Abstract
Multilayered feedforward artificial neural networks (ANNs) are black boxes. Several methods have been published to extract a fuzzy system from a network, where the input–output mapping of the fuzzy system is equivalent to the mapping of the ANN. These methods are generalized by means of a new fuzzy aggregation operator. It is defined by using the activation function of a network. This fact lets to choose among several standard aggregation operators. A method to extract fuzzy rules from ANNs is presented by using this new operator. The insertion of fuzzy knowledge with linguistic hedges into an ANN is also defined thanks to this operator.
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References
Alexander JA and Mozer MC (1999). Template-based procedures for neural network interpretation. Neural Netw 12: 479–498
Andrews R, Diederich J and Tickle AB (1995). Survey and critique of techniques for extracting rules from trained artificial neural networks. Knowledge-Based Syst 8(6): 373–389
Benítez JM, Castro JL and Requena I (1997). Are artificial neural networks black boxes?. IEEE Trans Neural Netw 8(5): 1156–164
Castro JL, Mantas CJ and Benítez JM (2002). Interpretation of artificial neural networks by means of fuzzy rules. IEEE Trans Neural Netw 13(1): 101–116
Chen C and Liu B (2003). Linguistic hedges and fuzzy rule based systems. In: Casillas, J, Cordon, O, Herrera, F and Magdalena, L (eds) Accuracy improvements in linguistic fuzzy modeling, vol 129 of studies in fuzziness and soft-computing, springer, Heidelberg
Detyniecki M (2000) Mathematical aggregation operators and their application to video querying. Doctoral thesis—research report 2001–2002, Laboratoire d’Informatique de Paris
Duch W, Setiono R and Zurada J (2004). Computational intelligence methods for rule-based data understanding. Proc IEEE 92(5): 769–770
Fu L (1994). Rule generation from neural networks. IEEE Trans Syst Man cybern 24(8): 1114–1124
Geva S, Malmstrom K and Sitte J (1998). Local cluster neural net: architecture, training and applications. Neurocomputing 20: 35–56
Hamacher H (1978) Über logische Aggregationen nicht-binär explizierter Entscheidungs-kriterien. Rita G. Fischer Verlag, Frankfurt
Haykin S (1994). Neural networks: a comprehensive foundation. McMillan College Publishing Company, New York
Jacobsson H and Henrik (2005). Rule extraction from recurrent neural networks: a taxonomy and review. Neural Comput 17(6): 1223–1263
Klement P, Mesiar R and Pap E (1996). On the relationship of associative compensatory operators to triangular norms and conorms. Int J Uncertainty Fuzziness Knowledge-Based Syst 4(2): 129–144
Klir GJ and Yuan B (1995). Fuzzy sets and fuzzy logic: theory and applications. Prentice Hall, Englewood Cliffs
Kolman E and Margaliot M (2005). Are neural networks white boxes?. IEEE Trans Neural Netw 16(4): 844–852
Kosko B (1994). Fuzzy systems as universal approximators. IEEE Transactions Computers 43 11: 1329–1333
Kuncheva LI (2000). Fuzzy classifier design. Studies in fuzziness and soft computing. Physica-Verlag, Heidelberg
Lapedes A and Farber R (1988). How neural nets work. In: Anderson, DZ (eds) Neural information processing systems, American Physical Society, New York
Maire F (1999). Rule-extraction by backpropagation of polyhedra. Neural Netw 12: 717–725
Mitra S and Hayashi Y (2000). Neuro-fuzzy rule generation: survey in soft computing framework. IEEE Trans Neural Netw 11(3): 748–768
Reyneri LM (1999). Unification of neural and wavelet networks and fuzzy systems. IEEE Trans Neural Netw 10(4): 801–814
Setiono R (2000). Extracting M-of-N rules from trained neural networks. IEEE Trans Neural Netw 11(2): 512–519
Silvert W (1993) Symmetric summation: a class of operations on fuzzy sets. IEEE Trans Syst Man Cybern, SMC-9, pp 657–659. In: Dubois D, Prade H, Yager RR (eds) (1979 Reprinted) Reading in fuzzy sets for intelligent systems. Morgan Kaufman, San Mateo, pp 77–79
Smith JW, Everhart JE, Dickson WC, Knowler WC, Johannes RS (1988) Using the ADAP learning algorithm to forecast the outset of diabetes mellitus. In: Proceedings of the Symposium on Computer Applications and Medical Care. IEEE Computer Society Press, Los Alamitos, pp 261–265
Taha I and Ghosh J (1999). Symbolic interpretation of artificial neural networks. IEEE Trans Knowl Data Eng 11(3): 448–463
Takagi T and Sugeno M (1985). Fuzzy identification of systems and its application to modeling and control. IEEE Trans Syst Man Cybern 15(1): 116–132
Tickle AB, Andrews R, Golea M and Diederich J (1998). The truth will come to light: Directions and challenges in extracting the knowledge embedded within trained artificial neural networks. IEEE Trans Neural Netw 9: 1057–1068
Tsukimoto H (2000). Extracting rules from trained neural networks. IEEE Trans Neural Netw 11(2): 377–389
Yager R and Rybalov A (1996). Uninorm aggregation operators. Fuzzy Sets Syst 80: 111–120
Yager R and Rybalov A (1998). Full reinforcement operators in aggregation techniques. IEEE Trans Syst Man Cybern 28: 757–769
Zadeh LA (1973). Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans Syst Man Cybern 3: 28–44
Zadeh LA (1975). The concept of a linguistic variable and its application to approximate reasoning, part 1. Inf Sci 8: 199–249
Zimmermann HJ and Zysno P (1980). Latent connectives in human decision making. Fuzzy Sets Syst 4: 37–51
Zimmermann HJ (1991). Fuzzy set theory and its applications, 2nd edn. Kluwer, Dordrecht
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Mantas, C.J. A generic fuzzy aggregation operator: rules extraction from and insertion into artificial neural networks. Soft Comput 12, 493–514 (2008). https://doi.org/10.1007/s00500-007-0221-8
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DOI: https://doi.org/10.1007/s00500-007-0221-8