jats:p>The goal of this paper is to design a new correlation coefficient for <jats:inline-formula>\n                     <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\">\n                        <a:mi>T<\/a:mi>\n                     <\/a:math>\n                  <\/jats:inline-formula>-spherical fuzzy sets (TSFSs), which can accurately measure the nature of correlation (i.e., positive and negative) as well as the degree of relationship between TSFS. In order to formulate our proposed idea, we had taken inspiration from the statistical concept of the correlation coefficient. While doing so, we firstly introduce the variance and covariance of two TSFS and then constructed our scheme using these two newly defined notions. The numerical value of our proposed correlation coefficient lies within the interval <jats:inline-formula>\n                     <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\">\n                        <c:mfenced open=\"[\" close=\"]\">\n                           <c:mrow>\n                              <c:mo>\u2212<\/c:mo>\n                              <c:mn>1<\/c:mn>\n                              <c:mrow>\n                                 <c:mo>,<\/c:mo>\n                              <\/c:mrow>\n                              <c:mrow>\n                                 <c:mo>+<\/c:mo>\n                              <\/c:mrow>\n                              <c:mn>1<\/c:mn>\n                           <\/c:mrow>\n                        <\/c:mfenced>\n                     <\/c:math>\n                  <\/jats:inline-formula>, as it should be from a statistical point of view, whereas the existing methods cannot measure the negative correlation between TSFS, as their numerical value falls within the interval <jats:inline-formula>\n                     <g:math xmlns:g=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\">\n                        <g:mfenced open=\"[\" close=\"]\">\n                           <g:mrow>\n                              <g:mn>0<\/g:mn>\n                              <g:mo>,<\/g:mo>\n                              <g:mn>1<\/g:mn>\n                           <\/g:mrow>\n                        <\/g:mfenced>\n                     <\/g:math>\n                  <\/jats:inline-formula>, which is not reasonable both statistically and intuitively. This aspect has also been thoroughly demonstrated using some numerical examples. The comparison results witnessed the dominance and upper hand of our proposed method over the existing definitions, with reliable and better results. In order to demonstrate the feasibility, usefulness, and practical application, we applied our proposed scheme to solve technical and scientific problems of multicriteria decision-making and pattern recognition. The numerical results show that our proposed scheme is practically suitable, technically applicable, and intuitively reasonable.<\/jats:p>","DOI":"10.1155\/2022\/4471945","type":"journal-article","created":{"date-parts":[[2022,7,27]],"date-time":"2022-07-27T20:05:07Z","timestamp":1658952307000},"page":"1-11","source":"Crossref","is-referenced-by-count":4,"title":["A New Correlation Coefficient for <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                     <a:mi>T<\/a:mi>\n                  <\/a:math>-Spherical Fuzzy Sets and Its Application in Multicriteria Decision-Making and Pattern Recognition"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3603-8145","authenticated-orcid":true,"given":"Wajid","family":"Ali","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Karakorum International University, Gilgit-Baltistan, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mehboob","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Chung Yuan Christian University, Zhongli, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Israr","family":"Hussain","sequence":"additional","affiliation":[{"name":"Department of Computer Sciences, Karakorum International University, Gilgit-Baltistan, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5406-0389","authenticated-orcid":true,"given":"Syed Sajid","family":"Ullah","sequence":"additional","affiliation":[{"name":"Department of Information and Communication Technology, University of Agder (UiA), N-4898 Grimstad, Norway"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1585-2962","authenticated-orcid":true,"given":"Roobaea","family":"Alroobaea","sequence":"additional","affiliation":[{"name":"Department of Computer Science, College of Computers and Information Technology, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1523-1330","authenticated-orcid":true,"given":"Saddam","family":"Hussain","sequence":"additional","affiliation":[{"name":"Department of Information Technology, Hazara University Mansehra, 21120 KP, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ahmed","family":"Binmahfoudh","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, College of Computers and Information Technology, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6307-5251","authenticated-orcid":true,"given":"Fazlullah","family":"Umar","sequence":"additional","affiliation":[{"name":"Department, Khana-e-Noor University, Pol-e-Mahmood Khan, Shashdarak, 1001 Kabul, Afghanistan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"issue":"3","key":"2","first-page":"287","article-title":"Neutrosophic set-a generalization of the intuitionistic fuzzy set","volume":"24","author":"F. Smarandache","year":"2005","journal-title":"International Journal of Pure and Applied Mathematics"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1002\/wics.82"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00347-9"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/J.CAM.2006.04.008"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/216414"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.3846\/13926292.2012.706656"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/s12543-011-0064-y"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(78)90045-8"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/J.ASOC.2008.05.005"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1007\/s11269-010-9681-1"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(93)90371-N"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/J.EJOR.2012.11.038"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/J.ASOC.2008.01.004"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-141440"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(93)90166-F"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/J.PATREC.2006.07.004"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1007\/S13534-018-0058-3"},{"key":"20","article-title":"Securing industrial Internet of Things against botnet attacks using hybrid deep learning approach","volume":"9","author":"T. Hasan","year":"2022","journal-title":"IEEE Transactions on Network Science and Engineering"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00235-8"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/J.INS.2020.08.096"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2008.06.008"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1080\/00207540210137639"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1007\/S12065-008-0013-9"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1109\/TII.2022.3161029"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1109\/wict.2013.7113099"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-018-3521-2"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2005.05.040"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1109\/91.995115"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1002\/INT.20418"},{"key":"32","doi-asserted-by":"publisher","DOI":"10.1002\/int.21584"},{"key":"33","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(85)90004-1"},{"key":"34","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(91)90031-K"},{"key":"35","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)00330-A"},{"key":"36","doi-asserted-by":"publisher","DOI":"10.1002\/INT.20004"},{"key":"37","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0255(02)00181-0"},{"key":"38","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(96)00311-9"},{"key":"39","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)00343-6"},{"key":"40","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-03664-4_66"},{"key":"41","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14049-5_18"},{"key":"42","doi-asserted-by":"publisher","DOI":"10.1007\/S00500-019-03993-6"},{"key":"43","doi-asserted-by":"publisher","DOI":"10.6688\/JISE.202103_37(2).0003"},{"key":"44","doi-asserted-by":"publisher","DOI":"10.15625\/1813-9663\/30\/4\/5032"},{"key":"45","doi-asserted-by":"publisher","DOI":"10.1109\/KSE.2016.7758023"},{"key":"46","doi-asserted-by":"publisher","DOI":"10.1007\/S00500-019-04457-7"},{"key":"47","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2007.11.006"},{"key":"48","volume-title":"Pattern Recognition and Machine Learning","author":"C. M. Bishop","year":"2006"},{"key":"49","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8655(01)00110-6"}],"container-title":["Journal of Sensors"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/js\/2022\/4471945.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/js\/2022\/4471945.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/js\/2022\/4471945.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,27]],"date-time":"2022-07-27T20:05:17Z","timestamp":1658952317000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/js\/2022\/4471945\/"}},"subtitle":[],"editor":[{"given":"Waliullah","family":"Khan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2022,7,27]]},"references-count":49,"alternative-id":["4471945","4471945"],"URL":"https:\/\/doi.org\/10.1155\/2022\/4471945","relation":{},"ISSN":["1687-7268","1687-725X"],"issn-type":[{"value":"1687-7268","type":"electronic"},{"value":"1687-725X","type":"print"}],"subject":[],"published":{"date-parts":[[2022,7,27]]}}}