Solving the Shortest Path Problem with Interval Arcs

This paper presents an algorithm for the shortest path problem when the connected arcs in a transportation network are represented as interval numbers. The methodology proposed in this paper considers fuzzy preference ordering of intervals (Sengupta and Pal (2000), European Journal of Operational Research 127, 28–43) from pessimistic and optimistic decision maker’s point of view.

[1]  Sukhamay Kundu,et al.  Min-transitivity of fuzzy leftness relationship and its application to decision making , 1997, Fuzzy Sets Syst..

[2]  Robert Lowen,et al.  On fuzzy complements , 1977, 1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications.

[3]  J. Yen,et al.  Fuzzy Logic: Intelligence, Control, and Information , 1998 .

[4]  Debjani Chakraborty,et al.  Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming , 2001, Fuzzy Sets Syst..

[5]  G. Alefeld,et al.  Introduction to Interval Computation , 1983 .

[6]  H. Zimmermann,et al.  Fuzzy Set Theory and Its Applications , 1993 .

[7]  Hans Schjaer-Jacobsen.  A new method for evaluating worst- and best-case (WBC) economic consequences of technological development , 1996 .

[8]  Hans-Jürgen Zimmermann,et al.  Fuzzy Set Theory - and Its Applications , 1985 .

[9]  H. Ishibuchi,et al.  Multiobjective programming in optimization of the interval objective function , 1990 .

[10]  H. Schjaer-Jacobsen,et al.  Representation and calculation of economic uncertainties: Intervals, fuzzy numbers, and probabilities , 2002 .

[11]  Mitsuo Gen,et al.  Order Relation between Intervals and Its Application to Shortest Path Problem , 1994 .

[12]  Ramon E. Moore.  Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.

[13]  Tapan Kumar Pal,et al.  On comparing interval numbers , 2000, Eur. J. Oper. Res..