{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,12]],"date-time":"2024-01-12T05:11:09Z","timestamp":1705036269628},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,11,11]],"date-time":"2023-11-11T00:00:00Z","timestamp":1699660800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,11,11]],"date-time":"2023-11-11T00:00:00Z","timestamp":1699660800000},"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":["Soft Comput"],"published-print":{"date-parts":[[2024,1]]},"DOI":"10.1007\/s00500-023-09371-7","type":"journal-article","created":{"date-parts":[[2023,11,11]],"date-time":"2023-11-11T12:01:22Z","timestamp":1699704082000},"page":"929-943","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Expressing and fusion computing of uncertain or imprecise digital information of multi-channel discrete quantity"],"prefix":"10.1007","volume":"28","author":[{"given":"Tengfei","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Shi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,11,11]]},"reference":[{"key":"9371_CR1","unstructured":"Abdolshah (2015) Measuring loss-based process capability index L-e and its generation L-e with fuzzy numbers. Math Probl Eng"},{"issue":"5","key":"9371_CR2","first-page":"381","volume":"4","author":"M Anisseh","year":"2009","unstructured":"Anisseh M, Yusuff RBM, Shakarami A (2009) Aggregating group MCDM problems using a fuzzy Delphi model for personnel performance appraisal. Sci Res Essays 4(5):381\u2013391","journal-title":"Sci Res Essays"},{"key":"9371_CR3","doi-asserted-by":"publisher","first-page":"573","DOI":"10.1007\/978-3-540-72434-6_58","volume":"42","author":"J Casasnovas","year":"2007","unstructured":"Casasnovas J, Riera JV (2007) Discrete fuzzy numbers defined on a subset of natural numbers, Theoretical advances and applications of fuzzy logic and soft computing. Adv Soft Comput 42:573\u2013582","journal-title":"Adv Soft Comput"},{"key":"9371_CR4","first-page":"273","volume":"163","author":"J Casasnovas","year":"2007","unstructured":"Casasnovas J, Riera JV (2007) Maximum and minimum of discrete fuzzy numbers. Front Artif Intell Appl 163:273\u2013280","journal-title":"Front Artif Intell Appl"},{"issue":"1","key":"9371_CR5","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.fss.2010.09.016","volume":"167","author":"J Casasnovas","year":"2011","unstructured":"Casasnovas J, Riera JV (2011) Extension of discrete t-norms and t-conorms to discrete fuzzy numbers. Fuzzy Sets Syst 167(1):65\u201381","journal-title":"Fuzzy Sets Syst"},{"key":"9371_CR6","unstructured":"Casasnovas J, Riera JV (2009) Lattice properties of discrete fuzzy numbers under extended min and max. In: Proceedings IFSA-EUSFLAT, pp 647\u2013652"},{"key":"9371_CR7","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1109\/TSMC.1972.5408553","volume":"2","author":"SSL Chang","year":"1972","unstructured":"Chang SSL, Zadeh LA (1972) On fuzzy mappings and control. IEEE Trans Syst Man Cybern 2:30\u201334","journal-title":"IEEE Trans Syst Man Cybern"},{"key":"9371_CR8","doi-asserted-by":"publisher","first-page":"25405","DOI":"10.1109\/ACCESS.2021.3057623","volume":"9","author":"Z Gong","year":"2021","unstructured":"Gong Z, Qin N, Zhang G (2021) Three-dimensional generalized discrete fuzzy number and applications in color mathematical morphology. IEEE Access 9:25405\u201325421","journal-title":"IEEE Access"},{"key":"9371_CR9","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2021.3139068","author":"A Gong","year":"2021","unstructured":"Gong A, Xie X, Yue D, Xia J (2021) Multi-instant observer design of discrete-time fuzzy systems via an enhanced gain-scheduling mechanism. IEEE Trans Cybern. https:\/\/doi.org\/10.1109\/TCYB.2021.3139068","journal-title":"IEEE Trans