Abstract
This chapter explains evolutionary multiobjective design of fuzzy rule-based systems in comparison with single-objective design. Evolutionary algorithms have been used in many studies on fuzzy system design for rule generation, rule selection, input selection, fuzzy partition, and membership function tuning. Those studies are referred to as genetic fuzzy systems because genetic algorithms have been mainly used as evolutionary algorithms. In many studies on genetic fuzzy systems, the accuracy of fuzzy rule-based systems is maximized. However, accuracy maximization often leads to the deterioration in the interpretability of fuzzy rule-based systems due to the increase in their complexity. Thus, multiobjective genetic algorithms were used in some studies to maximize not only the accuracy of fuzzy rule-based systems but also their interpretability. Those studies, which can be viewed as a subset of genetic fuzzy system studies, are referred to as multiobjective genetic fuzzy systems (GlossaryTerm
MoGFS
). A number of fuzzy rule-based systems with different complexities are obtained along the interpretability–accuracy tradeoff curve. One extreme of the tradeoff curve is a simple highly interpretable fuzzy rule-based system with low accuracy while the other extreme is a complicated highly accurate one with low interpretability. In GlossaryTermMoGFS
, multiple accuracy measures such as a true positive rate and a true negative rate can be simultaneously used as separate objectives. Multiple interpretability measures can also be simultaneously used in GlossaryTermMoGFS
.Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Abbreviations
- ACO:
-
ant colony optimization
- EMO:
-
evolutionary multiobjective optimization
- MOEA/D:
-
multiobjective evolutionary algorithm based on decomposition
- MoGFS:
-
multiobjective genetic fuzzy system
- NSGA:
-
nondominated sorting genetic algorithm
- PSO:
-
particle swarm optimization
- SMS-EMOA:
-
S-metric selection evolutionary multiobjective algorithm
- SPEA:
-
strength Pareto evolutionary algorithm
References
C.C. Lee: Fuzzy logic in control systems: Fuzzy logic controller – Part I, IEEE Trans. Syst. Man Cybern. 20(2), 404–418 (1990)
C.C. Lee: Fuzzy logic in control systems: Fuzzy logic controller – Part II, IEEE Trans. Syst. Man Cybern. 20(2), 419–435 (1990)
J.M. Mendel: Fuzzy logic systems for engineering: A tutorial, Proc. IEEE 83(3), 345–377 (1995)
L.A. Zadeh: The concept of a linguistic variable and its application to approximate reasoning – I, Inf. Sci. 8(3), 199–249 (1975)
L.A. Zadeh: The concept of a linguistic variable and its application to approximate reasoning – II, Inf. Sci. 8(4), 301–357 (1975)
L.A. Zadeh: The concept of a linguistic variable and its application to approximate reasoning – III, Inf. Sci. 9(1), 43–80 (1975)
B. Kosko: Fuzzy systems as universal approximators, Proc. 1992 IEEE Int. Conf. Fuzzy Syst. (IEEE, San Diego 1992) pp. 1153–1162
L.X. Wang: Fuzzy systems are universal approximators, Proc. 1992 IEEE Int. Conf. Fuzzy Syst. (IEEE, San Diego 1992) pp. 1163–1170
L.X. Wang, J.M. Mendel: Fuzzy basis functions, universal approximation, and orthogonal least-squares learning, IEEE Trans. Neural Netw. 3(5), 807–814 (1992)
K. Funahashi: On the approximate realization of continuous mappings by neural networks, Neural Netw. 2(3), 183–192 (1989)
K. Hornik, M. Stinchcombe, H. White: Multilayer feedforward networks are universal approximators, Neural Netw. 2(5), 359–366 (1989)
