{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T06:56:04Z","timestamp":1760597764227,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,8,25]],"date-time":"2017-08-25T00:00:00Z","timestamp":1503619200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This work is focused on creating fuzzy granular classification models based on general type-2 fuzzy logic systems when consequents are represented by interval type-2 TSK linear functions. Due to the complexity of general type-2 TSK fuzzy logic systems, a hybrid learning approach is proposed, where the principle of justifiable granularity is heuristically used to define an amount of uncertainty in the system, which in turn is used to define the parameters in the interval type-2 TSK linear functions via a dual LSE algorithm. Multiple classification benchmark datasets were tested in order to assess the quality of the formed granular models; its performance is also compared against other common classification algorithms. Shown results conclude that classification performance in general is better than results obtained by other techniques, and in general, all achieved results, when averaged, have a better performance rate than compared techniques, demonstrating the stability of the proposed hybrid learning technique.<\/jats:p>","DOI":"10.3390\/a10030099","type":"journal-article","created":{"date-parts":[[2017,8,25]],"date-time":"2017-08-25T11:03:17Z","timestamp":1503658997000},"page":"99","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Hybrid Learning for General Type-2 TSK Fuzzy Logic Systems"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7473-0546","authenticated-orcid":false,"given":"Mauricio","family":"Sanchez","sequence":"first","affiliation":[{"name":"School of Engineering, Universidad Autonoma de Baja California, Tijuana 22390, Mexico"}]},{"given":"Juan","family":"Castro","sequence":"additional","affiliation":[{"name":"School of Engineering, Universidad Autonoma de Baja California, Tijuana 22390, Mexico"}]},{"given":"Violeta","family":"Ocegueda-Miramontes","sequence":"additional","affiliation":[{"name":"School of Engineering, Universidad Autonoma de Baja California, Tijuana 22390, Mexico"}]},{"given":"Leticia","family":"Cervantes","sequence":"additional","affiliation":[{"name":"Division of Graduate Studies, Tijuana Institute of Technology, Tijuana 22414, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2017,8,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.eswa.2016.02.051","article-title":"Robust learning algorithm for multiplicative neuron model artificial neural networks","volume":"56","author":"Bas","year":"2016","journal-title":"Expert Syst. Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.neucom.2015.12.076","article-title":"An optimized second order stochastic learning algorithm for neural network training","volume":"186","author":"Liew","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ijepes.2016.03.001","article-title":"A systematic design of interval type-2 fuzzy logic system using extreme learning machine for electricity load demand forecasting","volume":"82","author":"Hassan","year":"2016","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1038\/323533a0","article-title":"Learning representations by back-propagating errors","volume":"323","author":"Rumelhart","year":"1986","journal-title":"Nature"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3438","DOI":"10.1016\/j.patcog.2014.03.019","article-title":"Hybrid learning of Bayesian multinets for binary classification","volume":"47","author":"Carvalho","year":"2014","journal-title":"Pattern Recognit."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1237","DOI":"10.1016\/j.neucom.2014.03.081","article-title":"Hybrid learning particle swarm optimizer with genetic disturbance","volume":"151","author":"Liu","year":"2015","journal-title":"Neurocomputing"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.asoc.2015.06.003","article-title":"A novel hybrid learning algorithm for full Bayesian approach of artificial neural networks","volume":"35","year":"2015","journal-title":"Appl. Soft Comput."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1807","DOI":"10.1109\/TSMCB.2012.2231068","article-title":"A hybrid learning method for constructing compact rule-based fuzzy models","volume":"43","author":"Zhao","year":"2013","journal-title":"IEEE Trans. Cybern."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Zadeh, L.A. (1996). Fuzzy sets and information granularity. Advances in Fuzzy Set Theory and Applications, North-Holland Publishing Company.","DOI":"10.1142\/9789814261302_0022"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1109\/TFUZZ.2007.905912","article-title":"Toward a theory of granular computing for human-centered information processing","volume":"16","author":"Bargiela","year":"2008","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1162","DOI":"10.1109\/TFUZZ.2013.2286414","article-title":"General type-2 fuzzy logic systems made simple: A tutorial","volume":"22","author":"Mendel","year":"2013","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"808","DOI":"10.1109\/TFUZZ.2006.879986","article-title":"Interval type-2 fuzzy logic systems made simple","volume":"14","author":"Mendel","year":"2006","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/j.compbiomed.2014.06.017","article-title":"Alpha-plane based automatic general type-2 fuzzy clustering based on simulated annealing meta-heuristic algorithm for analyzing gene expression data","volume":"64","year":"2015","journal-title":"Comput. Biol. Med."