Multiobjective Programming for Type-2 Hierarchical Fuzzy Inference Trees

This paper proposes a design of hierarchical fuzzy inference tree (HFIT). An HFIT produces an optimum tree-like structure, i.e., a natural hierarchical structure that accommodates simplicity by combining several low-dimensional fuzzy inference systems (FISs). Such a natural hierarchical structure pr...

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Published in:	IEEE transactions on fuzzy systems Vol. 26; no. 2; pp. 915 - 936
Main Authors:	Ojha, Varun Kumar, Snasel, Vaclav, Abraham, Ajith
Format:	Journal Article
Language:	English
Published:	IEEE 01.04.2018
Subjects:	Approximation Artificial neural networks Clustering methods Complexity theory differential evolution (DE) feature selection Fuzzy logic Heuristic algorithms hierarchical fuzzy inference system (HFIS) multiobjective genetic programming (MOGP) Optimization Tuning
ISSN:	1063-6706, 1941-0034
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Abstract	This paper proposes a design of hierarchical fuzzy inference tree (HFIT). An HFIT produces an optimum tree-like structure, i.e., a natural hierarchical structure that accommodates simplicity by combining several low-dimensional fuzzy inference systems (FISs). Such a natural hierarchical structure provides a high degree of approximation accuracy. The construction of the HFIT takes place in two phases. First, a nondominated sorting-based multiobjective genetic programming (MOGP) is applied to obtain a simple tree structure (a low complexity model) with a high accuracy. Second, the differential evolution algorithm is applied to optimize the obtained tree's parameters. In the derived tree, each node acquires a different input's combination, where the evolutionary process governs the input's combination. Hence, HFIT nodes are heterogeneous in nature, which leads to a high diversity among the rules generated by the HFIT. Additionally, the HFIT provides an automatic feature selection because it uses MOGP for the tree's structural optimization that accepts inputs only relevant to the knowledge contained in data. The HFIT was studied in the context of both type-1 and type-2 FISs, and its performance was evaluated through six application problems. Moreover, the proposed multiobjective HFIT was compared both theoretically and empirically with recently proposed FISs methods from the literature, such as McIT2FIS, TSCIT2FNN, SIT2FNN, RIT2FNS-WB, eT2FIS, MRIT2NFS, IT2FNN-SVR, etc. From the obtained results, it was found that the HFIT provided less complex and highly accurate models compared to the models produced by the most of other methods. Hence, the proposed HFIT is an efficient and competitive alternative to the other FISs for function approximation and feature selection.
AbstractList	This paper proposes a design of hierarchical fuzzy inference tree (HFIT). An HFIT produces an optimum tree-like structure, i.e., a natural hierarchical structure that accommodates simplicity by combining several low-dimensional fuzzy inference systems (FISs). Such a natural hierarchical structure provides a high degree of approximation accuracy. The construction of the HFIT takes place in two phases. First, a nondominated sorting-based multiobjective genetic programming (MOGP) is applied to obtain a simple tree structure (a low complexity model) with a high accuracy. Second, the differential evolution algorithm is applied to optimize the obtained tree's parameters. In the derived tree, each node acquires a different input's combination, where the evolutionary process governs the input's combination. Hence, HFIT nodes are heterogeneous in nature, which leads to a high diversity among the rules generated by the HFIT. Additionally, the HFIT provides an automatic feature selection because it uses MOGP for the tree's structural optimization that accepts inputs only relevant to the knowledge contained in data. The HFIT was studied in the context of both type-1 and type-2 FISs, and its performance was evaluated through six application problems. Moreover, the proposed multiobjective HFIT was compared both theoretically and empirically with recently proposed FISs methods from the literature, such as McIT2FIS, TSCIT2FNN, SIT2FNN, RIT2FNS-WB, eT2FIS, MRIT2NFS, IT2FNN-SVR, etc. From the obtained results, it was found that the HFIT provided less complex and highly accurate models compared to the models produced by the most of other methods. Hence, the proposed HFIT is an efficient and competitive alternative to the other FISs for function approximation and feature selection.