J. Park, I.W. Sandberg: Universal approximation using radial-basis-function networks, Neural Comput. 3(2), 246–257 (1991)
H. Ishibuchi, K. Nozaki, N. Yamamoto, H. Tanaka: Construction of fuzzy classification systems with rectangular fuzzy rules using genetic algorithms, Fuzzy Sets Syst. 65(2/3), 237–253 (1994)
H. Ishibuchi, K. Nozaki, N. Yamamoto, H. Tanaka: Selecting fuzzy if-then rules for classification problems using genetic algorithms, IEEE Trans. Fuzzy Syst. 3(3), 260–270 (1995)
H. Ishibuchi, T. Murata, I.B. Türkşen: Single-objective and two-objective genetic algorithms for selecting linguistic rules for pattern classification problems, Fuzzy Sets Syst. 89(2), 135–150 (1997)
H. Ishibuchi: Multiobjective genetic fuzzy systems: Review and future research directions, Proc. 2007 IEEE Int. Conf. Fuzzy Syst. (IEEE, London 2007) pp. 913–918
H. Ishibuchi, Y. Nojima, I. Kuwajima: Evolutionary multiobjective design of fuzzy rule-based classifiers. In: Computational Intelligence: A Compendium, ed. by J. Fulcher, L.C. Jain (Springer, Berlin 2008) pp. 641–685
H. Ishibuchi, Y. Nojima: Multiobjective genetic Fuzzy Systems. In: Computational Intelligence: Collaboration, Fusion and Emergence, ed. by C.L. Mumford, L.C. Jain (Springer, Berlin 2009) pp. 131–173
M. Fazzolari, R. Alcalá, Y. Nojima, H. Ishibuchi, F. Herrera: A review of the application of multiobjective evolutionary fuzzy systems: Current status and further directions, IEEE Trans. Fuzzy Syst. 21(1), 45–65 (2013)
K. Deb: Multi-Objective Optimization Using Evolutionary Algorithms (Wiley, Chichester 2001)
K.C. Tan, E.F. Khor, T.H. Lee: Multiobjective Evolutionary Algorithms and Applications (Springer, Berlin 2005)
C.A.C. Coello, G.B. Lamont: Applications of Multi-Objective Evolutionary Algorithms (World Scientific, Singapore 2004)
E.H. Mamdani, S. Assilian: An experiment in linguistic synthesis with a fuzzy logic controller, Int. J. Man-Mach. Stud. 7(1), 1–13 (1975)
E.H. Mamdani: Application of fuzzy logic to approximate reasoning using linguistic synthesis, IEEE Trans. Comput. C-26(12), 1182–1191 (1977)
L.X. Wang, J.M. Mendel: Generating fuzzy rules by learning from examples, IEEE Trans. Syst. Man Cybern. 22(6), 1414–1427 (1992)
T. Takagi, M. Sugeno: Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Syst. Man Cybern. 15(1), 116–132 (1985)
C.T. Lin, C.S.G. Lee: Neural-network-based fuzzy logic control and decision system, IEEE Trans. Comput. 40(12), 1320–1336 (1991)
S. Horikawa, T. Furuhashi, Y. Uchikawa: On fuzzy modeling using fuzzy neural networks with the back-propagation algorithm, IEEE Trans. Neural Netw. 3(5), 801–806 (1992)
J.S.R. Jang: ANFIS: Adaptive-network-based fuzzy inference system, IEEE Trans. Syst. Man Cybern. 23(3), 665–685 (1993)
O. Cordón, M.J. del Jesus, F. Herrera: A proposal on reasoning methods in fuzzy rule-based classification systems, Int. J. Approx. Reason. 20(1), 21–45 (1999)
L.I. Kuncheva: How good are fuzzy If-then classifiers?, IEEE Trans. Syst. Man Cybern. B 30(4), 501–509 (2000)
L.I. Kuncheva: Fuzzy Classifier Design (Physica, Heidelberg 2000)
H. Ishibuchi, K. Nozaki, H. Tanaka: Distributed representation of fuzzy rules and its application to pattern classification, Fuzzy Sets Syst. 52(1), 21–32 (1992)
H. Ishibuchi, T. Nakashima, M. Nii: Classification and Modeling with Linguistic Information Granules: Advanced Approaches to Linguistic Data Mining (Springer, Berlin 2004)
