{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T00:41:02Z","timestamp":1769992862397,"version":"3.49.0"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T00:00:00Z","timestamp":1757289600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T00:00:00Z","timestamp":1757289600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Syst Assur Eng Manag"],"published-print":{"date-parts":[[2026,1]]},"DOI":"10.1007\/s13198-025-02961-8","type":"journal-article","created":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T14:52:30Z","timestamp":1757343150000},"page":"249-255","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Development of a ranking function for a generalized $$L{-}R$$ fuzzy number"],"prefix":"10.1007","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7240-7836","authenticated-orcid":false,"given":"Diptiranjan","family":"Behera","sequence":"first","affiliation":[]},{"given":"Mahesha","family":"Narayana","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,9,8]]},"reference":[{"issue":"2","key":"2961_CR1","first-page":"23","volume":"3","author":"E Abbasi","year":"2018","unstructured":"Abbasi E, Saneifard R, Celik E (2018) A valid and advanced method for ranking the fuzzy numbers. Commun Math Model Appl 3(2):23\u201330","journal-title":"Commun Math Model Appl"},{"key":"2961_CR2","first-page":"1179","volume":"27","author":"ASA Bakar","year":"2014","unstructured":"Bakar ASA (2014) Ranking of fuzzy numbers based on centroid point and spread. J Intell Fuzzy Syst 27:1179\u20131186","journal-title":"J Intell Fuzzy Syst"},{"issue":"9","key":"2961_CR3","first-page":"4595","volume":"13","author":"SK Bharati","year":"2017","unstructured":"Bharati SK (2017) Ranking method of intuitionistic fuzzy numbers. Global J Pure Appl Math 13(9):4595\u20134608","journal-title":"Global J Pure Appl Math"},{"key":"2961_CR4","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1016\/j.ijar.2013.01.009","volume":"54","author":"M Brunelli","year":"2013","unstructured":"Brunelli M, Mezei J (2013) How different are ranking methods for fuzzy numbers? Numerical study. Int J Approx Reason 54:627\u2013639","journal-title":"Int J Approx Reason"},{"key":"2961_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2021.107217","volume":"156","author":"TY Chang","year":"2021","unstructured":"Chang TY, Ku CC (2021) Fuzzy filtering ranking method for multi-criteria decision making. Comput Ind Eng 156:107217. https:\/\/doi.org\/10.1016\/j.cie.2021.107217","journal-title":"Comput Ind Eng"},{"key":"2961_CR6","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1016\/S0165-0114(96)00272-2","volume":"95","author":"CH Cheng","year":"1998","unstructured":"Cheng CH (1998) A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets Syst 95:307\u2013317","journal-title":"Fuzzy Sets Syst"},{"issue":"2","key":"2961_CR7","first-page":"42","volume":"5","author":"AM El-Kholy","year":"2016","unstructured":"El-Kholy AM, Abdelalim AM (2016) A comparative study for fuzzy ranking methods in determining economic life of equipment. Int J Constr Eng Manag 5(2):42\u201354","journal-title":"Int J Constr Eng Manag"},{"key":"2961_CR8","first-page":"373","volume":"25","author":"R Eslamipoor","year":"2013","unstructured":"Eslamipoor R, Haji MJ, Sepehriar A (2013) Proposing a revised method for ranking fuzzy numbers. J Intell Fuzzy Syst 25:373\u2013378","journal-title":"J Intell Fuzzy Syst"},{"key":"2961_CR9","first-page":"49","volume":"19","author":"MA Firozja","year":"2022","unstructured":"Firozja MA, Balf FR, Agheli B, Chutia R (2022) Ranking of generalized fuzzy numbers based on accuracy of comparison. Iran J Fuzzy Syst 19:49\u201361","journal-title":"Iran J Fuzzy Syst"},{"key":"2961_CR10","first-page":"39","volume":"50","author":"MK Ghorabaee","year":"2016","unstructured":"Ghorabaee MK, Zavadskas EK, Amiri M, Antucheviciene J (2016) A new method of assessment based