Author	Snasel, Vaclav Ojha, Varun Kumar Abraham, Ajith
Author_xml	– sequence: 1 givenname: Varun Kumar orcidid: 0000-0002-9256-1192 surname: Ojha fullname: Ojha, Varun Kumar email: ojha@arch.ethz.ch organization: Chair of Information Architecture, Swiss Federal Institute of Technology (ETH) Zurich, Zurich, Switzerland – sequence: 2 givenname: Vaclav surname: Snasel fullname: Snasel, Vaclav email: vaclav.snasel@vsb.cz organization: Department of Computer Science, Technical University of Ostrava, Ostrava, Czech Republic – sequence: 3 givenname: Ajith surname: Abraham fullname: Abraham, Ajith email: ajith.abraham@ieee.org organization: Machine Intelligence Research Labs (MIR Labs), Auburn, WA, USA
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References	ref57 ref56 szalas (ref68) 1993 ref52 ref55 ref54 ref51 ref50 ref46 ref45 ref48 ref47 ref42 ref41 ref44 ref43 smith (ref8) 1980 goldberg (ref67) 1987 ref49 ref7 ref9 ref4 ref3 ref5 box (ref96) 1976 ref100 ref101 ref40 kolmogorov (ref72) 1963; 28 altenberg (ref71) 1994; 3 ref35 ref34 ref37 ref36 ref31 ref30 ref33 ref32 ref39 poli (ref53) 2008 mendel (ref88) 2001 eiben (ref59) 2003 ref24 ref23 ref26 ref25 ref20 ref22 ref21 ref28 ref27 ref29 deb (ref58) 2000; 1917 ref13 ref12 ref15 ref14 ref99 ref11 ref98 ref17 ref16 ref19 ref18 ref93 ref92 ref95 ref94 ref90 ref89 ref86 ref85 ref87 ref82 ref81 ref84 ref83 szlek (ref97) 2013; 8 ref80 ref79 ref78 ref75 ref74 ref77 ref102 ref76 ref2 ref1 booker (ref6) 1982 wu (ref10) 2000; 30 ishibuchi (ref38) 2007 ref70 ref73 snyman (ref64) 2005; 97 ref69 ref63 ref66 ref65 ref60 ref62 ref61 lichman (ref91) 2013
References_xml	– ident: ref76 doi: 10.1109/TNN.2002.1000126 – ident: ref25 doi: 10.1080/00207179108934205 – ident: ref30 doi: 10.1109/TFUZZ.2005.856559 – ident: ref42 doi: 10.1109/91.928739 – ident: ref86 doi: 10.1109/TFUZZ.2010.2046904 – ident: ref70 doi: 10.1007/978-1-4757-4032-5 – year: 1993 ident: ref68 article-title: Contractive mapping genetic algorithms and their convergence publication-title: Tech Rep – ident: ref40 doi: 10.1142/S0218488507004868 – ident: ref41 doi: 10.1016/j.ijar.2011.03.004 – year: 2013 ident: ref91 article-title: UCI machine learning repository – ident: ref29 doi: 10.1016/S0165-0114(02)00517-1 – ident: ref102 doi: 10.1007/978-3-319-29504-6_16 – ident: ref15 doi: 10.1109/91.660805 – ident: ref90 doi: 10.1109/72.80202 – ident: ref45 doi: 10.1109/TFUZZ.2010.2060200 – ident: ref2 doi: 10.1016/S0019-9958(65)90241-X – ident: ref49 doi: 10.1109/TFUZZ.2009.2023113 – ident: ref100 doi: 10.1038/nature02388 – year: 2001 ident: ref88 publication-title: Uncertain Rule-Based Fuzzy Logic Systems Introduction and New Directions – ident: ref27 doi: 10.1109/91.797984 – ident: ref84 doi: 10.1109/TFUZZ.2003.817839 – ident: ref43 doi: 10.1016/j.ijar.2006.01.004 – ident: ref56 doi: 10.1016/j.ins.2004.10.005 – ident: ref63 doi: 10.1016/j.swevo.2016.01.004 – ident: ref99 doi: 10.1163/156856206775997322 – year: 1980 ident: ref8 article-title: A learning system based on genetic adaptive algorithms – ident: ref79 doi: 10.1109/91.649900 – ident: ref44 doi: 10.1007/s00500-008-0359-z – ident: ref5 doi: 10.1109/TFUZZ.2004.832538 – ident: ref46 doi: 10.1109/TFUZZ.2012.2236096 – ident: ref65 doi: 10.1109/5.58337 – year: 2008 ident: ref53 publication-title: A Field Guide to Genetic Programming – ident: ref7 doi: 10.1109/ICSMC.1999.814106 – ident: ref87 doi: 10.1109/TSMCB.2003.817053 – ident: ref80 doi: 10.1109/TFUZZ.2007.895975 – start-page: 1 year: 1987 ident: ref67 article-title: Finite Markov chain analysis of genetic algorithms publication-title: Proc 2nd Int Conf Genetic Algorithms Appl – volume: 28 start-page: 55 year: 1963 ident: ref72 article-title: On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition publication-title: Transl Amer Math Soc – ident: ref34 doi: 10.1109/TFUZZ.2013.2253106 – ident: ref60 doi: 10.1016/j.asoc.2016.09.035 – ident: ref95 doi: 10.1109/TFUZZ.2011.2142314 – volume: 8 start-page: 4601 year: 2013 ident: ref97 article-title: Heuristic modeling of macromolecule release from PLGA microspheres publication-title: Int J Nanomed – ident: ref81 doi: 