Skip to main content
SpringerLink
Log in

Interpretability Issues in Evolutionary Multi-Objective Fuzzy Knowledge Base Systems

  • Conference paper
  • First Online:
Proceedings of Seventh International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA 2012)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 201))

Abstract

Interpretability and accuracy are two conflicting features of any Fuzzy Knowledge Based System during its design and implementation, this conflicting nature leads to Interpretability-Accuracy Trade-Off. Secondly, the assessment of interpretability is another important problem for researchers. Several indexes and methods have been proposed for assessing interpretability but this issue remains an open problem because of its subjective nature. This paper discusses two research issues, interpretability assessment and interpretability-accuracy trade-off in Fuzzy Knowledge Base System design using Evolutionary Multiobjective Optimization by proposing taxonomy for studying and evaluating the interpretability.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  • Alcala, R., Alcala-Fdez, J., Cassilas, J., Cordon, O., Herrera, F.: Hybrid learning models to get interpretability-accuracy trade-off in fuzzy modeling. Soft Computing. 10, 717-734 (2006).

    Google Scholar 

  • Cassilas, J., Cordon, O., Herrera, F., (Eds.): Interpretability Improvements in Linguistic Fuzzy Modeling. Heidelberg, Germany, Springer, (2003).

    Google Scholar 

  • Alonso, J. M., Magdalena, L.: Special issue on interpretable fuzzy systems. Information Sciences. 181, 4331-4339 (2011).

    Google Scholar 

  • Cassilas, J., Cordon, O., Herrera, F., Magdalena, L., (Eds.): Accuracy Improvements in Linguistic Fuzzy Modeling. Springer (2003).

    Google Scholar 

  • Alonso, J. M., Magdalena, L., Rodriguez, G. G.: Looking for a good fuzzy system interpretability index: an experimental approach. International Journal of Approximate Reasoning. 51, 115-134 (2009).

    Google Scholar 

  • Mencar, C., Fanelli, A. M.: Interpretability constraints for fuzzy information granulation. Information Sciences. 178, 4585-4618 (2008).

    Google Scholar 

  • Zhou, M., Gan, J. Q., Low level interpretability and high level interpretability: a unified view of data-driven interpretable fuzzy system modeling. Fuzzy Sets and Systems. 159 (23), 3091-3131 (2008).

    Google Scholar 

  • Gacto, M. J., Alcala, R., Herrera, F.: Interpretability of linguistic fuzzy rule-based systems: an overview of interpretability measures. Information Sciences. 181, 4340-4360 (2011).

    Google Scholar 

  • Cannone, R., Alonso, J. M., Magdalena, L.: An empirical study on interpretability indexes through Multiobjective evolutionary algorithms. WILF2011, LNAI 6857, 131-138 (2011).

    Google Scholar 

  • Botta, A., Lazzerini, B., Marcelloni, F., Stefanescu, D. C.: Context adaptation of fuzzy systems through a multi-objective evolutionary approach based on a novel interpretability index. Soft Computing. 13 (5), 437-449 (2008).

    Google Scholar 

  • Guillaume, S.: Designing fuzzy inference systems from data: an interpretability oriented review. IEEE Transactions of Fuzzy Systems. 9 (3), 426-443 (2001).

    Google Scholar 

  • Shukla, P.K., Tripathi, S. P., A review on the interpretability-accuracy trade –off in Evolutionary Multi-Objective Fuzzy Systems (EMOFS), Information, 3, 256-277 (2012).

    Google Scholar 

  • Deb, K., Multi-Objective Optimization Using Evolutionary Algorithms, John Wiley & Sons, Chichester (2001).

    Google Scholar 

  • Jin, Y.: Fuzzy modeling of high dimensional systems: complexity reduction and interpretability improvement. IEEE Transactions on Fuzzy Systems. 8(2), 212-221 (2000).

    Google Scholar 

  • Mencar, C., Castiello, C., Cannone, R., Fanelli, A. M.: Interpretability assessment of fuzzy knowledge bases: a cointension based approach. International Journal of Approximate Reasoning. 52, 501-518 (2011).

