Abstract
The morphological associative memories(MAM)are a class of extremely new artificial neural networks.Typical objects of MAM include real MAM(RMAM),complex MAM(CMAM),morphological bidirectional associative memories(MBAM),fuzzy MAM(FMAM),enhanced FMAM(EFMAM),fuzzy MBAM(FMBAM),and so on.They have many attractive advantages and features.However,they have the same morphological theoretical base in essence and it is therefore possible to unify them in a framework of MAM.At the same time,it is one of the most important and difficult researches to construct the unified framework of associative memories.The paper tries to solve the problem.Firstly,in this paper,the algebraic structure in computing of MAM is analyzed in order to establish reliable computing base of the framework.Secondly,the basic operations and the common features in the class of MAM are analyzed,and the essential attributes and methods of MAM are extracted.On this basis,the norms and operators of MAM are defined.And finally,the main theorems of MAM are refined and proved.Thus,a unified theoretical framework of MAM is established.The significance of the framework consists in:(1)The objects of MAM are unified together in mathematics and are therefore better for revealing their peculiarities and the essence of MAM;(2)It can help people find some new methods for morphological associative memories,thereby solving more problems of associative memories,pattern recognition and fuzzy reasoning.
Published Version
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