Document Type: Research Paper


1 Department of Mathematics, Jhargram Raj College, Jhargram, West Bengal, 721 507, India

2 Madhumangal Pal, Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal, 721 102, India


Here we consider the
p-center problem on different types of fuzzy
networks. In particular, we are interested in the networks with interval and
triangular fuzzy arc lengths and vertex-weights. A methodology to obtain the
best satisfaction level of the decision maker who wishes to reduce the cost
within the tolerance limits is proposed. Illustrative examples are provided.


[1] A. Al-khedhairi and S. Salhi,Enhancement to two exact algorithms for solving the vertex

p-center problem, Journal of Mathematical Modelling and Algorithms, 4(2) (2005), 129-147.

[2] D. Bespamyatnikh, B. Bhattacharya, M. Keil, D. Kirkpatric and D. Segal,Efficient algorithms

for centers and medians in interval and circular-arc graphs, Networks, 39 (1979),144-152.

[3] M. J. Can´os, C. Ivorra and V. Liern,An exact algorithm for the fuzzy p-median problem,

European Journal of Operational Research,116 (1999), 80-86.

[4] M. J. Can´os, C. Ivorra and V. Liern,The fuzzy p-median problem : a global analysis of the

solutions, European Journal of Operational Research, 130 (2001), 430-436.

[5] S. Chanas, M. Delgado, J. L. Verdegay and M. A. Vila,Fuzzy optimal flow on a imprecise

structures, European Journal of Operational Research, 83 (1995), 568-580.

[6] S. Chanas and W. Kolodziejczyk,Maximum flow in a network with fuzzy arc capacities,

Fuzzy Sets and Systems,8 (1982), 165-173.

[7] S. Chanas and W. Kolodziejczyk,Real valued flows in a network with fuzzy arc capacities,

Fuzzy Sets and Systems,13 (1984), 139-151.

[8] P. -T. Chang and E. S. Lee,Ranking fuzzy sets based on the concept of existence, Computers

and Mathematics with Applications,27 (1994), 1-21.

[9] P. -T. Chang and E. S. Lee,Fuzzy decision networks and deconvolution, Computers and

Mathematics with Applications,37 (1999), 53-63.

[10] R. Chandrasekharan and A. Tamir,Polynomial bounded algorithms for locating p-centers on

a tree, Mathematics in Programming, 22 (1982), 304-315.

[11] M. Daskin,Network and discrete location, Wiley, NewYork, 1995.


[12] M. Delgado, J. L. Verdegay and M. A. Vila,On fuzzy tree definition, European Journal of

Operational Research,22 (1985), 243-249.

[13] M. Delgado, J. L. Verdegay and M. A. Vila,A procedure for ranking fuzzy numbers using

fuzzy relations, Fuzzy Sets and Systems, 26 (1988), 49-62.

[14] M. Delgado, J. L. Verdegay and M. A. Vila,On valuation and problems in fuzzy graphs : a

general approach and some particular cases, ORSA Journal on Computing, 2 (1990), 74-84.

[15] H. Y. Handler and P. B. Mirchandani,Location on networks : theory and algorithms, MIT

Press, Cambridge, MA, 1979.


[16] F. Herrera and J. L. Verdegay,Three models of fuzzy integer linear programming, European

Journal of Operational Research,83 (1995), 581-593.

[17] O. Kariv and S. L. Hakimi,An algorithmic approach to network location problems, I: the

p-centers, SIAM Journal of Applied Mathematics, 37 (1979), 513-538.

[18] A. Kaufmann and M. M. Gupta,Introduction to fuzzy arithmetic : theory and applications,

Van Nostrand Reinhold, New York, 1985.


[19] P. B. Mirchandani and R. L. Francis,Discrete location theory, Wiley, New York, 1990.

[20] N. Mledanovic, M. Labb´e and P. Hansen,Solving the p-center problem with tabu search and

variable neighborhood search, Networks, 42(1) (2003), 48-64.

[21] R. E. Moore,Method and application of interval analysis, SIAM, Philadelphia, 1979.

[22] J. N. Mordeson and P. S. Nair,Fuzzy graphs and fuzzy hypergraphs, Studies in fuzzyness and

soft computing, Physica-Verlag, Wurzburg, 2000.

[23] J. A. Moreno P´erez, J. M. Moreno Vega and J. L. Verdegay,Fuzzy location problems on

networks, Fuzzy Sets and Systems, 142 (2004), 393-405.

[24] S. M. A. Nayeem and M. Pal,Genetic algorithm to solve p-center and p-radius problem on

a network, International Journal of Computer Mathematics, 82 (2005), 541-550.

[25] S. M. A. Nayeem and M. Pal,Shortest path problem on a network with imprecise edge weight,

Fuzzy Optimization and Decision Making,4 (2005), 293-312.

[26] S. M. A. Nayeem and M. Pal,PERT on a network with imprecise edge weight, communicated.

[27] S. Okada and T. Soper,A shortest path problem on a network with fuzzy arc lengths, Fuzzy

Sets and Systems,109 (2000), 129-140.

[28] F. A. ¨Ozsoy and MC¸ . Pinar,An exact algorithm for the capacitated vertex p-center problem,

Computers and Operations Research,33(5) (2006), 1420-1436.

[29] A. Rosenfeld,Fuzzy graph, In: L. A. Zadeh, K. S. Fu, K. Tanaka and M. Shimura Eds.,

Fuzzy sets and their application to cognitive and decision processes, Academic Press, New

York, (1975), 79-97.


[30] A. Sengupta, T. K. Pal,On comparing interval numbers, European Journal of Operational


127 (2000), 28-43.

[31] J. K. Sengupta,Optimal decision under uncertainty, Springer, New York, 1981.

[32] A. Tamir,Improved complexity bounds for center location problems on networks by using

dynamic data structures, SIAM Journal of Discrete Mathematics, 1 (1988), 377-396.

[33] L. A. Zadeh,Fuzzy sets, Information and Control, 8 (1965), 338-353.