    Google Scholar 

  • Mikut, R., Jakel, J., Groll, L.: Interpretability issues in data-based learning of fuzzy systems. Fuzzy Sets and Systems. 150, 179-197 (2005).

    Google Scholar 

  • Coello, C. A., Van Veldhuizen D. A., Lamont, G. B.: Evolutionary Algorithms for solving multi-objective problems. Kluwer Academic publishers. Newyork (2002).

    Google Scholar 

  • Coello C.: Recent trends in evolutionary multi-objective optimization, in: A. Abraham, L, Jain, R. Goldberg (Eds.), Evolutionary Multi-objective optimization: Theoretical Advances and Applications (Springer-Verlag, London 2005). 7-32 (2005).

    Google Scholar 

  • Coello, C., Toscano, G., Mezura, E.: Current and future research trends in evolutionary multi-objective optimization, in: M. Grana, R. Duro, A. d’ Anjou, P. P. Wang (Eds.) Information processing and Evolutionary Algorithms: From Industrial Applications to Academic Speculations (Spring-Verlag, London, 2005) 213-231 (2005).

    Google Scholar 

  • Coello, C.: Evolutionary multiobjective optimization: a historical view of the field. IEEE computational Intelligence Magazine. 1:1, 28-36 (2006).

    Google Scholar 

  • Goldberg, D.E.: Genetic algorithms in search optimization and machine learning, Addison Wesley Publishing Company Reading Massachusetts (1989).

    Google Scholar 

  • Schwefel, H.-P.: Evolution and optimization seeking. John Wiley & Sons. Newyork, (1995).

    Google Scholar 

  • Koza, J. R: Genetic Programming. On the programming of computers by means of natural selection. The MIT Press, Cambridge, Massachusetts (1992).

    Google Scholar 

  • Fogel, L. J.: Artificial Intelligence through simulated evolution, John Wiley, New York (1966).

    Google Scholar 

  • Erickson, M., Mayer, A., Horn, J.: The Niched Pareto Genetic Algorithms applied to the design of ground water remediation system. Ist International Conference on Evolutionary Multi Criteria Optimization. 681-695, Springer-Verlag, LNCS No. 1993 (2001).

    Google Scholar 

  • Corne, D. W., Knowles, J. D., Oates, M. J.: The pareto envelop based selection algorithm for multi-objective optimization. In Proc: VI Conference of Parallel Problem Solving from Nature. Paris, France, Springer LNCS 1917, 839-848 (2000).

    Google Scholar 

  • Coello, C. A. C., Pulido, G. T.: A microgenetic algorithm for Multiobjective optimization, In: proc. First International Conference on Evolutionary Multi-Criteria Optimization, pp. 126-140, LNCS 1993 (2001).

    Google Scholar 

  • Coello, C. A. C., Pulido, G. T.: Multi-objective optimization using a micro-genetic algorithm. In Proc.: Genetic and Evolutionary Computation Conference (GECCO’ 2001), Morgan Kaufmann Publishers. 274-282 (2001).

    Google Scholar 

  • Cordon, O., Herrera, F., del Jesus, M. J., Villar, P.: A Multi-objective genetic algorithm for feature selection and granularity learning in fuzzy rule based classification systems. In Proc:. of 9th IFSA World Congress 2001. 1253-1258 (2001).

    Google Scholar 

  • Ishibuchi, H., Nojima, Y.: Accuracy-complexity trade-off algorithms by Multi-objective rule selection, In Proc:.2005 Workshop on Computational Intelligence in Data Mining, 39-48 (2005).

    Google Scholar 

  • Alcala. R., Gacto, M. J., Herrera, F.: A Multi-objective genetic algorithm for tuning and Rule selection to obtain accurate and compact linguistic fuzzy rule-based systems. International Journal of Uncertainty, Fussiness and Knowledge Based Systems. 15(5), 539-557 (2007).

    Google Scholar 

  • Alcala. R., A-Fdez, J., Gacto, M. J., Herrera, F., A Multi-objective evolutionary algorithm for rule-selection and tuning on Fuzzy rule based systems. In Proc.: of FUZZ-IEEE 2007, 1367-1372 (2007).

