Hiérarchie des places centrales et graphes Φ-Flous

Abstract

This paper discusses the nature of the dominance relationships in a central-place system. The author takes account of the indeterminacy which fundamentally characterises the dominance relationship; one central place dominating another more or less. The formalisation put forward depends on the theory of fuzzy Φ-graphs. The first part describes the space of the influencing relations between agglomerations, and in the second part the indeterminate dominance relations are analysed. A central-place hierarchy exists if and only if the dominance-relations space can be partitioned into like classes. The author develops several theorems on fuzzy Φ-graphs. The model is operational. A numerical example is given in the three appendices which present, in conclusion, the necessary algorithms for putting it into practice.