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.ins.2014.01.050","article-title":"Similarity measures for general type-2 fuzzy sets based on the -plane representation","volume":"277","author":"Hao","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"842","DOI":"10.1016\/j.ins.2014.03.018","article-title":"Hierarchical collapsing method for direct defuzzification of general type-2 fuzzy sets","volume":"277","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/j.ins.2015.08.027","article-title":"Multi-central general type-2 fuzzy clustering approach for pattern recognitions","volume":"328","author":"Golsefid","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1155","DOI":"10.1016\/j.asoc.2014.01.013","article-title":"Online identification of evolving Takagi\u2013Sugeno\u2013Kang fuzzy models for crane systems","volume":"24","author":"Precup","year":"2014","journal-title":"Appl. Soft Comput."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.fss.2014.05.019","article-title":"Fuzzy dynamic output feedback control through nonlinear Takagi\u2013Sugeno models","volume":"263","author":"Klug","year":"2015","journal-title":"Fuzzy Sets Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.fss.2015.03.003","article-title":"Analysis of the dengue risk by means of a Takagi\u2013Sugeno-style model","volume":"277","author":"Silveira","year":"2015","journal-title":"Fuzzy Sets Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"5771","DOI":"10.1016\/j.eswa.2014.03.031","article-title":"Fuzzy model forecasting of offshore bar-shape profiles under high waves","volume":"41","author":"Kim","year":"2014","journal-title":"Expert Syst. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1016\/j.ins.2014.04.005","article-title":"Fuzzy granular gravitational clustering algorithm for multivariate data","volume":"279","author":"Sanchez","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5904","DOI":"10.1016\/j.eswa.2015.03.024","article-title":"Generalized Type-2 Fuzzy Systems for controlling a mobile robot and a performance comparison with Interval Type-2 and Type-1 Fuzzy Systems","volume":"42","author":"Sanchez","year":"2015","journal-title":"Expert Syst. Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2296","DOI":"10.1109\/TNN.2011.2170095","article-title":"Data-based system modeling using a type-2 fuzzy neural network with a hybrid learning algorithm","volume":"22","author":"Yeh","year":"2011","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_24","unstructured":"Mendel, J. (2001). Unnormalized interval type-2 TSK FLSs. Uncertain Rule-Based Fuzzy Logic System: Introduction and New Directions, Prentice-Hall."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"397","DOI":"10.3745\/JIPS.2011.7.3.397","article-title":"The principle of justifiable granularity and an optimization of information granularity allocation as fundamentals of granular computing","volume":"7","author":"Pedrycz","year":"2011","journal-title":"J. Inf. Process. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Bezdek, J.C. (1981). Pattern Recognition with Fuzzy Objective Function Algorithms, Springer.","DOI":"10.1007\/978-1-4757-0450-1"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1109\/21.256541","article-title":"ANFIS: Adaptive-network-based fuzzy inference system","volume":"23","author":"Jang","year":"1993","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_28","unstructured":"Jang, J.-S.R. (1991, January 14\u201319). Fuzzy modeling using generalized neural networks and Kalman filter algorithm. Proceedings of the Ninth National Conference on Artificial Intelligence, Anaheim, CA, USA."},{"key":"ref_29","unstructured":"Frank, A., and Asuncion, A. (2010). UCI Machine Learning Repository, University of California."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1109\/TFUZZ.2008.924342","article-title":"Improving generalization of fuzzy IF\u2013THEN Rules by maximizing fuzzy entropy","volume":"17","author":"Wang","year":"2009","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1109\/3477.809036","article-title":"On generating FC3 fuzzy rule systems from data using evolution strategies","volume":"29","author":"Jin","year":"1999","journal-title":"IEEE Trans. Syst. Man Cybern. Part B"},{"key":"ref_32","first-page":"2079","article-title":"On over-fitting in model selection and subsequent selection bias in performance evaluation","volume":"11","author":"Cawley","year":"2010","journal-title":"J. Mach. Learn. Res."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"267","DOI":"10.3233\/IFS-1994-2306","article-title":"Fuzzy model identification based on cluster estimation","volume":"2","author":"Chiu","year":"1994","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/BF00994018","article-title":"Support vector machine","volume":"20","author":"Cortes","year":"1995","journal-title":"Mach. Learn."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1080\/00031305.1992.10475879","article-title":"An introduction to kernel and nearest-neighbor nonparametric regression","volume":"46","author":"Altman","year":"1992","journal-title":"Am. Stat."},{"key":"ref_36","unstructured":"John, G.H., and Langley, P. (1995, January 18\u201320). Estimating continuous distributions in Bayesian classifiers. Proceedings of the 11th Conference on Uncertainty in Artificial Intelligence, Montr\u00e9al, QC, Canada."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/10\/3\/99\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:43:21Z","timestamp":1760208201000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/10\/3\/99"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,25]]},"references-count":36,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,9]]}},"alternative-id":["a10030099"],"URL":"https:\/\/doi.org\/10.3390\/a10030099","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2017,8,25]]}}}