Multilayer multidimensional affair element extension set and its operations

In reality, an object is often described as a complex system with multilayer structure, of which any sub-layer has many properties. According to the principle of extenics, in order to establish the extension model of affair element for a complex system, the concept of multilayer multidimensional affair element extension set and its positive field, negative field and extension boundary were presented based on the concept of n-dimensional affair element extension set. The definitions of positive extension field, negative extension field, positive stable field and negative stable field of a multilayer multidimensional affair element extension set were given. The properties and intersection operation of the set were discussed and proved strictly. The expressions of extension field and stable field for intersection operation of the set were gained.