Golnarkar, A., Alesheikh, A., Malek, M. (2010). SOLVING BEST PATH PROBLEM ON MULTIMODAL TRANSPORTATION NETWORKS WITH FUZZY COSTS. Iranian Journal of Fuzzy Systems, 7(3), 1-13. doi: 10.22111/ijfs.2010.184

Ali Golnarkar; Ali Asghar Alesheikh; Mohamad Reza Malek. "SOLVING BEST PATH PROBLEM ON MULTIMODAL TRANSPORTATION NETWORKS WITH FUZZY COSTS". Iranian Journal of Fuzzy Systems, 7, 3, 2010, 1-13. doi: 10.22111/ijfs.2010.184

Golnarkar, A., Alesheikh, A., Malek, M. (2010). 'SOLVING BEST PATH PROBLEM ON MULTIMODAL TRANSPORTATION NETWORKS WITH FUZZY COSTS', Iranian Journal of Fuzzy Systems, 7(3), pp. 1-13. doi: 10.22111/ijfs.2010.184

Golnarkar, A., Alesheikh, A., Malek, M. SOLVING BEST PATH PROBLEM ON MULTIMODAL TRANSPORTATION NETWORKS WITH FUZZY COSTS. Iranian Journal of Fuzzy Systems, 2010; 7(3): 1-13. doi: 10.22111/ijfs.2010.184

SOLVING BEST PATH PROBLEM ON MULTIMODAL TRANSPORTATION NETWORKS WITH FUZZY COSTS

^{}Department of GIS Engineering, K. N. Toosi University of Technology, ValiAsr Street, Mirdamad cross, P.C. 19967-15433, Tehran, Iran

Abstract

Numerous algorithms have been proposed to solve the shortest-path problem; many of them consider a single-mode network and crisp costs. Other attempts have addressed the problem of fuzzy costs in a single-mode network, the so-called fuzzy shortest-path problem (FSPP). The main contribution of the present work is to solve the optimum path problem in a multimodal transportation network, in which the costs of the arcs are fuzzy values. Metropolitan transportation systems are multimodal in that they usually contain multiple modes, such as bus, metro, and monorail. The proposed algorithm is based on the path algebra and dioid of $k$-shortest fuzzy paths. The approach considers the number of mode changes, the correct order of the modes used, and the modeling of two-way paths. An advantage of the method is that there is no restriction on the number and variety of the services to be considered. To track the algorithm step by step, it is applied to a pseudo-multimodal network.

bibitem{Abba:Alav} S. Abbasbandy and M. Alavi, {it A method for solving fuzzy linear systems}, Iranian Journal of Fuzzy Systems, {bf 4} (1988), 37-44.

bibitem{Biel:Boul:Moun} M. Bielli, A. Boulmakoul and H. Mouncif, {it Object modeling and path computation for multimodal travel systems}, Eur. J. Oper. Res., {bf 175} (2006), 1705-1730.

bibitem{Boul} A. Boulmakoul, {it Generalized path-finding algorithms on semirings and the fuzzy shortest path problem}, Comput. Appl. Math., {bf 162} (2004), 263-272.

bibitem{Boul:Laur:Moun:Taqa} A. Boulmakoul, R. Laurini, H. Mouncif and G. Taqafi, {it Path-finding operators for fuzzy multimodal spatial networks and their integration in mobile-GIS}, Proceedings of the IEEE International Symposium on Signal Processing and Information Technology, (2002), 51-56.

bibitem{Buht:Mord:Rose} K. R. Buhtani, J. Mordeson and A. Rosenfeld, {it On degrees of end nodes and cut nodes in fuzzy graphs}, Iranian Journal of Fuzzy Systems, {bf 1} (2004), 57-64.

bibitem{Cade:Verd} K. M. Cadenas and J. L. Verdegay, {it A primer on fuzzy optimization models and methods}, Iranian Journal of Fuzzy Systems, {bf 5} (2006), 1-22.