Cybern"},{"issue":"1\u20132","key":"9371_CR10","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1007\/s12190-018-1193-9","volume":"59","author":"M Javanmard","year":"2019","unstructured":"Javanmard M, Nehi HM (2019) Rankings and operations for interval type-2 fuzzy numbers: a review and some new methods. J Appl Math Comput 59(1\u20132):597\u2013630","journal-title":"J Appl Math Comput"},{"key":"9371_CR11","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2022.3151880","author":"Z Lian","year":"2022","unstructured":"Lian Z, Shi P, Lim C, Yuan X (2022) Fuzzy-Model-Based Lateral Control for Networked Autonomous Vehicle Systems Under Hybrid Cyber-Attacks. IEEE Trans Cybern. https:\/\/doi.org\/10.1109\/TCYB.2022.3151880","journal-title":"IEEE Trans Cybern"},{"key":"9371_CR12","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1016\/j.asoc.2019.01.008","volume":"77","author":"X Ma","year":"2019","unstructured":"Ma X, Zhao M, Zou X (2019) Measuring and reaching consensus in group decision making with the linguistic computing model based on discrete fuzzy numbers. Appl Soft Comput J 77:135\u2013154","journal-title":"Appl Soft Comput J"},{"issue":"2","key":"9371_CR13","doi-asserted-by":"publisher","first-page":"1549","DOI":"10.1016\/j.asoc.2009.12.029","volume":"11","author":"AK Maity","year":"2011","unstructured":"Maity AK (2011) One machine multiple-product problem with production-inventory system under fuzzy inequality constraint. Appl Soft Comput 11(2):1549\u20131555","journal-title":"Appl Soft Comput"},{"key":"9371_CR14","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1016\/j.ins.2013.06.055","volume":"258","author":"S Massanet","year":"2014","unstructured":"Massanet S, Riera JV, Torrens J, Herrera-Viedma E (2014) A new linguistic computational model based on discrete fuzzy numbers for computing with words. Inf Sci 258:277\u2013290","journal-title":"Inf Sci"},{"issue":"2\/3","key":"9371_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.5121\/ijsc.2018.9301","volume":"9","author":"R Nasiboglu","year":"2018","unstructured":"Nasiboglu R, Abdullayeva R (2018) Analytical formulations for the level based weighted average value of discrete trapezoidal fuzzy numbers. Int J Soft Comput 9(2\/3):1\u201315","journal-title":"Int J Soft Comput"},{"key":"9371_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2017\/3083745","volume":"2017","author":"TL Nguyen","year":"2017","unstructured":"Nguyen TL (2017) Methods in ranking fuzzy numbers: a unified index and comparative reviews. Complexity 2017:1\u201313","journal-title":"Complexity"},{"issue":"8","key":"9371_CR17","doi-asserted-by":"publisher","first-page":"3964","DOI":"10.1109\/TCYB.2020.3020885","volume":"51","author":"J Qiu","year":"2021","unstructured":"Qiu J, Ji W, Rudas IJ, Gao H (2021) Asynchronous sampled-data filtering design for fuzzy-affine-model-based stochastic nonlinear systems. IEEE Trans Cybern 51(8):3964\u20133974","journal-title":"IEEE Trans Cybern"},{"key":"9371_CR18","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/j.fss.2011.10.004","volume":"191","author":"JV Riera","year":"2012","unstructured":"Riera JV, Torrens J (2012) Aggregation of subjective evaluations based on discrete fuzzy number. Fuzzy Sets Syst 191:21\u201340","journal-title":"Fuzzy Sets Syst"},{"key":"9371_CR19","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/j.ins.2013.06.008","volume":"247","author":"JV Riera","year":"2013","unstructured":"Riera JV, Torrens J (2013) Residual implications on the set of discrete fuzzy numbers. Inf Sci 247:131\u2013143","journal-title":"Inf Sci"},{"key":"9371_CR20","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1016\/j.fss.2013.09.001","volume":"241","author":"JV Riera","year":"2014","unstructured":"Riera