{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T14:49:21Z","timestamp":1761490161681,"version":"3.37.3"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2016,12,20]],"date-time":"2016-12-20T00:00:00Z","timestamp":1482192000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation China","doi-asserted-by":"crossref","award":["61374009"],"award-info":[{"award-number":["61374009"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Mach. Learn. & Cyber."],"published-print":{"date-parts":[[2018,6]]},"DOI":"10.1007\/s13042-016-0622-z","type":"journal-article","created":{"date-parts":[[2016,12,20]],"date-time":"2016-12-20T14:14:09Z","timestamp":1482243249000},"page":"979-991","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Rule number and approximation of the hybrid fuzzy system based on binary tree hierarchy"],"prefix":"10.1007","volume":"9","author":[{"given":"Guijun","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoping","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,12,20]]},"reference":[{"issue":"5","key":"622_CR1","doi-asserted-by":"crossref","first-page":"1201","DOI":"10.1080\/00207179108934205","volume":"54","author":"GVS Raju","year":"1991","unstructured":"Raju GVS, Zhou J, Kisner RA (1991) Hierarchical fuzzy control. Int J Control 54(5):1201\u20131216","journal-title":"Int J Control"},{"key":"622_CR2","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1109\/21.247882","volume":"23","author":"GVS Raju","year":"1993","unstructured":"Raju GVS, Zhou J (1993) Adaptive hierarchical fuzzy controller. IEEE Trans Syst Man Cybernet 23:973\u2013980","journal-title":"IEEE Trans Syst Man Cybernet"},{"key":"622_CR3","doi-asserted-by":"crossref","unstructured":"Wang LX (1998) Universal approximation by hierarchical fuzzy systems. Fuzzy Set Syst 93(1):223\u2013230","DOI":"10.1016\/S0165-0114(96)00197-2"},{"issue":"5","key":"622_CR4","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1109\/91.797984","volume":"7","author":"LX Wang","year":"1999","unstructured":"Wang LX (1999) Analysis and design of hierarchical fuzzy systems. IEEE Trans Fuzzy Syst 7(5):617\u2013624","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"622_CR5","doi-asserted-by":"crossref","unstructured":"Chen W, Wang LX (2000) A note on universal approximation by hierarchical fuzzy systems. Inf Sci 123:241\u2013248","DOI":"10.1016\/S0020-0255(99)00126-7"},{"key":"622_CR6","doi-asserted-by":"crossref","unstructured":"Takagi T, Sugeno M (1985) Fuzzy identification of system and its applications to modeling and control. IEEE Trans Syst Man Cybernet 15:116\u2013132","DOI":"10.1109\/TSMC.1985.6313399"},{"key":"622_CR7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/91.660804","volume":"6","author":"WE Combs","year":"1998","unstructured":"Combs WE, Andrews JE (1998) Combinatorial rule explosion eliminated by a fuzzy rule configuration. IEEE Trans Fuzzy Syst 6:1\u201311","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"3","key":"622_CR8","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/S0165-0114(97)00300-X","volume":"106","author":"XZ Wang","year":"1999","unstructured":"Wang XZ, Hong JR (1999) Learning optimization in simplifying fuzzy rules. Fuzzy Sets Syst 106(3):349\u2013356","journal-title":"Fuzzy Sets Syst"},{"key":"622_CR9","doi-asserted-by":"crossref","unstructured":"Ying H (1998) Sufficient conditions on uniform approximation of multivariate functions by general Takagi-Sugeno fuzzy systems with linear rule consequent. IEEE Trans Syst Man Cybernet 28: 515\u2013520","DOI":"10.1109\/3468.686713"},{"key":"622_CR10","doi-asserted-by":"crossref","unstructured":"Yin TK (2004) A characteristic-point-based fuzzy inference system aimed to minimize the number of fuzzy rules. IEEE Trans Actions Fuzzy Syst 12(2):250\u2013273","DOI":"10.1109\/TFUZZ.2004.825088"},{"issue":"3","key":"622_CR11","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/S0165-0114(97)00030-4","volume":"99","author":"XZ Wang","year":"1998","unstructured":"Wang XZ, Hong JR (1998) On the handling of fuzziness for continuous-valued attributes in decision tree generation. Fuzzy Sets Syst 99(3):283\u2013290","journal-title":"Fuzzy Sets Syst"},{"issue":"5","key":"622_CR12","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1109\/91.873583","volume":"8","author":"ECC Tsang","year":"2000","unstructured":"Tsang ECC, Wang XZ, Yeung