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.