D. Nauck, R. Kruse: How the learning of rule weights affects the interpretability of fuzzy systems, Proc. IEEE Int. Conf. Fuzzy Syst. (IEEE, Anchorage 1998) pp. 1235–1240
H. Ishibuchi, T. Nakashima: Effect of rule weights in fuzzy rule-based classification systems, IEEE Trans. Fuzzy Syst. 9(4), 506–515 (2001)
H. Ishibuchi, T. Nakashima, T. Morisawa: Voting in fuzzy rule-based systems for pattern classification problems, Fuzzy Sets Syst. 103(2), 223–238 (1999)
O. Cordón, F. Herrera: A three-stage evolutionary process for learning descriptive and approximate fuzzy-logic-controller knowledge bases from examples, Int. J. Approx. Reason. 17(4), 369–407 (1997)
J.G. Marin-Blázquez, Q. Shen: From approximative to descriptive fuzzy classifiers, IEEE Trans. Fuzzy Syst. 10(4), 484–497 (2002)
P.K. Simpson: Fuzzy min-max neural networks – Part 1: Classification, IEEE Trans. Neural Netw. 3(5), 776–786 (1992)
S. Abe, M.S. Lan: A method for fuzzy rules extraction directly from numerical data and its application to pattern classification, IEEE Trans. Fuzzy Syst. 3(1), 18–28 (1995)
S. Abe, R. Thawonmas: A fuzzy classifier with ellipsoidal regions, IEEE Trans. Fuzzy Syst. 5(3), 358–368 (1997)
D. Nauck, F. Klawonn, R. Kruse: Foundations of Neuro-Fuzzy Systems (Wiley, New York 1997)
S. Abe: Pattern Classification: Neuro-Fuzzy Methods and Their Comparison (Springer, Berlin 2001)
O. Cordón, F. Herrera, F. Hoffmann, L. Magdalena: Genetic Fuzzy Systems (World Scientific, Singapore 2001)
O. Cordón, F. Gomide, F. Herrera, F. Hoffmann, L. Magdalena: Ten years of genetic fuzzy systems: Current framework and new trends, Fuzzy Sets Syst. 141(1), 5–31 (2004)
F. Herrera: Genetic fuzzy systems: Status, critical considerations and future directions, Int. J. Comput. Intell. Res. 1(1), 59–67 (2005)
F. Herrera: Genetic fuzzy systems: Taxonomy, current research trends and prospects, Evol. Intell. 1(1), 27–46 (2008)
K. Shimojima, T. Fukuda, Y. Hasegawa: Self-tuning fuzzy modeling with adaptive membership function, rules, and hierarchical structure based on genetic algorithm, Fuzzy Sets Syst. 71(3), 295–309 (1995)
H. Ishibuchi, T. Nakashima, T. Murata: Performance evaluation of fuzzy classifier systems for multidimensional pattern classification problems, IEEE Trans. Syst. Man Cybern. B 29(5), 601–618 (1999)
H. Ishibuchi, T. Yamamoto, T. Nakashima: Hybridization of fuzzy GBML approaches for pattern classification problems, IEEE Trans. Syst. Man Cybern. B 35(2), 359–365 (2005)
H. Ishibuchi, T. Nakashima, T. Murata: Three-objective genetics-based machine learning for linguistic rule extraction, Inf. Sci. 136(1–4), 109–133 (2001)
H. Ishibuchi, Y. Nojima: Analysis of interpretability-accuracy tradeoff of fuzzy systems by multiobjective fuzzy genetics-based machine learning, Int. J. Approx. Reason. 44(1), 4–31 (2007)
J.C. Dunn: A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters, J. Cybern. 3(3), 32–57 (1973)
J.C. Bezdek: Pattern Recognition with Fuzzy Objective Function Algorithms (Plenum Press, New York 1981)
J.C. Bezdek, R. Ehrlich, W. Full: FCM: The fuzzy c-means clustering algorithm, Comput. Geosci. 10(2/3), 191–203 (1984)
S.L. Chiu: Fuzzy model identification based on cluster estimation, J. Intell. Fuzzy Syst. 2(3), 267–278 (1994)
J.A. Dickerson, B. Kosko: Fuzzy function approximation with ellipsoidal rules, IEEE Trans. Syst. Man Cybern. 26(4), 542–560 (1996)
C.J. Lin, C.T. Lin: An ART-based fuzzy adaptive learning control network, IEEE Trans. Fuzzy Syst. 5(4), 477–496 (1997)
