Merging and Constrained Learning for Interpretability in Neuro-Fuzzy Systems



A methodology for development of linguistically interpretable fuzzy models from data is developed. The implementation of the model is conducted through the training of a neuro-fuzzy network. Structure of the model is firstly obtained by subtractive clustering, allowing the extraction of a set of relevant rules from input-output data. The model parameters are then tuned via the training of a neural network through backpropagation. Interpretability goals are pursued through membership function merging and some constrains on the tuning of parameters. The assignment of linguistic labels to each of the membership functions is then possible. The model obtained for the system under analysis can be described, in this way, by a set of linguistic rules, easily interpretable.


neuro-fuzzy learning, fuzzy systems, clustering, interpretability, transparency


Neuro-Fuzzy Modelling


International Workshop on Hybrid Methods for Adaptive Systems, December 2001

PDF File

Cited by

Year 2011 : 2 citations

 C. Mencar, C. Castiello, R. Cannone, A.M. Fanelli, Interpretability assessment of fuzzy knowledge bases: A cointension based approach, International Journal of Approximate Reasoning, Volume 52, Issue 4, June 2011, Pages 501-518.

 C. Mencar, C. Castiello, R. Cannone, A.M. Fanelli, Design of fuzzy rule-based classifiers with semantic cointension, Information Sciences, Volume 181, Issue 20, 15 October 2011, Pages 4361-4377

Year 2009 : 1 citations

 1. Gholizadeh S, Salajegheh E. (2009). “Optimal design of structures subjected to time history loading by swarm intelligence and an advanced metamodel”. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Volume: 198 Issue: 37-40 Pages: 2936-2949.

Year 2008 : 1 citations

 1. Mencar C. and Fanelli A. M. (2008). “Interpretability constraints for fuzzy information granulation”. Information Sciences, Vol. 178, No. 24, pp. 4585-4618.

Year 2007 : 2 citations

 Mencar C., Castellano G., Fanelli A. M. (2007). “Distinguishability Quantification of Fuzzy Sets”. Information Sciences, Vol. 177, No. 1, pp. 130-149.

 Shtovba SD (2007). “Ensuring the accuracy and transparency of the Mamdani fuzzy model with learning from experimental data”, Problems of Management and Informatics, Vol. 4. (?????? ?.?. ??????????? ???????? ? ???????????? ???????? ?????? ??????? ??? ???????? ?? ????????????????? ??????).

Year 2005 : 1 citations

 1. Mikut R. Jakel J and Groll L. (2005). “Interpretability issues in data-based learning of fuzzy systems”. Fuzzy Sets and Systems, Vol. 150 (2), pp.179-197.

Year 2004 : 1 citations

 1. Mencar C. (2004). “Theory of Fuzzy Information Granulation – Contributions to Interpretability Issues”. PhD Thesis, Department of Informatics, Faculty of Science, University of Bari, Italy.