Fuzzy Dijkstra algorithm for shortest path problem under uncertain environment

A common algorithm to solve the shortest path problem (SPP) is the Dijkstra algorithm. In this paper, a generalized Dijkstra algorithm is proposed to handle SPP in an uncertain environment. Two key issues need to be addressed in SPP with fuzzy parameters. One is how to determine the addition of two edges. The other is how to compare the distance between two different paths with their edge lengths represented by fuzzy numbers. To solve these problems, the graded mean integration representation of fuzzy numbers is adopted to improve the classical Dijkstra algorithm. A numerical example of a transportation network is used to illustrate the efficiency of the proposed method.

[1]  Yong Deng,et al.  A new fuzzy dempster MCDM method and its application in supplier selection , 2011, Expert Syst. Appl..

[2]  Deng Yong.  Plant location selection based on fuzzy TOPSIS , 2006 .

[3]  Qi Liu,et al.  A new similarity measure of generalized fuzzy numbers and its application to pattern recognition , 2004, Pattern Recognit. Lett..

[4]  Ming-Lang Tseng,et al.  Green supply chain management with linguistic preferences and incomplete information , 2011, Appl. Soft Comput..

[5]  Y. Q. Liu,et al.  An improved Dijkstra's shortest path algorithm for sparse network , 2007, Appl. Math. Comput..

[6]  Jung-Yuan Kung,et al.  A new algorithm for the discrete fuzzy shortest path problem in a network , 2006, Appl. Math. Comput..

[7]  Chien-Chang Chou,et al.  Application of FMCDM model to selecting the hub location in the marine transportation: A case study in southeastern Asia , 2010, Math. Comput. Model..

[8]  Chien-Chang Chou,et al.  An integrated quantitative and qualitative FMCDM model for location choices , 2010, Soft Comput..

[9]  Ming-Lang Tseng,et al.  Using linguistic preferences and grey relational analysis to evaluate the environmental knowledge management capacity , 2010, Expert Syst. Appl..

[10]  N. Mahdavi-Amiri,et al.  Computing a fuzzy shortest path in a network with mixed fuzzy arc lengths using α-cuts , 2010 .

[11]  Pei-Chann Chang,et al.  A Fuzzy Multiple Criteria Decision Making Model for Selecting the Distribution Center Location in China: A Taiwanese Manufacturer's Perspective , 2009, HCI.

[12]  Iraj Mahdavi,et al.  A dynamic programming approach for finding shortest chains in a fuzzy network , 2009, Appl. Soft Comput..

[13]  Xin-She Yang,et al.  Introduction to Algorithms , 2021, Nature-Inspired Optimization Algorithms.

[14]  C. Chou.  A FUZZY BACKORDER INVENTORY MODEL AND APPLICATION TO DETERMINING THE OPTIMAL EMPTY-CONTAINER QUANTITY AT A PORT , 2009 .

[15]  Ronald R. Yager,et al.  A procedure for ordering fuzzy subsets of the unit interval , 1981, Inf. Sci..

[16]  A. Boulmakoul.  Generalized path-finding algorithms on semirings and the fuzzy shortest path problem , 2004 .

[17]  Mehdi Ghatee,et al.  Application of fuzzy minimum cost flow problems to network design under uncertainty , 2009, Fuzzy Sets Syst..

[18]  Xing Pan,et al.  A fuzzy synthetic evaluation method for failure risk of aviation product R&D project , 2010, 2010 IEEE International Conference on Management of Innovation & Technology.

[19]  Ch.-Ch Chou.  The canonical representation of multiplication operation on triangular fuzzy numbers , 2003 .

[20]  Ying Wu,et al.  A new linguistic MCDM method based on multiple-criterion data fusion , 2011, Expert Syst. Appl..

[21]  Deng Yong,et al.  A new similarity measure of generalized fuzzy numbers and its application to pattern recognition , 2004 .