M. Delgado, A.F. Gomez-Skarmeta, F. Martin: A fuzzy clustering-based rapid prototyping for fuzzy rule-based modeling, IEEE Trans. Fuzzy Syst. 5(2), 223–233 (1997)
M. Setnes: Supervised fuzzy clustering for rule extraction, IEEE Trans. Fuzzy Syst. 8(4), 416–424 (2000)
M. Setnes, R. Babuska, H.B. Verbruggen: Rule-based modeling: Precision and transparency, IEEE Trans. Syst. Man Cybern. C 28(1), 165–169 (1998)
M. Setnes, R. Babuska, U. Kaymak, H.R. van Nauta Lemke: Similarity measures in fuzzy rule base simplification, IEEE Trans. Syst. Man Cybern. B 28(3), 376–386 (1998)
Y. Jin, W. von Seelen, B. Sendhoff: On generating FC3 fuzzy rule systems from data using evolution strategies, IEEE Trans. Syst. Man Cybern. B 29(6), 829–845 (1999)
M. Setnes, H. Roubos: GA-fuzzy modeling and classification: Complexity and performance, IEEE Trans. Fuzzy Syst. 8(5), 509–522 (2000)
H. Roubos, M. Setnes: Compact and transparent fuzzy models and classifiers through iterative complexity reduction, IEEE Trans. Fuzzy Syst. 9(4), 516–524 (2001)
J. Abonyi, J.A. Roubos, F. Szeifert: Data-driven generation of compact, accurate, and linguistically sound fuzzy classifiers based on a decision-tree initialization, Int. J. Approx. Reason. 32(1), 1–21 (2003)
R. Alcalá, J. Alcalá-Fdez, F. Herrera, J. Otero: Genetic learning of accurate and compact fuzzy rule based systems based on the 2-tuples linguistic representation, Int. J. Approx. Reason. 44(1), 45–64 (2007)
K. Miettinen: Nonlinear Multiobjective Optimization (Kluwer, Boston 1999)
K. Deb, A. Pratap, S. Agarwal, T. Meyarivan: A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)
E. Zitzler, L. Thiele: Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach, IEEE Trans. Evol. Comput. 3(4), 257–271 (1999)
Q. Zhang, H. Li: MOEA/D: A multiobjective evolutionary algorithm based on decomposition, IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)
N. Beume, B. Naujoks, M. Emmerich: SMS-EMOA: Multiobjective selection based on dominated hypervolume, Eur. J. Oper. Res. 181(3), 1653–1669 (2007)
P. Stewart, D.A. Stone, P.J. Fleming: Design of robust fuzzy-logic control systems by multi-objective evolutionary methods with hardware in the loop, Eng. Appl. Artif. Intell. 17(3), 275–284 (2004)
L.H. Chen, C.H. Chiang: An intelligent control system with a multi-objective self-exploration process, Fuzzy Sets Syst. 143(2), 275–294 (2004)
P. Ducange, B. Lazzerini, F. Marcelloni: Multi-objective genetic fuzzy classifiers for imbalanced and cost-sensitive datasets, Soft Comput. 14(7), 713–728 (2010)
C. Setzkorn, R.C. Paton: On the use of multi-objective evolutionary algorithms for the induction of fuzzy classification rule systems, BioSystems 81(2), 101–112 (2005)
H. Wang, S. Kwong, Y. Jin, W. Wei, K.F. Man: Agent-based evolutionary approach for interpretable rule-based knowledge extraction, IEEE Trans. Syst. Man Cybern. C 35(2), 143–155 (2005)
C.H. Tsang, S. Kwong, H.L. Wang: Genetic-fuzzy rule mining approach and evaluation of feature selection techniques for anomaly intrusion detection, Pattern Recognit. 40(9), 2373–2391 (2007)
H. Wang, S. Kwong, Y. Jin, W. Wei, K.F. Man: Multi-objective hierarchical genetic algorithm for interpretable fuzzy rule-based knowledge extraction, Fuzzy Sets Syst. 149(1), 149–186 (2005)
Z.Y. Xing, Y. Zhang, Y.L. Hou, L.M. Jia: On generating fuzzy systems based on Pareto multi-objective cooperative coevolutionary algorithm, Int. J. Control Autom. Syst. 5(4), 444–455 (2007)
J. Casillas, O. Cordón, F. Herrera, L. Magdalena (Eds.): Interpretability Issues in Fuzzy Modeling (Springer, Berlin 2003)
