CAJ | 학술논문

形态学联想记忆(MAM)是一类极为新颖的人工神经网络.典型的MAM实例对象包括:实域MAM(RMAM)、复域MAM(CMAM)、双向MAM(MBAM)、模糊MAM(FMAM)、增强的FMAM(EFMAM)、模糊MBAM(FMBAM)等.它们虽有许多诱人的优点和特点,但有相同的形态学理论基础,本质上足相通的,将其统一在一个MAM框架中是可能的.同时,联想记忆统一框架的建证也是当前的研究重点和难点之一.为此作者构建了一个形态学联想记忆框架.文中首先分析MAM类的代数结构,奠定可靠的MAM框架计算基础;其次,分析MAM类的基本操作和共同特征,抽取它们的本质属性和方法,引入形态学联想记忆范式和算子;最后,提炼并证明主要的框架定理.该框架的意义在于:(1)从数学的角度将MAM对象统一在一起,从而能以更高的视角揭示它们的特性和本质;(2)有助于发现一些新的形态学联想记忆方法,从而解决更多的联想记忆、模式识别、模糊推理等问题.
형태학련상기억(MAM)시일류겁위신영적인공신경망락.전형적MAM실례대상포괄:실역MAM(RMAM)、복역MAM(CMAM)、쌍향MAM(MBAM)、모호MAM(FMAM)、증강적FMAM(EFMAM)、모호MBAM(FMBAM)등.타문수유허다유인적우점화특점,단유상동적형태학이론기출,본질상족상통적,장기통일재일개MAM광가중시가능적.동시,련상기억통일광가적건증야시당전적연구중점화난점지일.위차작자구건료일개형태학련상기억광가.문중수선분석MAM류적대수결구,전정가고적MAM광가계산기출;기차,분석MAM류적기본조작화공동특정,추취타문적본질속성화방법,인입형태학련상기억범식화산자;최후,제련병증명주요적광가정리.해광가적의의재우:(1)종수학적각도장MAM대상통일재일기,종이능이경고적시각게시타문적특성화본질;(2)유조우발현일사신적형태학련상기억방법,종이해결경다적련상기억、모식식별、모호추리등문제.
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.