An Axiomatic Approach to a Measure of Land-Use Mixture

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Abstract
A class of axioms which seem reasonable properties of a measure of land-use mixture is proposed. There are ten axioms: continuity, homogeneity, strict quasi-concavity, symmetry, area independence, ascent direction, exchangeability, reducibility, isotropy, and consistency. The proposed measure satisfying these axioms is represented by a function of the distance between a land-use ratio vector of a region in question and an average land-use ratio vector of other regions.