Document Type: Research Paper
Authors
^{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
Abstract
Keywords
[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
Research,
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.