{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,18]],"date-time":"2026-02-18T01:42:48Z","timestamp":1771378968093,"version":"3.50.1"},"reference-count":19,"publisher":"Wiley","license":[{"start":{"date-parts":[[2018,9,2]],"date-time":"2018-09-02T00:00:00Z","timestamp":1535846400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Fuzzy Systems"],"published-print":{"date-parts":[[2018,9,2]]},"abstract":"<jats:p>In the present communication, a parametric (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><\/mml:math>, <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mi>S<\/mml:mi><\/mml:mrow><\/mml:math>)-norm information measure for the Pythagorean fuzzy set has been proposed with the proof of its validity. The monotonic behavior and maximality feature of the proposed information measure have been studied and presented. Further, an algorithm for solving the multicriteria decision-making problem with the help of the proposed information measure has been provided keeping in view of the different cases for weight criteria, when weights are unknown and other when weights are partially known. Numerical examples for each of the case have been successfully illustrated. Finally, the work has been concluded by providing the scope for future work.<\/jats:p>","DOI":"10.1155\/2018\/8023013","type":"journal-article","created":{"date-parts":[[2018,9,2]],"date-time":"2018-09-02T19:34:54Z","timestamp":1535916894000},"page":"1-11","source":"Crossref","is-referenced-by-count":15,"title":["Pythagorean Fuzzy <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>R<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>S<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>-Norm Information Measure for Multicriteria Decision-Making Problem"],"prefix":"10.1155","volume":"2018","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8756-0833","authenticated-orcid":true,"given":"Abhishek","family":"Guleria","sequence":"first","affiliation":[{"name":"Department of Mathematics, Jaypee University of Information Technology, Waknaghat, Solan, Pin-173 234, Himachal Pradesh, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9312-0866","authenticated-orcid":true,"given":"Rakesh Kumar","family":"Bajaj","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Jaypee University of Information Technology, Waknaghat, Solan, Pin-173 234, Himachal Pradesh, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1002\/int.21584"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2013.2278989"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1002\/int.21676"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1002\/int.21738"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1002\/int.21880"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-26302-1_9"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1142\/S0219622016500012"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2015.12.020"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2015.10.012"},{"issue":"12","key":"12","first-page":"2280","volume":"31","year":"2016","journal-title":"Control and Decision"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1002\/int.21886"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1002\/int.21941"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-32112-2_43"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1142\/S1230161216500153"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(80)90292-2"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1948.tb01338.x"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1002\/int.20131"},{"issue":"11","key":"21","first-page":"1694","volume":"27","year":"2012","journal-title":"Control and Decision"}],"container-title":["Advances in Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2018\/8023013.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2018\/8023013.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2018\/8023013.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,9,2]],"date-time":"2018-09-02T19:34:55Z","timestamp":1535916895000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/afs\/2018\/8023013\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9,2]]},"references-count":19,"alternative-id":["8023013","8023013"],"URL":"https:\/\/doi.org\/10.1155\/2018\/8023013","relation":{},"ISSN":["1687-7101","1687-711X"],"issn-type":[{"value":"1687-7101","type":"print"},{"value":"1687-711X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,9,2]]}}}