ON THE EXTENSION OF THE MEDIAN CENTER AND THE MIN-MAX CENTER TO FUZZY DEMAND POINTS

Julio Rojas-Mora, Didier Josselin, Marc Ciligot-Travain

2011

Abstract

A common research topic has been the search of an optimal center, according to some objective function that considers the distance between the potential solutions and a given set of points. For crisp data, closed form expressions obtained are the median center, for the Manhattan distance, and the min-max center, for the Chebyshev distance. In this paper, we prove that these closed form expressions can be extended to fuzzy sets by modeling data points with fuzzy numbers, obtaining centers that, through their membership function, model the “appropriateness” of the final location.

References

  1. Brandeau, M. L., Sainfort, F., and Pierskalla, W. P., editors (2004). Operations research and health care: A handbook of methods and applications. Kluwer Academic Press, Dordrecht.
  2. Canós, M. J., Ivorra, C., and Liern, V. (1999). An exact algorithm for the fuzzy p-median problem. European Journal of Operational Research, 116:80-86.
  3. Chan, Y. (2005). Location Transport and Land-Use: Modelling Spatial-Temporal Information. Springer, Berlin.
  4. Chen, C.-T. (2001). A fuzzy approach to select the location of the distribution center. Fuzzy Sets and Systems, 118:65-73.
  5. Chen, S.-H. and Hsieh, C.-H. (1999). Graded mean integration representation of generalized fuzzy number. Journal of Chinese Fuzzy System, 5(2):1-7.
  6. Chen, S.-H. and Wang, C.-C. (2009). Fuzzy distance using fuzzy absolute value. In Proceedings of the Eighth International Conference on Machine Learning and Cybernetics, Baoding.
  7. Ciligot-Travain, M. and Josselin, D. (2009). Impact of the norm on optimal location. In Proceedings of the ICCSA 2009 Conference, Seoul.
  8. Darzentas, J. (1987). On fuzzy location model. In Kacprzyk, J. and Orlovski, S. A., editors, Optimization Models Using Fuzzy Sets and Possibility Theory, pages 328-341. D. Reidel, Dordrecht.
  9. Drezner, Z. and Hamacher, H. W., editors (2004). Facility location. Applications and theory. Springer, Berlin.
  10. Dubois, D. and Prade, H. (1979). Fuzzy real algebra: some results. Fuzzy Sets and Systems, 2:327-348.
  11. Griffith, D. A., Amrhein, C. G., and Huriot, J. M. e. (1998). Econometric advances in spatial modelling and methodology. Essays in honour of Jean Paelinck, volume 35 of Advanced studies in theoretical and applied econometrics.
  12. Hakimi, S. (1964). Optimum locations of switching center and the absolute center and medians of a graph. Operations Research, 12:450-459.
  13. Hansen, P., Labbé, M., Peeters, D., Thisse, J. F., and Vernon Henderson, J. (1987). Systems of cities and facility locations. in Fundamentals of pure and applied economics. Harwood academic publisher, London.
  14. Kaufmann, A. and Gupta, M. M. (1985). Introduction to Fuzzy Arithmetic. Van Nostrand Reinhold, New York.
  15. Labbé, M., Peeters, D., and Thisse, J. F. (1995). Location on networks. In Ball, M., Magnanti, T., Monma, C., and Nemhauser, G., editors, Handbook of Operations Research and Management Science: Network Routing, volume 8, pages 551-624. North Holland, Amsterdam.
  16. Moreno Pérez, J. A., Moreno Vega, J. M., and Verdegay, J. L. (2004). Fuzzy location problems on networks. Fuzzy Sets and Systems, 142:393-405.
  17. Nickel, S. and Puerto, J. (2005). Location theory. A unified approach. Springer, Berlin.
  18. Thomas, I. (2002). Transportation Networks and the Optimal Location of Human Activities, a numerical geography approach. Transport economics, management and policy. Edward Elgar, Northampton.
  19. Zadeh, L. (1965). Fuzzy sets. Information and Control, 8(3):338-353.
  20. Zimmermann, H.-J. (2005). Fuzzy Sets: Theory and its Applications. Springer, 4 edition.
Download


Paper Citation


in Harvard Style

Rojas-Mora J., Josselin D. and Ciligot-Travain M. (2011). ON THE EXTENSION OF THE MEDIAN CENTER AND THE MIN-MAX CENTER TO FUZZY DEMAND POINTS . In Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: FCTA, (IJCCI 2011) ISBN 978-989-8425-83-6, pages 407-416. DOI: 10.5220/0003674604070416


in Bibtex Style

@conference{fcta11,
author={Julio Rojas-Mora and Didier Josselin and Marc Ciligot-Travain},
title={ON THE EXTENSION OF THE MEDIAN CENTER AND THE MIN-MAX CENTER TO FUZZY DEMAND POINTS},
booktitle={Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: FCTA, (IJCCI 2011)},
year={2011},
pages={407-416},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003674604070416},
isbn={978-989-8425-83-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: FCTA, (IJCCI 2011)
TI - ON THE EXTENSION OF THE MEDIAN CENTER AND THE MIN-MAX CENTER TO FUZZY DEMAND POINTS
SN - 978-989-8425-83-6
AU - Rojas-Mora J.
AU - Josselin D.
AU - Ciligot-Travain M.
PY - 2011
SP - 407
EP - 416
DO - 10.5220/0003674604070416