| تعداد نشریات | 31 |
| تعداد شمارهها | 834 |
| تعداد مقالات | 8,015 |
| تعداد مشاهده مقاله | 14,853,139 |
| تعداد دریافت فایل اصل مقاله | 9,586,950 |
ALGORITHMS FOR BIOBJECTIVE SHORTEST PATH PROBLEMS IN FUZZY NETWORKS | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 3، دوره 8، شماره 4، دی 2011، صفحه 9-37 اصل مقاله (407.21 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2011.306 | ||
| نویسندگان | ||
| Iraj Mahdavi1؛ Nezam Mahdavi-Amiri2؛ Shahrbanoo Nejati* 3 | ||
| 1Department of Industrial Engineering, Mazandaran University of Sci- ence & Technology, Babol, Iran | ||
| 2Faculty of Mathematical Sciences, Sharif University of Tech- nology, Tehran, Iran | ||
| 3Department of Industrial Engineering, Mazandaran University of Science & Technology, Babol, Iran | ||
| چکیده | ||
| We consider biobjective shortest path problems in networks with fuzzy arc lengths. Considering the available studies for single objective shortest path problems in fuzzy networks, using a distance function for comparison of fuzzy numbers, we propose three approaches for solving the biobjective prob- lems. The rst and second approaches are extensions of the labeling method to solve the single objective problem and the third approach is based on dynamic programming. The labeling methods usually producing several nondominated paths, we propose a fuzzy number ranking method to determine a fuzzy short- est path. Illustrative examples are worked out to show the e ectiveness of our algorithms. | ||
| کلیدواژهها | ||
| Biobjective shortest path؛ Fuzzy network؛ Labeling method؛ Dynamic programming؛ Fuzzy ranking methods | ||
| مراجع | ||
|
\bibitem{baas1977rating} S. M. Baas and H.~Kwakernaak, {\it Rating and ranking of multiple-aspect alternatives using fuzzy sets}, Automatica, {\bf 13}\textbf{(1)} (1977), 47-58. \bibitem{baldwin1979comparison} J. F. Baldwin and N. C. F Guild, {\it Comparison of fuzzy sets on the same decision space}, Fuzzy Sets and Systems, {\bf 2}\textbf{(3)} (1979), 213-231. \bibitem{bellman1958routing} R.~Bellman, {\it On a routing problem, Quart}, J. Appl. Math, {\bf 16}\textbf{(1)} (1958), 87-90. \bibitem{bortolan1985review} G.~Bortolan and R.~Degani, {\it A review of some methods for ranking fuzzy subsets}, Fuzzy Sets and Systems, {\bf 15}\textbf{(1)} (1985), 1-19. \bibitem{brumbaugh1989empirical} D.~Brumbaugh-Smith and D. Shier, {\it An empirical investigation of some bicriterion shortest path algorithms}, European Journal of Operational Research, {\bf 43}\textbf{(2)} (1989), 216-224. \bibitem{campos1989subjective} L.~Campos and A.~Munoz, {\it A subjective approach for ranking fuzzy numbers}, Fuzzy Sets and Systems, {\bf 29}\textbf{(12)} (1989), 145-153. \bibitem{chanas1995fuzzy} S.~Chanas, M.~Delgado, J. L. Verdegay, and M. A. Vila, {\it Fuzzy optimal flow on imprecise structures}, European Journal of Operational Research, {\bf 83}\textbf{(3)} (1995), 568-580. \bibitem{chang1981ranking} W.~Chang, {\it Ranking of fuzzy utilities with triangular membership functions}, In Proc. Int. Conf. of Policy Anal. and Inf. Systems, (1981), 263-272. \bibitem{chen1985ranking} S. H. Chen, {\it Ranking fuzzy numbers with maximizing set and minimizing set}, Fuzzy Sets and Systems, {\bf 17}\textbf{(2)} (1985), 113-129. \bibitem{choobineh1993index} F.~Choobineh and H.~Li, {\it An index for ordering fuzzy numbers}, Fuzzy Sets and Systems, {\bf 54}\textbf{(3)} (1993), 287-294. \bibitem{delgado1990valuation} M.