J.M. Alonso, L. Magdalena, G. González-Rodríguez: Looking for a good fuzzy system interpretability index: An experimental approach, Int. J. Approx. Reason. 51(1), 115–134 (2009)
H. Ishibuchi, Y. Kaisho, Y. Nojima: Design of linguistically interpretable fuzzy rule-based classifiers: A short review and open questions, J. Mult.-Valued Log. Soft Comput. 17(2/3), 101–134 (2011)
J.M. Alonso, L. Magdalena: Editorial: Special issue on interpretable fuzzy systems, Inf. Sci. 181(20), 4331–4339 (2011)
M.J. Gacto, R. Alcalá, F. Herrera: Interpretability of linguistic fuzzyrule-based systems: An overview of interpretability measures, Inf. Sci. 181(20), 4340–4360 (2011)
C. Mencar, C. Castiello, R. Cannone, A.M. Fanelli: Interpretability assessment of fuzzy knowledge bases: A cointension based approach, Int. J. Approx. Reason. 52(4), 501–518 (2011)
O. Cordón: A historical review of evolutionary learning methods for Mamdani-type fuzzy rule-based systems: Designing interpretable genetic fuzzy systems, Int. J. Approx. Reason. 52(6), 894–913 (2011)
H. Ishibuchi, Y. Nojima: Toward quantitative definition of explanation ability of fuzzy rule-based classifiers, Proc. 2011 IEEE Int. Conf. Fuzzy Syst. (IEEE, Taipei 2011) pp. 549–556
M. Antonelli, P. Ducange, B. Lazzerini, F. Marcelloni: Learning concurrently partition granularities and rule bases of Mamdani fuzzy systems in a multi-objective evolutionary framework, Int. J. Approx. Reason. 50(7), 1066–1080 (2009)
A. Botta, B. Lazzerini, F. Marcelloni, D.C. Stefanescu: Context adaptation of fuzzy systems through a multi-objective evolutionary approach based on a novel interpretability index, Soft Comput. 13(5), 437–449 (2009)
M.J. Gacto, R. Alcalá, F. Herrera: Integration of an index to preserve the semantic interpretability in the multiobjective evolutionary rule selection and tuning of linguistic fuzzy systems, IEEE Trans. Fuzzy Syst. 18(3), 515–531 (2010)
Y. Zhang, X.B. Wu, Z.Y. Xing, W.L. Hu: On generating interpretable and precise fuzzy systems based on Pareto multi-objective cooperative co-evolutionary algorithm, Appl. Soft Comput. 11(1), 1284–1294 (2011)
R. Alcalá, Y. Nojima, F. Herrera, H. Ishibuchi: Multiobjective genetic fuzzy rule selection of single granularity-based fuzzy classification rules and its interaction with the lateral tuning of membership functions, Soft Comput. 15(12), 2303–2318 (2011)
C.A.C. Coello, G.T. Pulido, M.S. Lechuga: Handling multiple objectives with particle swarm optimization, IEEE Trans. Evol. Comput. 8(3), 256–279 (2004)
D. Liu, K.C. Tan, C.K. Goh, W.K. Ho: A multiobjective memetic algorithm based on particle swarm optimization, IEEE Trans. Syst. Man Cybern. B 37(1), 42–50 (2007)
Y. Wang, Y. Yang: Particle swarm optimization with preference order ranking for multi-objective optimization, Inf. Sci. 179(12), 1944–1959 (2009)
A. Elhossini, S. Areibi, R. Dony: Strength Pareto particle swarm optimization and hybrid EA-PSO for multi-objective optimization, Evol. Comput. 18(1), 127–156 (2010)
C.K. Goh, K.C. Tan, D.S. Liu, S.C. Chiam: A competitive and cooperative co-evolutionary approach to multi-objective particle swarm optimization algorithm design, Eur. J. Oper. Res. 202(1), 42–54 (2010)
A.R.M. Rao, K. Sivasubramanian: Multi-objective optimal design of fuzzy logic controller using a self configurable swarm intelligence algorithm, Comput. Struct. 86(23/24), 2141–2154 (2008)