    Google Scholar 

  • Gacto, M. J., Alcala, R., Herrera, F.: An improved multi-objective genetic algorithm for tuning linguistic fuzzy systems. In Proc.: of IPMU’08, 1121-1128 (2008).

    Google Scholar 

  • Alcala, R., Alcala-Fdez, J., Gacto, M. J,. Herrera, F.: On the usefulness of MOEAs for getting compact FRBSs under parameter tuning and rule selection. Studies in Computational Intelligence (SCI). vol. 98, 91-107 (2008).

    Google Scholar 

  • Alcala, R., Ducange, P., Herrera, F., Lazzerini, B., Marcelloni, F.: A Multi-objective evolutionary approach to concurrently learn rule and databases of linguistic fuzzy rule based systems. IEEE Transactions on Fuzzy Systems. 17(5), 1106-1121 (2009).

    Google Scholar 

  • Antonelli, M., Ducange, P., Lazzerini, B., Marcelloni, F.: Learning concurrently partition granularities and rule bases of Mamdani fuzzy systems in a multi-objective evolutionary framework. International Journal of Approximate Reasoning. 50, 1066-1080 (2009).

    Google Scholar 

  • Gacto, M. J., Alcala, R., Herrera, F.: Multi-objective genetic fuzzy systems: on the necessity of including expert knowledge in the MOEA design process. In Proc.: IPMU 2008, 1446-1453 (2008).

    Google Scholar 

  • Gacto, M. J., Alcala, R., Herrera, F.: Adaptation and application of multi-objective evolutionary algorithms for rule reduction and parameter tuning of fuzzy rule based systems. Soft Computing. 13, 419-436 (2009).

    Google Scholar 

  • Di Nuovo, A. G., Catania, V.: Linguistic modifiers to improve the accuracy –interpretability trade-off in multi-objective genetic design of fuzzy rule based classifier systems, 2009 9th International Conference on Intelligent Systems Design and Applications, 128-133 (2009).

    Google Scholar 

  • Alcala, R., Nojima, Y., Herrera, F., Ishibuchi, H.: Multi-objective genetic fuzzy rule selection of single granularity –based fuzzy classification rules and its interaction with lateral tuning of membership functions. Soft Computing. 15(12), 2303-2318 (2011).

    Google Scholar 

  • Antonelli, M., Ducange, P., Lazzerini, B., Marcelloni, F.: Multi-objective Evolutionary Generation of Mamdani Fuzzy Rule Based Systems based on rule and condition selection, In Proc:. 5th IEEE International Workshop on Genetic and Evolutionary Fuzzy Systems 2011, 47-53 (2011).

    Google Scholar 

  • Cococcioni, M., Ducange, P., Lazzerini, B., Marcelloni, F.: A Pareto based multi-objective evolutionary approach to the identification of Mamdani fuzzy systems. Soft Computing. 11, 1013-1031 (2007).

    Google Scholar 

  • Ishibuchi, H., Nakashima, Y., Nojima, Y.: Effects of fine fuzzy partitions on the generalization ability of evolutionary multi-objective fuzzy rule based classifiers, In Proc:. of FUZZ-IEEE, 1-8 (2010).

    Google Scholar 

  • Ishibuchi, H., Nakashima, T., Murata, T.: Three-objectives genetics-based machine learning for linguistic rule extraction. Information Sciences. 136, 109-133 (2001).

    Google Scholar 

  • Ishibuchi, H., Yamamoto, T.: Fuzzy rule selection by multi-objective genetic local search algorithms and rule evaluation measures in data mining. Fuzzy Sets and Systems. 141, 59-88 (2004).

    Google Scholar 

  • Zhang, Y., Wu, X.-Bei, Xiang, Z.-Yi, Hu, W.-Li: On Generating Interpretable and Precise Fuzzy Systems based on Pareto Multi-objective Cooperating Co-evolutionary Algorithm. Applied Soft Computing. 11, 1289-1294 (2011).

    Google Scholar 

  • Ishibuchi, H., Nojima, Y.: Analysis of Interpretability- Accuracy Trade –Off of fuzzy systems by Multi-objective fuzzy genetics –based machine learning. International Journal of Approximate Reasoning. 44, 4-31 (2007).