[22]  Ming-Cheng Tsou,et al.  Application of a mixed fuzzy decision making and optimization programming model to the empty container allocation , 2010, Appl. Soft Comput..

[23]  Iraj Mahdavi,et al.  Computing a fuzzy shortest path in a network with mixed fuzzy arc lengths using alpha-cuts , 2010, Comput. Math. Appl..

[24]  Xiaoyu Ji,et al.  New models for shortest path problem with fuzzy arc lengths , 2007 .

[25]  Yong Deng,et al.  Modeling contaminant intrusion in water distribution networks: A new similarity-based DST method , 2011, Expert Syst. Appl..

[26]  Clifford Stein,et al.  Introduction to Algorithms, 2nd edition. , 2001 .

[27]  Jeng-Ming Yih,et al.  An evaluation of airline service quality using the fuzzy weighted SERVQUAL method , 2011, Appl. Soft Comput..

[28]  Jun Ye,et al.  Cosine similarity measures for intuitionistic fuzzy sets and their applications , 2011, Math. Comput. Model..

[29]  Drakoulis Martakos,et al.  In-depth analysis and simulation study of an innovative fuzzy approach for ranking alternatives in multiple attribute decision making problems based on TOPSIS , 2011, Appl. Soft Comput..

[30]  M. Tseng,et al.  Evaluating firm's green supply chain management in linguistic preferences , 2013 .

[31]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[32]  Maw-Sheng Chern,et al.  The fuzzy shortest path problem and its most vital arcs , 1993 .

[33]  Solomon Tesfamariam,et al.  Risk analysis in a linguistic environment: A fuzzy evidential reasoning-based approach , 2011, Expert Syst. Appl..

[34]  Ming-Lang Tseng,et al.  Using a hybrid MCDM model to evaluate firm environmental knowledge management in uncertainty , 2011, Appl. Soft Comput..

[35]  Esmaile Khorram,et al.  Preemptive priority-based algorithms for fuzzy minimal cost flow problem: An application in hazardous materials transportation , 2009, Comput. Ind. Eng..

[36]  Huawen Liu,et al.  New similarity measures between intuitionistic fuzzy sets and between elements , 2005, Math. Comput. Model..

[37]  Wei Chen,et al.  Fuzzy portfolio selection problem under uncertain exit time , 2009, 2009 IEEE International Conference on Fuzzy Systems.

[38]  Drakoulis Martakos,et al.  A utility-based fuzzy TOPSIS method for energy efficient network selection in heterogeneous wireless networks , 2012, Appl. Soft Comput..

[39]  ChamodrakasIoannis,et al.  A utility-based fuzzy TOPSIS method for energy efficient network selection in heterogeneous wireless networks , 2011 .

[40]  Qi Rong-guang,et al.  Research on comprehensive evaluation of enterprises knowledge management capabilities , 2010, 2010 International Conference on Management Science & Engineering 17th Annual Conference Proceedings.

[41]  Jung-Yuan Kung,et al.  The fuzzy shortest path length and the corresponding shortest path in a network , 2005, Comput. Oper. Res..

[42]  Keeheon Lee,et al.  Agent-based diffusion model for an automobile market with fuzzy TOPSIS-based product adoption process , 2011, Expert Syst. Appl..

[43]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[44]  Shiang-Tai Liu,et al.  Network flow problems with fuzzy arc lengths , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[45]  Xin Lu,et al.  Finding the shortest paths by node combination , 2011, Appl. Math. Comput..

[46]  S. Tesfamariam,et al.  Developing environmental indices using fuzzy numbers ordered weighted averaging (FN-OWA) operators , 2008 .

[47]  Ming-Cheng Tsou,et al.  Application of a combined fuzzy multiple criteria decision making and optimization programming model to the container transportation demand split , 2010, Appl. Soft Comput..

[48]  Esmaile Khorram,et al.  A fuzzy shortest path with the highest reliability , 2009 .