on fuzzy ranking and aggregated weights (AFRAW) for MCDM problems under type-2 fuzzy environment. Econ Comput Econ Cybern Stud Res 50:39\u201368","journal-title":"Econ Comput Econ Cybern Stud Res"},{"key":"2961_CR11","first-page":"179","volume":"35","author":"GA Hande","year":"2024","unstructured":"Hande GA, Semiha A (2024) A new standardization-based ranking method for generalized trapezoidal picture fuzzy numbers. Yugosl J Oper Res 35:179\u2013207","journal-title":"Yugosl J Oper Res"},{"key":"2961_CR12","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1007\/s40815-023-01571-5","volume":"26","author":"W He","year":"2024","unstructured":"He W, Rodr\u00edguez RM, Takac Z, Martinez L (2024) Ranking of fuzzy numbers on the basis of new fuzzy distance. Int J Fuzzy Syst 26:17\u201333","journal-title":"Int J Fuzzy Syst"},{"key":"2961_CR13","doi-asserted-by":"publisher","first-page":"558","DOI":"10.1002\/int.22311","volume":"36","author":"MJ Khan","year":"2021","unstructured":"Khan MJ, Ali MI, Kumam P (2021) A new ranking technique for q-rung orthopair fuzzy values. Int Intell Syst 36:558\u2013592","journal-title":"Int J Intell Syst"},{"key":"2961_CR14","doi-asserted-by":"publisher","first-page":"1049","DOI":"10.3390\/axioms12111049","volume":"12","author":"THP Le","year":"2023","unstructured":"Le THP, Chu TC (2023) Novel method for ranking generalized fuzzy numbers based on normalized height coefficient and benefit and cost areas. Axioms 12:1049. https:\/\/doi.org\/10.3390\/axioms12111049","journal-title":"Axioms"},{"key":"2961_CR15","doi-asserted-by":"publisher","DOI":"10.3390\/math9040337","author":"SM Li","year":"2021","unstructured":"Li SM, Chan FTS, Tsang YP, Lam HY (2021) New product idea selection in the fuzzy front end of innovation: a fuzzy best-worst method and group decision-making process. Mathematics. https:\/\/doi.org\/10.3390\/math9040337","journal-title":"Mathematics"},{"key":"2961_CR16","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1016\/0165-0114(92)90223-Q","volume":"50","author":"TS Liou","year":"1992","unstructured":"Liou TS, Wang MJ (1992) Ranking fuzzy numbers with integral value. Fuzzy Sets Syst 50:247\u2013255","journal-title":"Fuzzy Sets Syst"},{"key":"2961_CR17","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/S0165-0114(98)00066-9","volume":"109","author":"HR Maleki","year":"2000","unstructured":"Maleki HR, Tata M, Mashinchi M (2000) Linear programming with fuzzy variables. Fuzzy Sets Syst 109:21\u201333","journal-title":"Fuzzy Sets Syst"},{"key":"2961_CR18","doi-asserted-by":"publisher","DOI":"10.1088\/1742-6596\/1176\/3\/032007","volume":"1176","author":"QS Mao","year":"2019","unstructured":"Mao QS (2019) Ranking fuzzy numbers based on weighted distance. IOP Conf Series J Phys Conf Series 1176:032007. https:\/\/doi.org\/10.1088\/1742-6596\/1176\/3\/032007","journal-title":"IOP Conf Series J Phys Conf Series"},{"issue":"1","key":"2961_CR19","doi-asserted-by":"publisher","first-page":"4","DOI":"10.21123\/bsj.2021.18.1.0144","volume":"18","author":"RJ Mitlif","year":"2021","unstructured":"Mitlif RJ (2021) Ranking function to solve a fuzzy multiple objective function. Baghdad Sci J 18(1):4","journal-title":"Baghdad Sci J"},{"key":"2961_CR20","doi-asserted-by":"publisher","first-page":"1492","DOI":"10.3390\/sym16111492","volume":"16","author":"L Popa","year":"2024","unstructured":"Popa L (2024) Centroid-induced ranking of triangular picture fuzzy numbers and applications in decision-making. Symmetry 16:1492. https:\/\/doi.org\/10.3390\/sym16111492","journal-title":"Symmetry"},{"key":"2961_CR21","doi-asserted-by":"publisher","first-page":"1551","DOI":"10.26713\/cma.v14i5.2286","volume":"14","author":"S Prasad","year":"2023","unstructured":"Prasad S, Sinha S, Sen RG (2023) A new approach of centroid based ranking fuzzy numbers and its comparative reviews. Commun Math Appl 