Fuzzy associative memory
Encyclopedia
Research on fuzzy associative memory (FAM) models originated in the early 1990s with the advent of Kosko's FAM1,2. Like many other associative memory models, Kosko's FAM consists of a single-layer feed-forward fuzzy neural network that stores fuzzy rules "If 
is 
then 
is 
" 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.
is then is " by means of a fuzzy associative matrixFuzzy associative matrix
A fuzzy associative matrix expresses fuzzy logic rules in tabular form. These rules usually take two variables as input, mapping cleanly to a two-dimensional matrix, although theoretically a matrix of any number of dimensions is possible....
.
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.