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中文摘要：
为研究多层高维复杂系统中各子系统之间的相互作用和相互关系，运用可拓学原理，提出了多层高维关系元可拓集及其正域、负域、零界的概念。给出了多层高维关系元可拓集的可拓域、稳定域的定义。研究了多层高维关系元可拓集的并等运算，并证明了有关性质。多层高维关系元可拓集是描述多层结构复杂系统的关系及其变化的一种形式化工具。
英文摘要：
In order to study interactions and interrelations amongst subsystems in complex systems with multilayer multidimensional structure, according to the principle of extenics, the concepts of multilayer multidimensional relation element extension set and its positive field, negative field, zero boundary are presented. Definitions of an extension field, and a stable field of multilayer multidimensional relation element extension set are given. Then, the union operation of the multilayer multidimensional relation element extension set is researched, some properties having been proven. The multilayer multidimensional relation element extension set is a formalization tool of describing relations and its variations of complex systems with multilayer structure.
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