A solution method for truncated normalized max product fuzzy set of equations. (English) Zbl 1075.68658
Summary: An iterative method of solving a set of equations based on the truncated normalized max product is described. The operation may serve as the transformation for the set of fully connected units in a fully recurrent network that might otherwise consist of linear threshold units. Because of truncation and normalization the network acting under this transformation has a finite number of states and components of the state vector are bounded. Component values however are not restricted to binary values as would be the case if the network consisted of linear threshold units but can now take on the values in the set \(\{0, 0.1,..0.9, 1\}\). This means that each unit although still having discrete output can provide finer granularity compared to the case where a linear threshold unit is used. Truncation is natural in hardware implementation where only a finite number of places behind the decimal are retained.
MSC:
| 68T37 | Reasoning under uncertainty in the context of artificial intelligence |
| 68T05 | Learning and adaptive systems in artificial intelligence |
| 03E72 | Theory of fuzzy sets, etc. |
Keywords:
fuzzy neural networks; fuzzy relational equations; max-product composition; inverse problem; fuzzy model; relational matrix; fuzzy matrix equation; recurrent neural networksReferences:
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