    Google Scholar 

  • Antonelli, M., Ducange, P., Lazzrini, B., Mareclloni, F.: Multi-objective evolutionary learning of granularity, membership function parameters and rules of Mamdani fuzzy systems. Evolutionary Intelligence. 2, 21-37 (2009).

    Google Scholar 

  • Marquez, A. A., Marquez, F. A., Peregrin, A.: A mechanism to improve the interpretability of linguistic fuzzy systems with adaptive defuzzification based on the use of a multi-objective evolutionary algorithms. International Journal of Computational Intelligence Systems. 5(2), 297-321 (2012).

    Google Scholar 

  • Pulkkinen, P., Koivisto, H.: A dynamically constrained multiobjective genetic fuzzy systems for regression problems. IEEE Transactions on Fuzzy Systems, 18 (1), 161-167 (2010).

    Google Scholar 

  • Antonelli, M., Ducange, P., Lazzerini, B., Marcelloni, F.: Learning knowledge bases of multi-objective evolutionary fuzzy systems by simultaneously optimizing accuracy, complexity and partition integrity. Soft Computing. 15(12), 2335-2354 (2011).

    Google Scholar 

  • Antonelli, M., Ducange, P., Lazzerini, B.: A three- objective evolutionary approach to gene rate mamdani fuzzy rule based systems, E. Corchado et. al. (eds.): HAIS 2009, LNAI 5572, pp. 613-620 (2009).

    Google Scholar 

  • Gonzalez, M., Cassilas, J., Morell, C.: Dealing with three uncorrelated criteria by multi-objective genetic fuzzy systems. In Proc.: 5th International Workshop on Genetic and Evolutionary Fuzzy Systems 2011, pp. 39-46 (2011).

    Google Scholar 

  • Ishibuchi, H., Nojima, Y.: Fuzzy ensemble design thorough multi-objective fuzzy rule selection, Studies in Computational Intelligence (SCI). 16, 507-530 (2006).

    Google Scholar 

  • Ishibuchi, H., Nojima, Y.: Evolutionary Multi-objective optimization for the design of fuzzy rule based ensemble classifiers, International Journal of Hybrid Intelligent Systems, 3(3), 129-145 (2006).

    Google Scholar 

  • Branke, J., Deb, K.: Integrating user preferences into Evolutionary Multi-objective Optimization, J. Yaochu (eds.), Knowledge Incorporation in Evolutionary Computation, Springer, vol. 167 (2004).

    Google Scholar 

  • Nojima, Y., Ishibuchi, H.: Interactive fuzzy modeling by evolutionary Multi-objective optimization with user preferences, In Proc: IFSA-EUSFLAT 2009, pp. 1839-1844 (2009).

    Google Scholar 

  • Nojima, Y., Ishibuchi, H.: Incorporation of user preference into multi-objective genetic fuzzy rule selection for pattern classification problems. In Proc: 14th International Symposium on Artificial Life and Robotics 2009, pp. 186-189 (2009).

    Google Scholar 

  • Nojima, Y., Ishibuchi, H.: Interactive genetic fuzzy rule selection through evolutionary multi-objective optimization with user preference. In Proc: 2009 IEEE Symposium on Computational Intelligence in Multicriteria Decision-Making, pp. 141-148 (2009).

    Google Scholar 

  • Ishibuchi, H., Namba, S.: Evolutionary multi-objective knowledge extraction for high dimensional pattern classification problems, X. Yao et. al. (Eds.), PPSN VIII, LNCS, 3242, pp. 1123-1132 (2004).

    Google Scholar 

  • Antonelli, M., Ducange, P., Marcelloni, F.: A new approach to handle high dimensional and large data sets in multi-objective evolutionary fuzzy systems. In Proc.: FUZZ- IEEE 2011, 1286-1293 (2011).

    Google Scholar 

  • Cannone, R., Alonso, J. M., Magdalena, L.: Multi-objective design of highly interpretable fuzzy rule based classifiers with semantic co-intention, In Proc.: 5th International Workshop on Genetic and Evolutionary Fuzzy Systems 2011, 1-8 (2011).

