Abstract
Here, we consider a network, whose arc lengths are intervals or triangular fuzzy numbers. A new comparison technique based on the expected value of intervals and triangular fuzzy numbers is introduced. These expected values depend on a parameter which reflects the optimism/pessimism level of the decision-maker. Moreover, they can be used for negative intervals or triangular fuzzy numbers.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Klein, C.M.: Fuzzy shortest paths. Fuzzy Sets and System 39, 27–41 (1991)
Okada, S., Gen, M.: Order relation between intervals and its application to shortest path problem. Comput. Ind. Eng. 25, 147–150 (1993)
Okada, S., Gen, M.: Fuzzy shortest path problem. Comput. Ind. Eng. 27, 465–468 (1994)
Nayeem, S.M.A., Pal, M.: Shortest path problem on a network with imprecise edge weight. Fuzzy Optim. Decis. Making 4, 293–312 (2005)
Hernandes, F., Lamata, M.T., Verdegay, J.L., Yamakami, A.: The shortest path problem on networks with fuzzy parameters. Fuzzy Sets and Syst. 158, 1561–1570 (2007)
Tajdin, A., Mahdavi, I., Mahdavi-Amiri, N., Sadeghpour-Gildeh, B.: Computing a fuzzy shortest path in a network with mixed fuzzy arc lengths using \(\alpha \)-cuts. Comput. Math. Appl. 60, 989–1002 (2010)
Liu, B.: Theory and Practice of Uncertain Programming. Physica-Verlag, Heidelberg (2002)
Liu, B.: Uncertainty theory: An introduction to its axiomatic foundations. Springer-Verlag, Berlin (2004)
Yang, L., Iwamura, K.: Fuzzy chance-constrained programming with linear combination of possibility measure and necessity measure. Appl. Math. Sci. 2, 2271–2288 (2008)
Dijkstra, E.W.: A note on two problems in connection with graphs. Numerische Mathematik 1, 269–271 (1959)
Sengupta, A., Pal, T.K.: On comparing interval numbers. Eur. J. Oper. Res. 127, 28–43 (2000)
Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Syst. 1, 3–28 (1978)
Dubois, D., Prade, H.: Possibility theory. Plenum, New York (1988)
Nayeem, S.M.A.: An expected value model of quadratic clique problem on a graph with fuzzy parameters. Proceedings of 12th international conference on intelligent systems design and applications (ISDA), Kochi, India, (to appear).
Liou, T.-S., Wang, M.-J.: Ranking fuzzy numbers with integral interval. Fuzzy Sets and Syst. 50, 247–255 (1992)
Bellman, R.E.: On a routing problem. Quart. Appl. Math. 16, 87–90 (1958)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer India
About this paper
Cite this paper
Nayeem, S.M.A. (2014). A New Expected Value Model for the Fuzzy Shortest Path Problem. In: Babu, B., et al. Proceedings of the Second International Conference on Soft Computing for Problem Solving (SocProS 2012), December 28-30, 2012. Advances in Intelligent Systems and Computing, vol 236. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1602-5_23
Download citation
DOI: https://doi.org/10.1007/978-81-322-1602-5_23
Published:
Publisher Name: Springer, New Delhi
Print ISBN: 978-81-322-1601-8
Online ISBN: 978-81-322-1602-5
eBook Packages: EngineeringEngineering (R0)