M. Marinaki, Y. Marinakis, G.E. Stavroulakis: Fuzzy control optimized by a multi-objective particle swarm optimization algorithm for vibration suppression of smart structures, Struct. Multidiscip. Optim. 43(1), 29–42 (2011)
C.N. Nyirenda, D.S. Dawoud, F. Dong, M. Negnevitsky, K. Hirota: A fuzzy multiobjective particle swarm optimized TS fuzzy logic congestion controller for wireless local area networks, J. Adv. Comput. Intell. Intell. Inf. 15(1), 41–54 (2011)
Q. Zhang, M. Mahfouf: A hierarchical Mamdani-type fuzzy modelling approach with new training data selection and multi-objective optimisation mechanisms: A special application for the prediction of mechanical properties of alloy steels, Appl. Soft Comput. 11(2), 2419–2443 (2011)
B.J. Park, J.N. Choi, W.D. Kim, S.K. Oh: Analytic design of information granulation-based fuzzy radial basis function neural networks with the aid of multiobjective particle swarm optimization, Int. J. Intell. Comput. Cybern. 5(1), 4–35 (2012)
H. Ishibuchi, N. Tsukamoto, Y. Nojima: Evolutionary many-objective optimization: A short review, Proc. 2008 IEEE Congr. Evol. Comput. (IEEE, Hong Kong 2008) pp. 2424–2431
H. Ishibuchi, N. Akedo, H. Ohyanagi, Y. Nojima: Behavior of EMO algorithms on many-objective optimization problems with correlated objectives, Proc. 2011 IEEE Congr. Evol. Comput. (IEEE, New Orleans 2011), pp. 1465–1472
O. Schutze, A. Lara, C.A.C. Coello: On the influence of the number of objectives on the hardness of a multiobjective optimization problem, IEEE Trans. Evol. Comput. 15(4), 444–455 (2011)
C.F. Juang, C.M. Lu, C. Lo, C.Y. Wang: Ant colony optimization algorithm for fuzzy controller design and its FPGA implementation, IEEE Trans. Ind. Electron. 55(3), 1453–1462 (2008)
C.F. Juang, C.Y. Wang: A self-generating fuzzy system with ant and particle swarm cooperative optimization, Expert Syst. Appl. 36(3), 5362–5370 (2009)
C.F. Juang, P.H. Chang: Designing fuzzy-rule-based systems using continuous ant-colony optimization, IEEE Trans. Fuzzy Syst. 18(1), 138–149 (2010)
C.F. Juang, P.H. Chang: Recurrent fuzzy system design using elite-guided continuous ant colony optimization, Appl. Soft Comput. 11(2), 2687–2697 (2011)
G.M. Fathi, A.M. Saniee: A fuzzy classification system based on ant colony optimization for diabetes disease diagnosis, Expert Syst. Appl. 38(12), 14650–14659 (2011)
S. Wang, M. Mahfouf: Multi-objective optimisation for fuzzy modelling using interval type-2 fuzzy sets, Proc. 2012 IEEE Int. Conf. Fuzzy Syst. (IEEE, Brisbane 2012) pp. 722–729
O. Castillo, P. Melin, A.A. Garza, O. Montiel, R. Sepúlveda: Optimization of interval type-2 fuzzy logic controllers using evolutionary algorithms, Soft Comput. 15(6), 1145–1160 (2011)
O. Castillo, P. Melin: A review on the design and optimization of interval type-2 fuzzy controllers, Appl. Soft Comput. 12(4), 1267–1278 (2012)
O. Castillo, R. Martínez-Marroquín, P. Melin, F. Valdez, J. Soria: Comparative study of bio-inspired algorithms applied to the optimization of type-1 and type-2 fuzzy controllers for an autonomous mobile robot, Inf. Sci. 192(1), 19–38 (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Ishibuchi, H., Nojima, Y. (2015). Multiobjective Genetic Fuzzy Systems. In: Kacprzyk, J., Pedrycz, W. (eds) Springer Handbook of Computational Intelligence. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43505-2_77
Download citation
DOI: https://doi.org/10.1007/978-3-662-43505-2_77
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-43504-5
Online ISBN: 978-3-662-43505-2
eBook Packages: EngineeringEngineering (R0)