摘要
According to the description effect range, the method of scaling system in cartography is with the precision of four grades： nominal scaling, ordinal scaling, interval scaling and ratio scaling. The authors have researched their innate character and inherent relations. The essence of evaluation partialordering set （A ,≤） is the mapping of evaluation object （X, ≤） under fixed condition. The collection and classification of xi ∈ X corresponds how to express Aj ∈ A, i.e. , V xi ∈ X→f（xi ） = Aj → A, Aj is the image of xi under mapping f. The function relation between evaluation partial-ordering set （A, ≤） and evaluation object （X, ≤） is decided by the space character and the way of collection and classification. The different space character and way of collection and classification will produce the different express method and evaluation result, accordingly the authors give out the mathematical definitions for nominal scaling, ordinal scaling, interval scaling and ratio scaling respectively. These results have been proved through the examples.
According to the description effect range, the method of scaling system in cartography is with the precision of four grades: nominal scaling, ordinal scaling, interval scaling and ratio scaling. The authors have researched their innate character and inherent relations. The essence of evaluation partialordering set (A, ≤) is the mapping of evaluation object (X, ≤) under fixed condition. The collection and classification of x_i∈X corresponds how to express A_ j ∈A, i.e.,x_i∈Xf(x_ i )=A_ j ∈A, A_ j is the image of x_ i under mapping f. The function relation between evaluation partial-ordering set (A, ≤) and evaluation object (X, ≤) is decided by the space character and the way of collection and classification. The different space character and way of collection and classification will produce the different express method and evaluation result, accordingly the authors give out the mathematical definitions for nominal scaling, ordinal scaling, interval scaling and ratio scaling respectively. These results have been proved through the examples.
