On Fuzzy Neural Network's Property & Learning Algorithm And Interval-Valued Fuzzy Set

Fuzzy neural networks are important tools to build nonlinear systems with uncertain knowledge. In the paper, the fuzzy associative memories and fuzzy bi-directional associative memories are researched deeply. In addition, the properties and improvement and propagation of compatibility measures between interval-valued fuzzy sets are investigated.The problems have been researched as follow:(1) A new concept is established in the paper that the robustness of a feed-forward fuzzy associative memory to perturbations of training pattern pair. Then for a Max-product-based fuzzy associative memory (Max-Product FAM), the investigation reveals that such robustness of the memory is good when the fuzzy Hebbian learning algorithm is used, however such robustness of the memory is poor when another learning algorithm is employed. Finally, an experiment is given to testify the theoretical conclusion and illustrate practical application of Max-product FAM.(2) A key issue on a neural network is to find its efficient learning algorithm. Based on the fuzzy composition of Max operation and triangular norm T where T is TL or Ses, a type of fuzzy bidirectional associative memory (Max-T FBAM) is proposed here. By means of concomitant implication operator of a triangular norm, simple efficient learning algorithm is proposed for the network. When T is continuous triangular norm, it is proved theoretically that, for any given set of pattern pairs, if there exist pairs of connection weight matrices which make the set to become a set of the equilibrium states of Max-T FBAM, then the presented learning algorithms can give the maximum of all such pairs of weight matrices. And the learning algorithm can ensure that, the Max- Ses FBAM with this maximal pair of connection weight matrices can be convergent to an equilibrium state in one iterative process for any input.(3) There are some defects in known compatibility measure between interval-valued fuzzy sets, so the properties of such compatibility measure are discussed carefully. Then the old compatibility is improved into a new formula, so called harmoniousness. The harmoniousness holds the symmetry and inherits basic characteristics rather than non-symmetry of the old compatibility. For the first time, the problem is also discussed how fuzzy inference methods propagate the compatibility and harmoniousness. The work of the paper is advantageous to neatening fuzzy rule database based on interval-valued fuzzy sets as well as to analyses and choice of fuzzy inference methods.