10.1016/S0893-6080(99)00067-2 – year: 2003 ident: ref59 publication-title: Introduction to Evolutionary Computing doi: 10.1007/978-3-662-05094-1 – ident: ref26 doi: 10.1109/FUZZY.1995.409976 – ident: ref78 doi: 10.1109/3477.969494 – ident: ref14 doi: 10.1016/j.knosys.2015.01.013 – volume: 30 start-page: 358 year: 2000 ident: ref10 article-title: Dynamic fuzzy neural networks-A novel approach to function approximation publication-title: IEEE Trans Syst Man Cybern B Cybern doi: 10.1109/3477.836384 – ident: ref12 doi: 10.1109/TFUZZ.2014.2374194 – ident: ref85 doi: 10.1016/j.ins.2012.02.031 – ident: ref16 doi: 10.1109/TFUZZ.2008.925907 – ident: ref18 doi: 10.1109/91.995117 – ident: ref48 doi: 10.1109/TFUZZ.2006.889954 – ident: ref93 doi: 10.1109/TFUZZ.2008.924340 – ident: ref73 doi: 10.1109/CEC.2005.1554689 – ident: ref77 doi: 10.1023/A:1008202821328 – ident: ref101 doi: 10.3390/polym3031377 – start-page: 1 year: 2007 ident: ref38 article-title: Multiobjective genetic fuzzy systems: Review and future research directions publication-title: Proc IEEE Int Fuzzy Syst Conf – ident: ref35 doi: 10.1109/TFUZZ.2006.882472 – ident: ref82 doi: 10.1007/s005000100144 – volume: 3 start-page: 47 year: 1994 ident: ref71 article-title: The evolution of evolvability in genetic programming publication-title: Advances in Genetic Programming – ident: ref62 doi: 10.1007/s11721-007-0002-0 – ident: ref51 doi: 10.1109/TFUZZ.2011.2173582 – ident: ref13 doi: 10.1016/j.ins.2012.04.003 – ident: ref54 doi: 10.1109/TEVC.2008.927706 – ident: ref36 doi: 10.1162/evco.1997.5.2.123 – ident: ref39 doi: 10.1016/S0165-0114(96)00098-X – ident: ref24 doi: 10.1109/TFUZZ.2015.2403793 – ident: ref21 doi: 10.1109/TIE.2013.2248332 – ident: ref74 doi: 10.1007/978-3-642-01527-4_3 – ident: ref66 doi: 10.1002/0471221546 – ident: ref28 doi: 10.1016/S0020-0255(01)00140-2 – ident: ref19 doi: 10.1109/TNN.2011.2167720 – ident: ref83 doi: 10.1016/0165-0114(95)00322-3 – year: 1982 ident: ref6 article-title: Intelligent behavior as an adaptation to the task environment – ident: ref69 doi: 10.4064/fm-3-1-133-181 – ident: ref89 doi: 10.1109/TFUZZ.2003.822681 – volume: 1917 start-page: 849 year: 2000 ident: ref58 article-title: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II publication-title: Parallel Problem Solving from Nature - PPSN V Lecture Notes in Computer Science doi: 10.1007/3-540-45356-3_83 – ident: ref20 doi: 10.1109/TFUZZ.2013.2255613 – ident: ref57 doi: 10.1007/978-3-540-31880-4_52 – ident: ref50 doi: 10.1007/s00500-010-0665-0 – volume: 97 year: 2005 ident: ref64 publication-title: Practical Mathematical Optimization An Introduction to Basic Optimization Theory and Classical and New Gradient-Based Algorithms – year: 1976 ident: ref96 publication-title: Time Series Analysis Forecasting and Control – ident: ref61 doi: 10.1007/s10898-007-9149-x – ident: ref23 doi: 10.1109/TFUZZ.2013.2279554 – ident: ref22 doi: 10.1109/TNNLS.2013.2284603 – ident: ref4 doi: 10.1109/91.811231 – ident: ref92 doi: 10.1109/TFUZZ.2004.836085 – ident: ref31 doi: 10.1002/int.10036 – ident: ref52 doi: 10.1109/TFUZZ.2012.2201338 – ident: ref9 doi: 10.1109/21.256541 – ident: ref75 doi: 10.1155/2013/193196 – ident: ref32 doi: 10.1109/TFUZZ.2004.840096 – ident: ref33 doi: 10.1016/j.ijar.2008.11.004 – ident: ref17 doi: 10.1109/TFUZZ.2012.2230179 – ident: ref11 doi: 10.1109/TFUZZ.2008.2012033 – ident: ref55 doi: 10.1109/TFUZZ.2012.2227488 – ident: ref37 doi: 10.1109/TFUZZ.2013.2291568 – ident: ref1 doi: 10.1109/TSMC.1985.6313399 – ident: ref94 doi: 10.1109/TFUZZ.2007.902038 – ident: ref47 doi: 10.1016/j.fss.2004.07.013 – ident: ref3 doi: 10.1016/0020-0255(75)90036-5 – ident: ref98 doi: 10.2147/IJN.S71847
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SubjectTerms	Approximation Artificial neural networks Clustering methods Complexity theory differential evolution (DE) feature selection Fuzzy logic Heuristic algorithms hierarchical fuzzy inference system (HFIS) multiobjective genetic programming (MOGP) Optimization Tuning
Title	Multiobjective Programming for Type-2 Hierarchical Fuzzy Inference Trees
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