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Notes sur l'intérêt des sous-ensembles flous en analyse de l'attraction de points de vente

Author

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  • Didier Dubois

    (Institut Informatique et Mathématiques Appliquées de Grenoble (IMAG))

Abstract

La représentation mathématique des phénomènes d'attraction des points de ventes dans une zone géographique donnée a fait l'objet de nombreuses recherches. Le but est de pouvoir simuler le comportement du consommateur selon son lieu de résidence, ce qui permet de mieux visualiser les zones d'influence de centres commerciaux. Les raisons qui font qu'un consommateur se rendra ici ou là pour effectuer ses achats sont extrêmement difficiles à analyser de façon globale parce qu'elles peuvent beaucoup varier d'un individu à l'autre. Il est souvent possible de dégager un certain nombre de facteurs importants tels que distance, surface de vente, qualité des produits, etc.; on peut ainsi rassembler un certain nombre d'informations pour évaluer ces facteurs. Tous les modèles d'attraction essaient de définir le traitement numérique le plus judicieux pour ces informations, lesquelles sont pourtant souvent plutôt qualitatives que quantitatives. On a souvent recours à des indices numériques objectifs pour chiffrer des grandeurs qui ne sont que subjectivement perçues (par exemple la distance géographique se substitue à une distance psychologique qui est celle qui conditionne réellement l'individu). Le propos de cette note n'est que de suggérer l'utilisation de certains outils de la théorie des sous-ensembles flous pour affiner certains modèles d'attraction déjà existants. Ces outils sont décrits en détail dans le livre de Dubois et Prade (4). On esquisse d'abord une critique de l'interprétation probabiliste d'un modèle mathématique proposé par Huff (7). Puis dans le cadre d'hypothèses simples, une méthode d'estimation d'un paramètre flou (Chang (1)) est proposée. Comme conséquence, il est possible de définir l'utilité floue d'un point de vente et de localiser une frontière floue entre zones d'influences. Dans le cadre du modèle d'attraction multi-aspect, on rappelle l'approche de Zadeh (14) pour étendre la notion d'optimalité au sens de Pareto. Enfin des indices de similitude permettant de comparer des zones d'attraction imprécises au sens de Fustier (5),(6)sont définis, notamment la distance floue entre sous-ensembles flous.

Suggested Citation

  • Didier Dubois, 1979. "Notes sur l'intérêt des sous-ensembles flous en analyse de l'attraction de points de vente," Working Papers hal-01527211, HAL.
    • Handle: RePEc:hal:wpaper:hal-01527211
    Note: View the original document on HAL open archive server: https://hal.science/hal-01527211
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    References listed on IDEAS

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    1. FUSTIER, Bernard, 1975. "L’attraction des points de vente dans des espaces précis et imprécis," Institut des Mathématiques Economiques – Document de travail de l’I.M.E. (1974-1993) 10, Institut des Mathématiques Economiques. LATEC, Laboratoire d'Analyse et des Techniques EConomiques, CNRS, Université de Bourgogne.
    2. David L. Huff, 1963. "A Probabilistic Analysis of Shopping Center Trade Areas," Land Economics, University of Wisconsin Press, vol. 39(1), pages 81-90.
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    Cited by:

    1. Claude Ponsard, 1980. "Fuzzy economic spaces," Working Papers hal-01527230, HAL.
    2. Jean-Marie Huriot & Jacky Perreur, 1991. "Qualitative reality and economic spatial analysis [Réalité qualitative et analyse économique spatiale]," Working Papers hal-01542061, HAL.

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