Abstract
The calculation of the center of a set of points in an open space, subject to a given metric, has been a widely explored topic in operations research. In this paper, we present the extension of two of these centers, the median and the min-max centers, when there is uncertainty in the location of the points. These points, modeled by two-dimensional trapezoidal fuzzy numbers (TrFN), induce uncertainties in the distance between them and the center, causing that the resulting center may also be a two-dimensional TrFN. The solution gives flexibility to planners, as the value of the membership function at any given coordinate can be seen as a degree of “appropriateness” of the final location of the center. We further consider how to model the existing space constraints and what is their effect on the calculated centers. Finally, in the case of temporal analysis, we can determine the durability of the location of the center at a given point of the study area.
This work was funded by the French ANR ROLSES Project.
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References
Brandeau, M.L., Sainfort, F., Pierskalla, W.P. (eds.): Operations research and health care: A handbook of methods and applications. Kluwer Academic Press, Dordrecht (2004)
Canós, M.J., Ivorra, C., Liern, V.: An exact algorithm for the fuzzy p-median problem. European Journal of Operational Research 116, 80–86 (1999)
Chan, Y.: Location Transport and Land-Use: Modelling Spatial-Temporal Information. Springer, Berlin (2005)
Chen, C.-T.: A fuzzy approach to select the location of the distribution center. Fuzzy Sets and Systems 118, 65–73 (2001)
Chen, S.-H., Hsieh, C.-H.: Graded mean integration representation of generalized fuzzy number. Journal of Chinese Fuzzy System 5(2), 1–7 (1999)
Chen, S.-H., Wang, C.-C.: Fuzzy distance using fuzzy absolute value. In: Proceedings of the Eighth International Conference on Machine Learning and Cybernetics, Baoding (2009)
Ciligot-Travain, M., Josselin, D.: Impact of the Norm on Optimal Locations. In: Gervasi, O., Taniar, D., Murgante, B., Laganà, A., Mun, Y., Gavrilova, M.L. (eds.) ICCSA 2009, Part I. LNCS, vol. 5592, pp. 426–441. Springer, Heidelberg (2009)
Darzentas, J.: On fuzzy location model. In: Kacprzyk, J., Orlovski, S.A. (eds.) Optimization Models Using Fuzzy Sets and Possibility Theory, pp. 328–341. D. Reidel, Dordrecht (1987)
Drezner, Z., Hamacher, H.W. (eds.): Facility location. Applications and theory. Springer, Berlin (2004)
Dubois, D., Prade, H.: Fuzzy real algebra: some results. Fuzzy Sets and Systems 2, 327–348 (1979)
Griffith, D.A., Amrhein, C.G., Huriot, J.M. (eds.): Econometric advances in spatial modelling and methodology. Essays in honour of Jean Paelinck. Advanced studies in theoretical and applied econometrics, vol. 35 (1998)
Hakimi, S.L.: Optimum locations of switching center and the absolute center and medians of a graph. Operations Research 12, 450–459 (1964)
Hansen, P., Labbé, M., Peeters, D., Thisse, J.F., Vernon Henderson, J.: Systems of cities and facility locations. In: Fundamentals of Pure and Applied Economics. Harwood Academic Publisher, London (1987)
Kaufmann, A., Gupta, M.M.: Introduction to Fuzzy Arithmetic. Van Nostrand Reinhold, New York (1985)
Labbé, M., Peeters, D., Thisse, J.F.: Location on networks. In: Ball, M.O., Magnanti, T.L., Monma, C.L., Nemhauser, G.L. (eds.) Handbook of Operations Research and Management Science: Network Routing, vol. 8, pp. 551–624. North Holland, Amsterdam (1995)
Moreno Pérez, J.A., Marcos Moreno Vega, J., Verdegay, J.L.: Fuzzy location problems on networks. Fuzzy Sets and Systems 142, 393–405 (2004)
Nickel, S., Puerto, J.: Location theory. A unified approach. Springer, Berlin (2005)
Thomas, I.: Transportation Networks and the Optimal Location of Human Activities, a numerical geography approach. Transport Economics, Management and Policy. Edward Elgar, Northampton (2002)
Zadeh, L.: Fuzzy sets. Information and Control 8(3), 338–353 (1965)
Zimmermann, H.-J.: Fuzzy Sets. In: Theory and its Applications, 4th edn. Springer (2005)
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Rojas-Mora, J., Josselin, D., Ciligot-Travain, M. (2013). Fuzzy Median and Min-Max Centers: An Spatiotemporal Solution of Optimal Location Problems with Bidimensional Trapezoidal Fuzzy Numbers. In: Madani, K., Dourado, A., Rosa, A., Filipe, J. (eds) Computational Intelligence. IJCCI 2011. Studies in Computational Intelligence, vol 465. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35638-4_15
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DOI: https://doi.org/10.1007/978-3-642-35638-4_15
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