Abstract
This paper presents a model for solving probabilistic travel distribution problems that involves fuzzy uncertainty. Using entropy measures for interval-valued problems, we extend those results to a fuzzy environment via extension principle and nonlinear mathematical programming methods. An application example is solved using the proposed fuzzy entropy method in order to analyze their results.
J.P. León is undergraduate student of the Industrial Engineering Dept. of the Universidad Distrital Francisco José de Caldas, Bogotá - Colombia.
J.C. Figueroa-García is Assistant Professor of the Universidad Distrital Francisco José de Caldas, Bogotá - Colombia.
H. López-Ospina is Associate Professor of the Pontificia Universidad Javeriana, Bogotá - Colombia.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall, Upper Saddle River (1995)
Klir, G.J., Folger, T.A.: Fuzzy Sets, Uncertainty and Information. Prentice Hall, Upper Saddle River (1992)
Bazaraa, M.S., Jarvis, J.J., Sherali, H.D.: Linear Programming and Networks Flow. Wiley, New York (1998)
Carlsson, C., Fedrizzi, M., Fullér, R.: Fuzzy Logic in Management, vol. 66. Springer, New York (2012)
Ortúzar, J., Willumsen, L.G.: Modelos de distribución zonal. Modelos de Transporte 1, 265–271 (2008)
Fang, S., Rajasekera, J., Tsao, H.: Entropy Optimization and Mathematical Programming. Operations Research & Management Science, vol. 8. Kluwer Academic Publishers, New York (1997)
Shannon, C.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 393 (1948)
Romik, D.: Stiriling’s approximation for \(n!\): the ultimate short proof? Am. Math. Monthly 107, 556–567 (2000)
López-Ospina, H.: Modelo de maximización de la entropía y costos generalizados intervalares para la distribución de viajes urbanos. Ingeniería y Universidad 17, 390–407 (2013)
Yager, R.: A procedure for ordering fuzzy subsets of the unit interval. Inf. Sci. 24, 143–161 (1981)
Figueroa-García, J.C.: A general model for linear programming with interval type-2 fuzzy technological coefficients. In: 2012 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), pp. 1–6 (2012)
Wu, D., Mendel, J.M.: Uncertainty measures for interval type-2 fuzzy sets. Inf. Sci. 177, 5378–5393 (2007)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
León, J.P., Figueroa-García, J.C., López-Ospina, H. (2016). A Model for Fuzzy-Cost Travel Distribution Problems Using Entropy Measures. In: Figueroa-García, J., López-Santana, E., Ferro-Escobar, R. (eds) Applied Computer Sciences in Engineering. WEA 2016. Communications in Computer and Information Science, vol 657. Springer, Cham. https://doi.org/10.1007/978-3-319-50880-1_24
Download citation
DOI: https://doi.org/10.1007/978-3-319-50880-1_24
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-50879-5
Online ISBN: 978-3-319-50880-1
eBook Packages: Computer ScienceComputer Science (R0)