Fuzzy associative memory

Research on fuzzy associative memory (FAM) models originated in the early 1990's with the advent of Kosko's FAM^1,2. Like many other associative memory models, Kosko's FAM consists of a single-layer feed-forward fuzzy neural network that stores fuzzy rules "If $x$ is $X\_k$ then $y$ is $Y\_k$" by means of a fuzzy associative matrix.

Despite successful applications of Kosko's FAMs to problems such as backing up a truck and trailer, target tracking, and voice cell control in ATM networks, Kosko's FAM suffers from an extremely low storage capacity of one rule per FAM matrix. Therefore, Kosko's overall fuzzy system comprises several FAM matrices. Given a fuzzy input, the FAM matrices generate fuzzy outputs which are then combined to yield the final result.

To overcome the original FAMs severe limitations in storage capacity, several researchers have developed improved FAM versions that are capable of storing multiple pairs of fuzzy patterns. For example, Chung and Lee generalized Kosko's model by proposing a max-t composition for the synthesis of a FAM matrix³. Chung and Lee showed that all fuzzy rules can be perfectly recalled by means of a single FAM matrix using max-t composition provided that the input patterns satisfy certain orthogonality conditions. Junbo et al. had previously presented an improved learning algorithm for Kosko's max-min FAM model⁴. Liu modified the Junbo's FAM et al. by adding a threshold activation function to each node of the network⁵. Sussner and Valle recently established implicative fuzzy associative memories (IFAMs)^6,7, a class of associative memories that grew out of morphological associative memories (MAMs)⁸. Interestingly, one can store as many patterns as desired in an auto-associative IFAM. Furthermore, one particular IFAM model can be viewed as an improved version of Liu's FAM.

References

1. S.-G. Kong and B. Kosko, Adaptive fuzzy systems for backing up a truck-and-trailer. IEEE Transactions on Neural Networks 3, 2 (Mar. 1992), 211–223.

2. B. Kosko, Neural Networks and Fuzzy Systems: A Dynamical Systems Approach to Machine Intelligence. Prentice Hall, Englewood Cliffs, N.J., 1992.

3. F. Chung and T. Lee, On fuzzy associative memory with multiple-rule storage capacity. IEEE Transactions on Fuzzy Systems 4, 3 (August 1996), 375–384.

4. F. Junbo, J. Fan, and S. Yan, A learning rule for fuzzy associative memories. In Proceedings of the IEEE International Joint Conference on Neural Networks (June 1994), vol. 7, pp. 4273 – 4277.

5. P. Liu, The fuzzy associative memory of max-min fuzzy neural networks with threshold. Fuzzy Sets and Systems 107 (1999), 147–157.

6. P. Sussner and M.E. Valle, Implicative fuzzy associative memories. IEEE Transactions on Fuzzy Systems 14, 6 (2006), 793–807.

7. M.E. Valle, P. Sussner, and F. Gomide, Introduction to implicative fuzzy associative memories. In Proceedings of the IEEE International Joint Conference on Neural Networks (Budapest, Hungary, July 2004), pp. 925 – 931.

8. G.X. Ritter, P. Sussner, and J.L.D. De Leon, Morphological associative memories. IEEE Transactions on Neural Networks 9, 2 (1998), 281–293.