{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:40:40Z","timestamp":1777704040057,"version":"3.51.4"},"reference-count":29,"publisher":"SAGE Publications","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2016,6,13]]},"DOI":"10.3233\/ifs-162146","type":"journal-article","created":{"date-parts":[[2016,6,14]],"date-time":"2016-06-14T17:01:58Z","timestamp":1465923718000},"page":"333-344","source":"Crossref","is-referenced-by-count":0,"title":["Decompositions and representations of\u00a0L-fuzzy natural numbers"],"prefix":"10.1177","volume":"31","author":[{"given":"Xiu-Yun","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Hunan University ofScience and Engineering, Hunan, China"},{"name":"Shool of Mathematics and Computational Science, Xiangtan University, Hunan, China"}]},{"given":"Shi-Zhong","family":"Bai","sequence":"additional","affiliation":[{"name":"Shool of Mathematics and Computational Science, Xiangtan University, Hunan, China"},{"name":"School of Mathematics and Computational Science, Wuyi University, Guangdong, China"}]}],"member":"179","reference":[{"key":"10.3233\/IFS-162146_ref1","first-page":"734","article-title":"Statistically monotonic and statistically bounded sequences of fuzzy numbers","volume":"176","author":"Aytar","year":"2006","journal-title":"Inform Control"},{"key":"10.3233\/IFS-162146_ref2","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/S0020-0255(03)00054-9","article-title":"Alpha-bounds of fuzzy numbers","volume":"8","author":"Bodjanova","year":"2003","journal-title":"Inform Sci"},{"key":"10.3233\/IFS-162146_ref3","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/S0165-0114(02)00345-7","article-title":"An axiomatic approach to the fuzzy cardinality of finite fuzzy sets","volume":"133","author":"Casasnovas","year":"2003","journal-title":"Fuzzy Sets Syst"},{"key":"10.3233\/IFS-162146_ref4","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1007\/978-3-540-72434-6_58","article-title":"Discrete fuzzy numbers defined on a subset of natural numbers","volume":"42","author":"Casasnovas","year":"2007","journal-title":"Adv Soft Comput"},{"key":"10.3233\/IFS-162146_ref5","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/978-3-642-16292-3_9","article-title":"Aggregation of bounded fuzzy natural number-valued multisets","author":"Casasnovas","year":"2010","journal-title":"Model Decis Artif Intell"},{"key":"10.3233\/IFS-162146_ref6","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/j.fss.2005.03.002","article-title":"Fuzzy process control: Construction of control charts with fuzzy numbers","volume":"154","author":"Cheng","year":"2005","journal-title":"Fuzzy Sets Syst"},{"key":"10.3233\/IFS-162146_ref7","doi-asserted-by":"crossref","first-page":"137","DOI":"10.3233\/HIS-130189","article-title":"On L-fuzzy proximity spaces","volume":"11","author":"El-Dardery","year":"2014","journal-title":"Int J Hybrid Intell Syst"},{"key":"10.3233\/IFS-162146_ref8","doi-asserted-by":"crossref","first-page":"685","DOI":"10.3233\/IFS-2012-0588","article-title":"L-Fuzzy topogenous orders and L-Fuzzy topologies","volume":"24","author":"El-Dardery","year":"2013","journal-title":"J Intell Fuzzy Syst"},{"key":"10.3233\/IFS-162146_ref9","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1080\/00207727808941724","article-title":"Operations on fuzzy numbers","volume":"9","author":"Dubois","year":"1978","journal-title":"Int J Syst Sci"},{"key":"10.3233\/IFS-162146_ref10","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/S0165-0114(97)00135-8","article-title":"Operations on fuzzy numbers via fuzzy reasoning","volume":"91","author":"Filev","year":"1997","journal-title":"Fuzzy Sets Syst"},{"key":"10.3233\/IFS-162146_ref11","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/S0165-0114(97)00140-1","article-title":"A parametric representation of fuzzy numbers and their arithmetic operators","volume":"91","author":"Giachetti","year":"1997","journal-title":"Fuzzy Sets Syst"},{"key":"10.3233\/IFS-162146_ref12","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/S0165-0114(96)00322-3","article-title":"Metrics and orders in space of fuzzy numbers","volume":"97","author":"Grzegorzewski","year":"1998","journal-title":"Fuzzy Sets Syst"},{"key":"10.3233\/IFS-162146_ref13","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/S0165-0114(02)00098-2","article-title":"Nearest