bibitem{Chua:Kung} T. N. Chuang and J. Y. Kung, {it A new algorithm for the discrete fuzzy shortest path problem in a network}, Appl. Math. Comput., {bf 174} (2006), 660-668.

bibitem{Chua:Kung2} T. N. Chuang and J. Y. Kung, {it The fuzzy shortest path length and the corresponding shortest path in a network}, Comput. Oper. Res., {bf 32} (2005), 1409-1428.

bibitem{Corm:Leis:Rive:Stei} T. H. Cormen, C. E. Leiserson, R. L. Rivest and C. Stein, {it Introduction to algorithms}, Second ed., MIT Press and McGraw-Hill, (2001), 588-601.

bibitem{Dech:Pear} R. Dechter and J. Pearl, {it Generalized best-first search strategies and the optimality of $A^*$}, J. ACM, {bf 32} (1985), 505-536.

bibitem{Dubo:Prad} D. Dubois and H. Prade, {it Fuzzy sets and systems: theory and applications}, Academic Press, New York, 1980.

bibitem{Gond:Mino} M. Gondran and M. Minoux, {it Dioids and semirings: links to fuzzy sets and other applications}, Fuzzy Sets and Systems, {bf 158} (2007), 1273-1294.

bibitem{Gond:Mino2} M. Gondran and M. Minoux, {it Linear algebra in dioids: a survey of recent results}, Ann. Discrete Math., {bf 19} (1984), 147-164.

bibitem{Hern:Lama:Verd:Yama} F. Hernandes, M. T. Lamata, J. L. Verdegay and A. Yamakami, {it The shortest path problem on networks with fuzzy parameters}, Fuzzy Sets and Systems, {bf 158} (2007), 1561-1570.

bibitem{Ji:Iwam:Sha} X. Ji, K. Iwamura and Z. Shao, {it New models for shortest path problem with fuzzy arc lengths}, Appl. Math. Modell., {bf 31} (2007), 259-269.

bibitem{Kesh:Ales:Khei} A. Keshtiarast, A. A. Alesheikh and A. Kheirbadi, {it Best route finding based on cost in multimodal network with care of networks constraints}, Map Asia Conference, India, {bf 66} (2006).

bibitem{Lin:Cher} K. C. Lin and M. S. Chern, {it The fuzzy shortest path problem and its most vital arcs}, Fuzzy Sets and Systems, {bf 58} (1993), 343-353.

bibitem{Loza:Stor} A. Lozano and G. Storchi, {it Shortest viable path algorithm in multimodal networks}, Transport. Res., {bf 35} (2001), 225-241.

bibitem{Mill:Stor:Bowe} H. J. Miller, J. D. Storm and M. Bowen, {it GIS design for multimodal networks analysis}, GIS/LIS 95 Annual Conference and Exposition Proceedings of GIS/LIS, (1995), 750-759.

bibitem{Moaz} S. Moazeni, {it Fuzzy shortest path problem with finite fuzzy quantities}, Appl. Math. Comput., {bf 183} (2006), 160-169.

bibitem{Mode:Scio} P. Modesti and A. Sciomachen, {it A utility measure for finding multiobjective shortest paths in urban multimodal transportation networks}, Eur. J. Oper. Res., {bf 111} (1998), 495-508.

bibitem{Naye:Pal} S. Nayeem and M. Pal, {it Shortest path problem on a network with imprecise edge weight}, Fuzzy Optim. Decis. Making, {bf 4} (2005), 293-312.

bibitem{Okad} S. Okada, {it Fuzzy shortest path problems incorporating interactivity among paths}, Fuzzy Sets and Systems, {bf 142} (2004), 335-357.

bibitem{Okad:Sope} S. Okada and T. Soper, {it A shortest path problem on a network with fuzzy arc lengths}, Fuzzy Sets and Systems, {bf 109} (2000), 129-140.

bibitem{Shie} D. Shier, {it On algorithms for finding the K-shortest paths in a network}, Networks, {bf 9} (1979), 195-214.