JV, Torrens J (2014) Aggregation functions on the set of discrete fuzzy numbers defined from a pair of discrete aggregations. Fuzzy Sets Syst 241:76\u201393","journal-title":"Fuzzy Sets Syst"},{"key":"9371_CR21","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1016\/j.fss.2014.05.005","volume":"264","author":"JV Riera","year":"2015","unstructured":"Riera JV, Torrens J (2015) Using discrete fuzzy numbers in the aggregation of incomplete qualitative information. Fuzzy Sets Syst 264:121\u2013137","journal-title":"Fuzzy Sets Syst"},{"issue":"11","key":"9371_CR22","doi-asserted-by":"publisher","first-page":"1272","DOI":"10.3390\/math9111272","volume":"9","author":"B Stanojevic","year":"2021","unstructured":"Stanojevic B, Stanojevic M, Nadaban S (2021) Reinstatement of the extension principle in approaching mathematical programming with fuzzy numbers. Mathematics 9(11):1272. https:\/\/doi.org\/10.3390\/math9111272","journal-title":"Mathematics"},{"issue":"2","key":"9371_CR23","doi-asserted-by":"publisher","first-page":"1335","DOI":"10.1109\/TCYB.2020.2997348","volume":"52","author":"J Sun","year":"2022","unstructured":"Sun J, Zhang H, Wang Y, Sun S (2022) Fault-tolerant control for stochastic switched IT2 fuzzy uncertain time-delayed nonlinear systems. IEEE Trans Cybern 52(2):1335\u20131346","journal-title":"IEEE Trans Cybern"},{"key":"9371_CR24","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1016\/S0165-0114(99)00053-6","volume":"118","author":"W Voxman","year":"2001","unstructured":"Voxman W (2001) Canonical representations of discrete fuzzy numbers. Fuzzy Sets Syst 118:457\u2013466","journal-title":"Fuzzy Sets Syst"},{"issue":"4","key":"9371_CR25","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1007\/s40815-015-0038-z","volume":"17","author":"G Wang","year":"2015","unstructured":"Wang G, Wang J (2015) Generalized discrete fuzzy number and application in risk evaluation. Int J Fuzzy Syst 17(4):531\u2013543","journal-title":"Int J Fuzzy Syst"},{"issue":"6","key":"9371_CR26","first-page":"29","volume":"18","author":"G Wang","year":"2021","unstructured":"Wang G, Xu Y (2021) Calculation of centroid of high dimensional fuzzy number and application. Iran J Fuzzy Syst 18(6):29\u201344","journal-title":"Iran J Fuzzy Syst"},{"key":"9371_CR27","first-page":"1003","volume":"28","author":"G Wang","year":"2005","unstructured":"Wang G, Wu C, Zhao C (2005) Representation and operations of discrete fuzzy numbers. Southeast Asian Bull Math 28:1003\u20131010","journal-title":"Southeast Asian Bull Math"},{"key":"9371_CR28","doi-asserted-by":"publisher","first-page":"3846","DOI":"10.1016\/j.ins.2011.04.032","volume":"181","author":"G Wang","year":"2011","unstructured":"Wang G, Shi P, Wen C (2011) Fuzzy approximation relations on fuzzy n-cell number space and their applications in classification. Inf Sci 181:3846\u20133860","journal-title":"Inf Sci"},{"issue":"5","key":"9371_CR29","doi-asserted-by":"publisher","first-page":"1113","DOI":"10.1109\/TFUZZ.2013.2282167","volume":"22","author":"G Wang","year":"2014","unstructured":"Wang G, Shi P, Wang B, Zhang J (2014) Fuzzy n-ellipsoid numbers and representations of uncertain multichannel digital information. IEEE Trans Fuzzy Syst 22(5):1113\u20131126","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"9371_CR30","doi-asserted-by":"publisher","first-page":"258","DOI":"10.1016\/j.ins.2015.07.045","volume":"326","author":"G Wang","year":"2016","unstructured":"Wang G, Shi P, Xie Y, Shi Y (2016) Two-dimensional discrete fuzzy numbers and applications. Inf Sci 326:258\u2013269","journal-title":"Inf Sci"},{"key":"9371_CR31","doi-asserted-by":"publisher","first-page":"1855","DOI":"10.3233\/JIFS-17383","volume":"33","author":"T Wang","year":"2017","unstructured":"Wang T, Yang Y, Wang G (2017) Constructing of fuzzy integer valued mapping and the application of its integral. J Intell Fuzzy Syst 33:1855\u20131866","journal-title":"J Intell Fuzzy Syst"},{"key":"9371_CR32","doi-asserted-by":"publisher","first-page":"919","DOI":"10.1007\/s00500-019-04612-0","volume":"24","author":"T Wang","year":"2020","unstructured":"Wang T, Shi P, Wang G (2020) Solving fuzzy regression equation and its approximation for random fuzzy variable and their application. Soft Comput 24:919\u2013933","journal-title":"Soft Comput"},{"key":"9371_CR33","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2021.3118781","author":"G Wang","year":"2021","unstructured":"Wang G, Wang Y, Tang J (2021) Fuzzy option pricing based on fuzzy number binary tree model. IEEE Trans Fuzzy Syst. https:\/\/doi.org\/10.1109\/TFUZZ.2021.3118781","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"9371_CR34","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2021.3123788","author":"W Wu","year":"2021","unstructured":"Wu W, Tong S (2021) Fuzzy adaptive consensus control for nonlinear multiagent systems with intermittent actuator faults. IEEE Trans Cybern. https:\/\/doi.org\/10.1109\/TCYB.2021.3123788","journal-title":"IEEE Trans Cybern"},{"issue":"6","key":"9371_CR35","doi-asserted-by":"publisher","first-page":"4198","DOI":"10.1109\/TCYB.2020.3024754","volume":"52","author":"Y Zeng","year":"2022","unstructured":"Zeng Y, Lam HK, Xiao B, Wu L (2022) $$l^2-l^{\\infty }$$ control of discrete-time state-delay interval type-2 fuzzy systems via dynamic output feedback. IEEE Trans Cybern 52(6):4198\u20134208","journal-title":"IEEE Trans Cybern"},{"key":"9371_CR36","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2021.3088994","author":"Y Zhan","year":"2021","unstructured":"Zhan Y, Tong S (2021) Adaptive fuzzy output-feedback decentralized control for fractional-order nonlinear large-scale systems. IEEE Trans Cybern. https:\/\/doi.org\/10.1109\/TCYB.2021.3088994","journal-title":"IEEE Trans Cybern"},{"key":"9371_CR37","doi-asserted-by":"publisher","first-page":"9345609","DOI":"10.1155\/2018\/9345609","volume":"2018","author":"M Zhao","year":"2018","unstructured":"Zhao M, Liu T, Su J, Liu M (2018) A method adjusting consistency and consensus for group decision-making problems with hesitant fuzzy linguistic preference relations based on discrete fuzzy numbers. Complexity 2018:9345609. https:\/\/doi.org\/10.1155\/2018\/9345609","journal-title":"Complexity"},{"key":"9371_CR38","doi-asserted-by":"publisher","first-page":"13569","DOI":"10.1007\/s00500-019-03895-7","volume":"23","author":"M Zhao","year":"2019","unstructured":"Zhao M, Liu M, Su J, Liu T (2019) A shape similarity-based ranking method of hesitant fuzzy linguistic preference relations using discrete fuzzy number for group decision making. Soft Comput 23:13569\u201313589","journal-title":"Soft Comput"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-023-09371-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-023-09371-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-023-09371-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,12]],"date-time":"2024-01-12T03:09:59Z","timestamp":1705028999000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-023-09371-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,11]]},"references-count":38,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,1]]}},"alternative-id":["9371"],"URL":"https:\/\/doi.org\/10.1007\/s00500-023-09371-7","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,11,11]]},"assertion":[{"value":"10 October 2023","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 November 2023","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}