基于布尔代数的地图符号修正的数学模型

Mathematical Model of Map Symbol Correction Based on Boolean Algebra

摘要: 地图符号是制图对象从制图区域到地球椭球面的映射，从地球椭球面到制图主体的认知结构的映射，再到地图平面的映射的同胚象。地图符号与其指代地物的双函数关系是拓扑变换必须遵循的原则。由于地物在时空中演化的普遍性、经常性和连续性及资料的收集欠缺等原因，使编图过程总会在个别地方出现地图符号与指代地物的对应性破缺的问题，这就是地图的错误。对符号失实、遗漏、错位等错误给出了数学定义。根据具有包含关系的地图的幂集属于布尔代数系的原理，提出了基于布尔运算的修改错误符号的操作定义。以实例演算了地图从包含错误符号集的qghf(A)_A到消除错误的成图qghf(A)_B的变换过程。

Abstract: Map symbols are homeomorphic images of mapping objects from mapping regions to the earth ellipsoid, from the earth ellipsoid to the cognitive structure of mapping subjects, and then to the map plane. The relationship between map symbols and their referent objects is a principle to be followed in topological transformation. Due to the universality, regularity and continuity of the evolution of ground objects in time and space and the lack of collection of data, there is always a problem of broken correspondence between map symbols and referring ground objects in some places in the process of map compilation, which is the mistake of maps. The mathematical definition of false symbol, omission and dislocation is given. According to the principle that the power set of the map with inclusion relation belongs to the Boolean algebra system, an operation definition for modifying error symbols based on Boolean operation is proposed. An example is given to calculate the trans-formation process of map from qghf(A)_A which contains the wrong symbol set to qghf(A)_B which eliminates the error.