DS (2000) Improving learning accuracy of fuzzy decision trees by hybrid neural networks. IEEE Trans Fuzzy Syst 8(5):601\u2013614","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"622_CR13","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.3233\/IFS-151729","volume":"29","author":"XZ Wang","year":"2015","unstructured":"Wang XZ, Aamir R, Aimin F (2015) Fuzziness based sample categorization for classifier performance improvement. J Intell Fuzzy Syst 29:1185\u20131196","journal-title":"J Intell Fuzzy Syst"},{"key":"622_CR14","unstructured":"Liu PY, Li HX (2000) Approximation of generalized fuzzy systems to integrable functions. Sci China Ser E 30(5):413\u2013423"},{"issue":"2","key":"622_CR15","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/S0020-0255(01)00128-1","volume":"138","author":"PY Liu","year":"2001","unstructured":"Liu PY, Li HX (2001) Analyses for Lp-norm approximation capability of generalized Mamdani fuzzy systems. Inf Sci 138(2):195\u2013210","journal-title":"Inf Sci"},{"issue":"3","key":"622_CR16","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/j.ins.2004.04.008","volume":"169","author":"PY Liu","year":"2005","unstructured":"Liu PY, Li HX (2005) Hierarchical T-S fuzzy system and its universal approximation. Inf Sci 169(3):279\u2013303","journal-title":"Inf Sci"},{"issue":"5","key":"622_CR17","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1109\/TFUZZ.2005.856559","volume":"13","author":"XJ Zeng","year":"2005","unstructured":"Zeng XJ, John AK (2005) Approximation capabilities of hierarchical fuzzy systems. IEEE Trans Fuzzy Syst 13(5):659\u2013672","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"3","key":"622_CR18","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1109\/TFUZZ.2006.876365","volume":"14","author":"J Ricardo","year":"2006","unstructured":"Ricardo J, Campello GB, Wagner C (2006) Hierarchical fuzzy relational models: linguistic interpretation and universal approximation. IEEE Trans Fuzzy Syst 14(3):446\u2013453","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"4","key":"622_CR19","first-page":"674","volume":"41","author":"XH Yuan","year":"2013","unstructured":"Yuan XH, Li HX, Yang X (2013) Fuzzy system and fuzzy inference modeling method based on fuzzytransformation. Acta Electron Sin 41(4):674\u2013680","journal-title":"Acta Electron Sin"},{"key":"622_CR20","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.ins.2013.05.011","volume":"245","author":"DG Wang","year":"2013","unstructured":"Wang DG, Song WY, Shi P, Li HX (2013) Approximation to a class of non-autonomous systems by dynamic fuzzy inference marginal linearization method. Inf Sci. 245:197\u2013217","journal-title":"Inf Sci."},{"key":"622_CR21","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/j.neucom.2014.02.070","volume":"149","author":"DG Wang","year":"2015","unstructured":"Wang DG, Song WY, Li HX (2015) Approximation properties of ELM-fuzzy systems for smooth functions and their derivatives. Neurocomputing 149:265\u2013274","journal-title":"Neurocomputing"},{"issue":"1","key":"622_CR22","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1109\/TFUZZ.2008.2007570","volume":"17","author":"GJ Moon","year":"2009","unstructured":"Moon GJ, Thomas S (2009) A method of converting a fuzzy system to a two-layered hierarchical fuzzy system and its run-time efficiency. IEEE Trans Fuzzy Syst 17(1):93\u2013103","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"24","key":"622_CR23","doi-asserted-by":"crossref","first-page":"3530","DOI":"10.1016\/j.fss.2009.02.001","volume":"160","author":"SK Vassilis","year":"2009","unstructured":"Vassilis SK, Yannis AP (2009) On the monotonicity of hierarchical sum-product fuzzy systems. Fuzzy Sets Syst 160(24):3530\u20133538","journal-title":"Fuzzy Sets Syst"},{"issue":"1","key":"622_CR24","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1109\/TFUZZ.2009.2034531","volume":"18","author":"M Abdolreza","year":"2010","unstructured":"Abdolreza M, Mohammad R (2010) A novel hierarchical clustering combination scheme based on fuzzy similarity relations. IEEE Trans Fuzzy Syst 18(1):27\u201339","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"1","key":"622_CR25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.fss.2011.03.008","volume":"174","author":"L Zsofia","year":"2011","unstructured":"Zsofia L, Robert B, Bart DS (2011) Sequential stability analysis and observer design for distributed T-S fuzzy systems. Fuzzy Sets Syst 174(1):1\u201330","journal-title":"Fuzzy Sets Syst"},{"issue":"6","key":"622_CR26","doi-asserted-by":"crossref","first-page":"1032","DOI":"10.1109\/TFUZZ.2013.2240690","volume":"21","author":"MN Luo","year":"2013","unstructured":"Luo MN, Sun FC, Liu HP (2013) Hierarchical structured sparse representation for T-S fuzzy systems identification. IEEE Trans Fuzzy Syst 21(6):1032\u20131043","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"15","key":"622_CR27","doi-asserted-by":"crossref","first-page":"8277","DOI":"10.1016\/j.amc.2013.02.026","volume":"219","author":"CH Chen","year":"2013","unstructured":"Chen CH (2013) Design of TSK-type fuzzy controllers using differential evolution with adaptive mutation strategy for nonlinear system control. Appl Math Comput 219(15):8277\u20138294","journal-title":"Appl Math Comput"},{"issue":"5","key":"622_CR28","first-page":"673","volume":"29","author":"GJ Wang","year":"2012","unstructured":"Wang GJ, Duan CX (2012) Generalized hierarchical hybrid fuzzy systems and their universal approximation. Control Theory Appl 29(5):673\u2013680","journal-title":"Control Theory Appl"},{"key":"622_CR29","unstructured":"Wang GJ, Li XP, Sui XL (2014) Universal approximation and its realization of generalized Mamdani fuzzy system based on K-integral norms. Acta Autom Sin 40(1):143\u2013148"},{"issue":"10","key":"622_CR30","first-page":"1742","volume":"30","author":"GJ Wang","year":"2015","unstructured":"Wang GJ, Song WW, Han QJ (2015) Generalized hybrid fuzzy system based on consequent direct link type-hierarchy and its integral norm approximation. Control Decis 30(10):1742\u20131750","journal-title":"Control Decis"},{"issue":"11","key":"622_CR31","first-page":"2284","volume":"43","author":"YJ Tao","year":"2015","unstructured":"Tao YJ, Wang HZ, Wang GJ (2015) Approximation ability and its realization of the generalized Mamdan fuzzy system in the sense of Kp-integral norm. Acta Electron Sin 43(11):2284\u20132291","journal-title":"Acta Electron Sin"},{"key":"622_CR32","unstructured":"Du XY, Zhang NY (2004) Equivalence analysis of binary-tree-type hierarchical fuzzy system. J Tsinghua Univ 44(7):33\u201336"},{"issue":"1","key":"622_CR33","first-page":"37","volume":"47","author":"XY Zhang","year":"2007","unstructured":"Zhang XY, Zhang NY (2007) Universal approximation of general binary-tree-type hierarchical fuzzy systems. J Tsinghua Univ 47(1):37\u201341","journal-title":"J Tsinghua Univ"},{"issue":"6","key":"622_CR34","first-page":"765","volume":"30","author":"Y Yang","year":"2013","unstructured":"Yang Y, Wang GJ, Yang YQ (2013) Reducing the number of inference rules for generalized hybrid fuzzy systems based on binary tree type hierarchy. Control Theory Appl 30(6):765\u2013772","journal-title":"Control Theory Appl"},{"issue":"11","key":"622_CR35","doi-asserted-by":"crossref","first-page":"2307","DOI":"10.1007\/s11432-011-4364-y","volume":"54","author":"GJ Wang","year":"2011","unstructured":"Wang GJ, Li XP (2011) Universal approximation of polygonal fuzzy neural networks in sense of K-integral norms. Sci China Inf Sci 54(11):2307\u20132323","journal-title":"Sci China Inf Sci"},{"key":"622_CR36","volume-title":"A course in fuzzy systems and control (Chinese Version)","author":"LX Wang","year":"2003","unstructured":"Wang LX (2003) A course in fuzzy systems and control (Chinese Version). Tsinghua University Press, Beijing"}],"container-title":["International Journal of Machine Learning and Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s13042-016-0622-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-016-0622-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-016-0622-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,28]],"date-time":"2020-09-28T03:32:44Z","timestamp":1601263964000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s13042-016-0622-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,12,20]]},"references-count":36,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2018,6]]}},"alternative-id":["622"],"URL":"https:\/\/doi.org\/10.1007\/s13042-016-0622-z","relation":{},"ISSN":["1868-8071","1868-808X"],"issn-type":[{"type":"print","value":"1868-8071"},{"type":"electronic","value":"1868-808X"}],"subject":[],"published":{"date-parts":[[2016,12,20]]}}}