~Delgado, J. L. Verdegay and M. A. Vila, {\it On valuation and optimization problems in fuzzy graphs: a general approach and some particular cases}, INFORMS Journal on Computing, {\bf 2}\textbf{(1)} (1990), 74. \bibitem{dijkstra1959note} E. W. Dijkstra, {\it A note on two problems in connexion with graphs}, Numerische mathematik, {\bf 1}\textbf{(1)} (1959), 269-271. \bibitem{dreyfus1969appraisal} S. E. Dreyfus, {\it An appraisal of some shortest-path algorithms}, Operations Research, {\bf 17}\textbf{(3)} (1969), 395-412. \bibitem{dubois1978algorithmes} D.~Dubois and H.~Prade, {\it Algorithmes de plus courts chemins pour traiter des donnees floues. RAIRO-Recherche Op{\'e}rationnelle}, Operations Research, {\bf 12}(1978), 212--227. \bibitem{dubois1980fuzzy} D.~Dubois and H.~Prade, {\it Fuzzy sets and systems: theory and applications}, Academic Pr, 1980. \bibitem{furukawa1994parametric} N.~Furukawa, {\it A parametric total order on fuzzy numbers and a fuzzy shortest route problem}, Optimization, {\bf 30}\textbf{(4)} (1994), 367-377. \bibitem{hansen1980bicriterion} P.~Hansen, {\it Bicriterion path problems}, In Multiple criteria decision making: theory and application: proceedings of the third conference, Hagen/K{\`e}onigswinter, West Germany, August 20-24, (1979), 109, Springer, 1980. \bibitem{helgason1995primal} R.V. Helgason and J. L. Kennington, {\it Primal simplex algorithms for minimum cost network flows}, Handbooks in Operations Research and Management Science, {\bf 7} (1995), 85-133. \bibitem{huarng1996computational} F.~Huarng, P. Pulat, and L. S. Shih, {\it A computational comparison of some bicriterion shortest path algorithms}, Journal of the Chinese Institute of Industrial Engineers, {\bf 13}\textbf{(2)} (1996), 121-125. \bibitem{klein1991fuzzy} C. M. Klein, {\it Fuzzy shortest paths}, Fuzzy Sets and Systems, {\bf 39}\textbf{(1)} (1991), 27-41. \bibitem{k—czy1992fuzzy} L. T. K{\'o}czy, {\it Fuzzy graphs in the evaluation and optimization of networks}, Fuzzy Sets and Systems, {\bf 46}\textbf{(3)} (1992), 307-319. \bibitem{lin1993fuzzy} K. C. Lin and M. S. Chern, {\it The fuzzy shortest path problem and its most vital arcs}, Fuzzy Sets and Systems, {\bf 58}\textbf{(3)} (1993), 343-353. \bibitem{liou1992ranking} T. S. Liou and M. J. J. Wang, {\it Ranking fuzzy numbers with integral value}, Fuzzy Sets and Systems, {\bf 50}\textbf{(3)} (1992), 247-255. \bibitem{mahdavi2009dynamic} I.~Mahdavi, R.~Nourifar, A.~Heidarzade and N. M. Amiri, {\it A dynamic programming approach for finding shortest chains in a fuzzy network}, Applied Soft Computing, {\bf 9}\textbf{(2)} (2009), 503-511. \bibitem{martins1984multicriteria} E. Q. V. Martins, {\it On a multicriteria shortest path problem}, European Journal of Operational Research, {\bf 16}\textbf{(2)} (1984), 236-245. \bibitem{ishwar1991parametric} J.~Mote, I.Murthy and D. L. Olson {\it A parametric approach to solving bicriterion shortest path problems}, European Journal of Operational Research, {\bf 53}\textbf{(1)} (1991), 81-92. \bibitem{namorado1982bicriterion} J. C. Namorado~Climaco and E.~Queiros Vieira~Martins, {\it A bicriterion shortest path algorithm}, European Journal of Operational Research, {\bf 11}\textbf{(4)} (1982), 399-404. \bibitem{okada2000shortest} S.~Okada and T.~Soper, {\it A shortest path problem on a network with fuzzy arc lengths}, Fuzzy Sets and Systems, {\bf 109}\textbf{(1)} (2000), 129-140. \bibitem{prade1979using} H.