14:1551\u20131563","journal-title":"Commun Math Appl"},{"key":"2961_CR22","doi-asserted-by":"publisher","first-page":"674","DOI":"10.1016\/j.cam.2016.05.017","volume":"309","author":"G Qiupeng","year":"2017","unstructured":"Qiupeng G, Zuxing X (2017) A new approach for ranking fuzzy numbers based on possibility theory. J Comput Appl Math 309:674\u2013682","journal-title":"J Comput Appl Math"},{"key":"2961_CR23","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/178308","author":"PPB Rao","year":"2011","unstructured":"Rao PPB, Shankar NR (2011) Ranking fuzzy numbers with a distance method using circumcenter of centroids and an index of modality. Adv Fuzzy Syst. https:\/\/doi.org\/10.1155\/2011\/178308","journal-title":"Adv Fuzzy Syst"},{"key":"2961_CR24","first-page":"1373","volume":"31","author":"P Singh","year":"2015","unstructured":"Singh P (2015) A novel method for ranking generalized fuzzy numbers. J Inf Sci Eng 31:1373\u20131385","journal-title":"J Inf Sci Eng"},{"key":"2961_CR25","doi-asserted-by":"publisher","first-page":"81","DOI":"10.5267\/j.dsl.2018.5.001","volume":"8","author":"A Sotoudeh-Anvari","year":"2019","unstructured":"Sotoudeh-Anvari A, Sadjadi SJ, Molana SMH, Sadi-Nezhad S (2019) A note on A new approach for ranking fuzzy numbers based on possibility theory. Decis Sci Lett 8:81\u201384","journal-title":"Decis Sci Lett"},{"key":"2961_CR26","doi-asserted-by":"publisher","DOI":"10.1080\/02522667.2018.1450196","author":"S Suneela","year":"2018","unstructured":"Suneela S, Chakraverty S (2018) New ranking function for fuzzy linear programming problem and system of linear equations. J Inf Opt Sci. https:\/\/doi.org\/10.1080\/02522667.2018.1450196","journal-title":"J Inf Opt Sci"},{"key":"2961_CR27","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/0020-0255(81)90017-7","volume":"24","author":"RR Yager","year":"1981","unstructured":"Yager RR (1981) A procedure for ordering fuzzy subsets of the unit interval. Inf Sci 24:143\u2013161","journal-title":"Inf Sci"},{"issue":"5","key":"2961_CR28","doi-asserted-by":"publisher","first-page":"1279","DOI":"10.1007\/s40815-016-0223-8","volume":"19","author":"VF Yu","year":"2016","unstructured":"Yu VF, Van LH, Dat LQ, Chi HTX, Chou SY, Duong TTT (2016) Analyzing the ranking method for fuzzy numbers in fuzzy decision making based on the magnitude concepts. Int J Fuzzy Syst 19(5):1279\u20131289. https:\/\/doi.org\/10.1007\/s40815-016-0223-8","journal-title":"Int J Fuzzy Syst"},{"key":"2961_CR29","first-page":"71","volume":"30","author":"J Zhou","year":"2016","unstructured":"Zhou J, Yang F, Wang K (2016) Fuzzy arithmetic on L\u2013R fuzzy numbers with applications to fuzzy programming. J Intell Fuzzy Syst 30:71\u201387","journal-title":"J Intell Fuzzy Syst"}],"container-title":["International Journal of System Assurance Engineering and Management"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13198-025-02961-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13198-025-02961-8","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13198-025-02961-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T14:45:10Z","timestamp":1769957110000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13198-025-02961-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,8]]},"references-count":29,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["2961"],"URL":"https:\/\/doi.org\/10.1007\/s13198-025-02961-8","relation":{},"ISSN":["0975-6809","0976-4348"],"issn-type":[{"value":"0975-6809","type":"print"},{"value":"0976-4348","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,8]]},"assertion":[{"value":"21 December 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 August 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 September 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no Conflict of interest to declare that are relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}