A Definition of Interpretability of Fuzzy Systems

Importance of Interpretability of Fuzzy Systems

Interpretability of fuzzy systems has not received much attention in the fuzzy community so far. One main reason is that most earlier fuzzy systems are abstracted from human experts or heuristics and they are usually well understandable for human beings. However, more and more fuzzy systems have been automatically generated using experiment data, which are not necessarily comprehensible to human beings. In addition, it is a common practice to update the fuzzy systems that are abstracted from experts using different learning methods in order to improve their performance. This can also lead to the loss of interpretability of fuzzy systems.

As it is well known, one basic motivation to implement a fuzzy model lies in its transparency. That is, by building a fuzzy model of an unknown system, one is able to get insight into the system and acquire important knowledge. Besides, as one important tool for data mining and knowledge discovery, the importance of interpretability cannot be overemphasized [1-4].

As there is always a trade-off between interpretability and performance of fuzzy systems, Pareto-based multi-objective learning is shown to be more powerful, see e.g., [5]-[6].

Aspects of Interpretability

  • Completeness of fuzzy partitions
  • Distinguishability of fuzzy partitions
  • Consistency of the fuzzy rules in a rule base
  • Number of variables in the premise of the rules should not exceeds 10
  • Number of fuzzy rules in the rule base should be small
  • References

    [1] Y. Jin, W. von Seelen and B. Sendhoff. An approach to rule-based knowledge extraction. In: Proceedings of IEEE Conference on Fuzzy Systems, pp.1188-1193, Anchorage, Alaska, 1998
    [2] Y. Jin, W. von Seelen and B. Sendhoff. On generating flexible, complete, consistens and compact (FC3) fuzzy rules from data using evolution strategies. IEEE Transactions on Systems, Man, and Cybernetics, 29(4):829-845, 1999
    [3] Y. Jin, Fuzzy modeling of high-dimensional systems: complexity reduction and interpretability improvement. IEEE Transactions on Fuzzy Systems, 8(2):212-221, 2000
    [4] Y. Jin, Advanced Fuzzy Systems Design and Applications. Springer/Physica, November, 2002
    [5] H. Wang, S. Kwong, Y. Jin, W. Wei and K. Man. Agent-based evolutionary approach to interpretable rule-based knowledge extraction. IEEE Transactions Systems, Man, and Cybernetics, Part C, 29(2), 143-155, 2005
    [6] H. Wang, S. Kwong, Y. Jin, W. Wei and K. Man. A multi-objective hierarchical genetic algorithm for interpretable rule-based knowledge extraction. Fuzzy Sets and Systems, 149(1), 149-186, 2005

    For discussions, please contact Yaochu Jin.