~Prade, {\it Using fuzzy set theory in a scheduling problem: a case study}, Fuzzy Sets and Systems, {\bf 2}\textbf{(2)} (1979), 153-165. \bibitem{przybylski2008two} A.~Przybylski, X.~Gandibleux and M.~Ehrgott, {\it Two phase algorithms for the bi-objective assignment problem}, European Journal of Operational Research, {\bf 185}\textbf{(2)} (2008), 509-533. \bibitem{ram’k1985inequality} J. Ram{\'\i}k and J. Rimanek, {\it Inequality relation between fuzzy numbers and its use in fuzzy optimization}, Fuzzy Sets and Systems, {\bf 16}\textbf{(2)} (1985), 123-138. \bibitem{saade1992ordering} J. J. Saade and H.~Schwarzlander, {\it Ordering fuzzy sets over the real line: an approach based on decision making under uncertainty}, Fuzzy Sets and Systems, {\bf 50}\textbf{(3)} (1992), 237-246. \bibitem{sadeghpour2001distance} B.~Sadeghpour~Gildeh and D.~Gien, {\it La distance-Dp, q et le cofficient de corr{\'e}lation entre deux variables al{\'e}atoires floues}, Actes de LFA, (2001), 97-102. \bibitem{serafini1987some} P.~Serafini, {\it Some considerations about computational complexity for multi objective combinatorial problems}, In Recent Advances and Historical Development of Vector Optimization: Proceedings of an International Conference of Vector Optimization Held at the Technical University of Darmstadt, FRG, August 4-7, (1986), 222, Springer, 1987. \bibitem{skriver2000label} A. J. V. Skriver and K. A. Andersen, {\it A label correcting approach for solving bicriterion shortest-path problems}, Computers \& Operations Research, {\bf 27}\textbf{(6)} (2000), 507-524. \bibitem{skriver2000classification} A. J. V. Skriver, {\it A classification of bicriterion shortest path (BSP) algorithms}, Asia Pacific Journal of Operational Research, {\bf 17}\textbf{(2)} (2000), 199-212. \bibitem{TajdinMahdavi2010} A.~Tajdin, I.~Mahdavi, N.~Mahdavi-Amiri and B.~Sadeghpour-Gildeh, {\it Computing a fuzzy shortest path in a network with mixed fuzzy arc lengths using $\alpha$ -cuts}, Computer and Mathematics with Applications, 2010. \bibitem{tung1988bicriterion} C. T. Tung and K. L. Chew, {\it A bicriterion Pareto-optimal path algorithm}, ASIA-PACIFIC J. OPER. RES., {\bf 5}\textbf{(2)} (1988), 166-172. \bibitem{tung1992multicriteria} C.~Tung and K.~Lin~Chew, {\it A multicriteria Pareto-optimal path algorithm}, European Journal of Operational Research, {\bf 62}\textbf{(2)} (1992), 203-209. \bibitem{wang1997comparative} X.~Wang, {\it A comparative study of the ranking methods for fuzzy quantities}, Ghent University, Ghent, 1997. \bibitem{wang2001reasonable} X.~Wang and E. E. Kerre, {\it Reasonable properties for the ordering of fuzzy quantities (I)}, Fuzzy Sets and Systems, {\bf 118}\textbf{(3)} (2001), 375-385. \bibitem{wang2001reasonable2} X.~Wang and E. E. Kerre, {\it Reasonable properties for the ordering of fuzzy quantities (II)}, Fuzzy Sets and Systems, {\bf 118}\textbf{(3)} (2001), 387-405. \bibitem{yager1980general} R. A. Yager, {\it On a general class of fuzzy connectives}, Fuzzy sets and Systems, {\bf 4}\textbf{(3)} (1980), 235-242. \bibitem{yager1986paths} R. A. Yager, {\it Paths of least resistance in possibilistic production systems}, Fuzzy Sets and Systems, {\bf 19}\textbf{(2)} (1986), 121-132. \bibitem{zadeh1965fuzzy} L. A. Zadeh, {\it Fuzzy sets}, Information and control, {\bf 8}\textbf{(3)} (1965), 338-353. | ||
|
آمار تعداد مشاهده مقاله: 2,813 تعداد دریافت فایل اصل مقاله: 2,319 |
||