    Google Scholar 

  • Botta, A., Lazzerini, B., Marcelloni, F., Stefanescu, D.C.: Context adaptation of fuzzy systems through a multi-objective evolutionary approach based on a novel interpretability index. Soft Computing. 13, 437-449 (2009).

    Google Scholar 

  • Moraga, C.: An essay on interpretability of fuzzy systems. Combining Experimentation and Theory. Studies in Fuzziness and Soft Computing. 271/2012, 61-72 (2012).

    Google Scholar 

  • Shukla, P. K., Tripathi, S. P.: A Survey on Interpretability-Accuracy (I-A) Trade-Off in Evolutionary Fuzzy Systems. 2011 Fifth International Conference on Genetic and Evolutionary Computation (ICGEC). Xiamen. 97-101 (2011).

    Google Scholar 

  • Gorzalczany, M. B., Rudziriski, F.: Accuracy vs. interpretability of fuzzy rule based classifiers: an evolutionary approach. Swarm and Evolutionary Computation. LNCS, 7296/2012, 222-230 (2012).

    Google Scholar 

  • G.-Hernandez, M., S.-Palmero, G. I., F.-Apricio, M. J.: Complexity reduction and interpretability improvement for fuzzy rule systems based on simple interpretability measures and indices by bi-objective evolutionary rule selection. Soft Computing. 16 (3), 451-470 (2012).

    Google Scholar 

  • Villar, P., Fernandez, A., Carrasco, R. A., Herrera, F., Feature selection and granularity learning in genetic fuzzy rule based classification systems for imbalanced data sets. International Journal of Uncertainty, Fuzziness and Knowledge Based Systems. 20 (3), 369-397 (2012).

    Google Scholar 

  • Alcalá, R., Alcalá-Fdez, J., Herrera, F.: A proposal for the genetic lateral tuning of linguistic fuzzy systems and its interaction with rule selection. IEEE Transactions on Fuzzy Systems. 15, 616–635 (2007).

    Google Scholar 

  • Alcalá, R., Alcalá-Fdez, J., Herrera, F., Otero, J., Genetic learning of accurate and compact fuzzy rule based systems based on the 2-tuples linguistic representation. International Journal of Approximate Reasoning. 44, 45–64 (2007).

    Google Scholar 

  • Alonso, J. M., Magdalena, L., Combining user’s preference and quality criteria into a new index for guiding the design of fuzzy systems with a good interpretability-accuracy trade-off, In Proc: IEEE World Congress on Computational Intelligence, 961–968 (2010).

    Google Scholar 

  • Alonso, J. M., Magdalena, L.: HILK ++: an interpretability-guided fuzzy modeling methodology for learning readable and comprehensible fuzzy rule-based classifiers, Soft Computing. 15 (10), 1959-1980 (2011).

    Google Scholar 

  • Casillas, J., Cordón, O., del Jesus, M. J., Herrera, F.: Genetic tuning of fuzzy rule deep structures preserving interpretability and its interaction with fuzzy rule set reduction. IEEE Transactions on Fuzzy Systems. 13, 13–29 (2005).

    Google Scholar 

  • Cordón, O., Herrera, F., Magdalena, L., Villar P.: A genetic learning process for the scaling factors granularity and contexts of the fuzzy rule-based system data base. Information Science. 136, 85–107 (2001).

    Google Scholar 

  • Furuhashi, T., Suzuki, T., On interpretability of fuzzy models based on conciseness measure, In Proc: IEEE International Conference on Fuzzy Systems (FUZZIEEE’01), 284–287 (2001).

    Google Scholar 

  • Gacto, M. J., Alcalá, R., Herrera, F.: Integration of an index to preserve the semantic interpretability in the multi-objective evolutionary rule selection and tuning of linguistic fuzzy systems. IEEE Transactions on Fuzzy Systems. 18, 515–531 (2010).

    Google Scholar 

  • Guillaume, S., Designing fuzzy inference systems from data: an interpretability-oriented review. IEEE Transactions on Fuzzy Systems. 9, 426–443 (2001).