interval approximation of a fuzzy number","volume":"130","author":"Grzegorzewski","year":"2012","journal-title":"Fuzzy Sets Syst"},{"key":"10.3233\/IFS-162146_ref14","first-page":"109","article-title":"Multiplication and exponentiation of L-fuzzy natural numbers","volume":"1","author":"Han","year":"2010","journal-title":"Fuzzy Syst Math"},{"key":"10.3233\/IFS-162146_ref15","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.1016\/j.ins.2007.10.001","article-title":"L-fuzzy numbers and there applications","volume":"178","author":"Huang","year":"2008","journal-title":"Inform Sci"},{"key":"10.3233\/IFS-162146_ref16","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1007\/s00521-013-1541-5","article-title":"A developed distance method for ranking generalized fuzzy numbers","volume":"25","author":"Janizade-Haji","year":"2014","journal-title":"Neural Comput Appl"},{"key":"10.3233\/IFS-162146_ref17","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/0165-0114(84)90069-1","article-title":"On fuzzy metric spaces","volume":"12","author":"Kaleva","year":"1984","journal-title":"Fuzzy Sets Syst"},{"key":"10.3233\/IFS-162146_ref18","first-page":"2010","author":"Lowen","journal-title":"Fuzzy set theory"},{"key":"10.3233\/IFS-162146_ref19","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/S0165-0114(85)80013-0","article-title":"Inequality between fuzzy numbers and its use in fuzzy potimization","volume":"16","author":"Ranik","year":"1985","journal-title":"Fuzzy Sets Syst"},{"key":"10.3233\/IFS-162146_ref20","first-page":"45","article-title":"A new approach ranking of exponential trapezoidal fuzzy numbers","volume":"16","author":"Rezvani","year":"2012","journal-title":"J Phys Sci"},{"key":"10.3233\/IFS-162146_ref21","first-page":"65","article-title":"Theory of L\u03b2-nested mappings and L\u03b1-nested mappings and applications","volume":"4","author":"Shi","year":"1995","journal-title":"Fuzzy Syst Math"},{"key":"10.3233\/IFS-162146_ref22","doi-asserted-by":"crossref","first-page":"696","DOI":"10.1016\/j.fss.2008.05.007","article-title":"A new approach to the fuzzification of matroids","volume":"160","author":"Shi","year":"2009","journal-title":"Fuzzy Sets Syst"},{"key":"10.3233\/IFS-162146_ref23","doi-asserted-by":"crossref","first-page":"2387","DOI":"10.1016\/j.fss.2009.02.025","article-title":"(L, M)-fuzzy matroids","volume":"160","author":"Shi","year":"2009","journal-title":"Fuzzy Sets Syst"},{"key":"10.3233\/IFS-162146_ref24","doi-asserted-by":"crossref","first-page":"2423","DOI":"10.1016\/j.fss.2006.02.002","article-title":"Parametric representation of fuzzy numbers and application to fuzzy calculus","volume":"157","author":"Stefaninia","year":"2006","journal-title":"Fuzzy Sets Syst"},{"key":"10.3233\/IFS-162146_ref25","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.fss.2014.08.013","article-title":"A probabilistic approach to the arithmetics of fuzzy numbers","volume":"264","author":"Stup\u0148anov\u00e1","year":"2015","journal-title":"Fuzzy Sets Syst"},{"key":"10.3233\/IFS-162146_ref26","first-page":"31","article-title":"Rank functions for closed and perfect [0,1]-matroids","volume":"39","author":"Xin","year":"2010","journal-title":"Hacettetepe J Math Statist"},{"key":"10.3233\/IFS-162146_ref27","unstructured":"Wang G.J. , Theory of L-fuzzy topological spaces, Xi\u2019an: Shanxi Normal University Press (1988). (Chinese)."},{"key":"10.3233\/IFS-162146_ref28","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/0165-0114(92)90301-J","article-title":"Theory of topological molecular lattice","volume":"47","author":"Wang","year":"1992","journal-title":"Fuzzy Sets Syst"},{"key":"10.3233\/IFS-162146_ref29","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inform Control"}],"container-title":["Journal of Intelligent & Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/IFS-162146","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:40:16Z","timestamp":1777455616000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/IFS-162146"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6,13]]},"references-count":29,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.3233\/ifs-162146","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,6,13]]}}}