基于三角模的模糊联想记忆网络

Fuzzy Associative Memories Based on Triangular Norms

当T为t-模时,基于模糊取大和T的模糊联想记忆网络(FAM)存在局限性,当T为三角模,是t-模的广义形式,将这种FAM推广成基于Max-T的模糊联想记忆网络Max-TFAM.则Max-TFAM实现了从一个向量空间到另一向量空间的映射,从Max-TFAM的值域角度,分析了它的存储能力,并建立了一个三角模T的伴随蕴涵算子新概念,利用该伴随蕴涵算子,在无需T为连续的、严格增等条件下,提出了Max-TFAM的一个简洁的通用离线学习算法和通用在线学习算法.从理论上严格证明了只要Max-TFAM能完整可靠地存储所给的多个模式对,则这两种算法都能轻易找到使得网络能完整可靠存储这些模式对的所有连接权矩阵的最大者.最后,用实验证明了Max-TFAM模型和所提出的学习算法的有效性.

Some demerits of fuzzy associative memory （FAM） based on Max-T are shown when T is any t-norm, so this type of FAM is extended into a new form. So the classed Max-T FAM where T is now a triangular norm, is the generalization of t-norm. Since a Max-T FAM can be actually a mapping from a vector space to another vector space, the storage ability of the Max-T FAM where T is a triangular norm is partly analyzed with the aid of the analyses of its value domain. Further, a new concept of concomitant implication operator of a triangular norm T is presented here. It is with such concomitant implication operator that a simple general off-line learning algorithm and a general on-line learning algorithm are proposed for a class of the Max-T FAMs based on arbitrary triangular norm T. In this case, T needs no restriction of continuity, strictly increasing, archimedean property, and so on. When T is any triangular norm, it is carefully proved that, if any given multiple pattern pairs can be reliably and perfectly stored in a Max-T FAM, then the two presented learning algorithms can easily give the maximum of all the weight matrices which can be reliably and perfectly stored in the Max-T FAM. Finally, several experiments are given to testify the effectivity of a class of Max-T FAMs and its learning algorithms.