    Google Scholar 

  • Guillaume, S., Charnomordic, B.: Generating an interpretable family of fuzzy partitions from data. IEEE Transactions on Fuzzy Systems. 12, 324–335 (2004).

    Google Scholar 

  • Fazzolari, M., Alcala, R., Nojima, Y., Ishibuchi, H., Herrera, F.: A review of the application of Multi-Objective Evolutionary Fuzzy systems: current status and further directions. IEEE Transactions on Fuzzy Systems. doi: 10.1109/TFUZZ.2012.2201338.

  • Pedrycz, W., Mingli, S.: A genetic reduction of feature space in the design of fuzzy models. Applied Soft Computing. in press: http://dx.doi.org/10.1016/j.asoc.2012.03.055.

  • Chen, J., Mahfouf, M.: Improving transparency in approximate fuzzy modeling using multi-objective immune inspired optimization. International Journal of Computational Intelligence Systems. 5(2), 322-342 (2012).

    Google Scholar 

  • Srinivas, N., Deb, K.: Multiobjective optimization using non-dominated sorting in genetic algorithms. Evolutionary Computation. 2(3). 221-248 (1994).

    Google Scholar 

  • Horn, J., Nafpliotis, N., Goldberg, D.E.: A niched pareto genetic algorithm for multi-objective optimization. In Proc.: Ist IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence. 1, 82-87 (1994).

    Google Scholar 

  • Fonseca, C. M., Fleming, P. J.: Genetic algorithms for multiobjective optimization: formulation, discussion and generalization. In proc.: 5th International Conference on Genetic Algorithms. 416-423 (1993).

    Google Scholar 

  • Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Transactions on Evolutionary Computation. 3 (4), 257-271 (1999).

    Google Scholar 

  • Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength pareto evolutionary algorithms. Technical Report 103. Computer Engineering & Networks Laboratory (TIK). Swiss Federal Institute of Technology (ETH). Zurich, Switzerland (2001).

    Google Scholar 

  • Knowles, J. D., Corne, D. W.: Approximating the non-dominated front using the pareto achieved evolution strategy. Evolutionary Computation. 8(2), 149-172 (2000).

    Google Scholar 

  • Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA II. IEEE Transactions on Evolutionary Computation. 6 (2), 182-197 (2002).

    Google Scholar 

  • Herrera, F.: Genetic fuzzy systems: taxonomy, current research trends and prospects. Evolutionary Intelligence. 1, 27-46 (2008).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information Technology, Babu Banarasi Das Northern India Institute of Technology, Lucknow, India

    Praveen Kumar Shukla & Surya Prakash Tripathi

Authors
  1. Praveen Kumar Shukla
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Surya Prakash Tripathi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Praveen Kumar Shukla .

Editor information

Editors and Affiliations

  1. South Asian University, Chankya Puri, New Delhi, 110021, India

    Jagdish Chand Bansal

  2. ABV - IIITM, Gwalior, Gwalior, 474015, Madhya Pradesh, India

    Pramod Kumar Singh

  3. , Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    Kusum Deep

  4. , Department of Paper Technology, Indian Institute of Technology Roorkee, Saharanpur Campus, Roorkee, India

    Millie Pant

  5. , Department of Computer Science, Liverpool Hope University, Office: FML 412, Liverpool, Liverpool, L16 9JD, United Kingdom

    Atulya K. Nagar

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer India

About this paper

Cite this paper

Shukla, P.K., Tripathi, S.P. (2013). Interpretability Issues in Evolutionary Multi-Objective Fuzzy Knowledge Base Systems. In: Bansal, J., Singh, P., Deep, K., Pant, M., Nagar, A. (eds) Proceedings of Seventh International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA 2012). Advances in Intelligent Systems and Computing, vol 201. Springer, India. https://doi.org/10.1007/978-81-322-1038-2_40

Download citation

  • DOI: https://doi.org/10.1007/978-81-322-1038-2_40

  • Published:

  • Publisher Name: Springer, India

  • Print ISBN: 978-81-322-1037-5

  • Online ISBN: 978-81-322-1038-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation