185
Views
12
CrossRef citations to date
0
Altmetric
Original Articles

Fuzzy α-minimum spanning tree problem: definition and solutions

, , &
Pages 311-335 | Received 10 Aug 2014, Accepted 27 Jan 2015, Published online: 12 Apr 2016

References

  • Ahuja, R. K., T. L. Magnanti, and J. B. Orlin. 1993. Network Flows: Theory, Algorithms, and Applications. Englewood Cliffs, NJ: Prentice Hall.
  • Cayley, A. 1889. “A Theorem on Trees.” Quarterly Journal of Mathematics 23: 376–378.
  • Chang, P. T., and E. S. Lee. 1999. “Fuzzy Decision Networks and Deconvolution.” Computers & Mathematics with Applications 37 (11): 53–63.
  • Chiang, T. C., C. Liu, and Y. Huang. 2007. “A Near-optimal Multicast Scheme for Mobile Ad Hoc networks using a Hybrid Genetic Algorithm.” Expert Systems with Applications 33 (3): 734–742.
  • De Almeida, T. A., A. Yamakami, and M. T. Takahashi. 2005. “An Evolutionary Approach to Solve Minimum Spanning Tree Problem with Fuzzy Parameters.” In Proceedings of the International Conference on Computational Intelligence for Modelling, Control and Automation, November 28--30, 203–208. Vienna, Austria.
  • Dhamdhere, K., R. Ravi, and M. Singh. 2005. “On Two-stage Stochastic Minimum Spanning Trees.” In Integer Programming and Combinatorial Optimization, edited by M. Jünger and V. Kaibel, 321–334. Berlin: Springer.
  • Dubois, D., and H. Prade. 1988. Possibility Theory. New York: Pelnum Press.
  • Gao, J., and M. Lu. 2005. “Fuzzy Quadratic Minimum Spanning Tree Problem.” Applied Mathematics and Computation 164 (3): 773–788.
  • Gower, J. C., and G. J. S. Ross. 1969. “Minimum Spanning Trees and Single Linkage Cluster Analysis.” Applied Statistics 18: 54–64.
  • Graham, R. L., and P. Hell. 1985. “On the History of the Minimum Spanning Tree Problem.” Annals of the History of Computing 7 (1): 43–57.
  • Ishii, H., and T. Matsutomi. 1995. “Confidence Regional Method of Stochastic Spanning Tree Problem.” Mathematical and Computer Modelling 22 (10): 77–82.
  • Ishii, H., S. Shiode, T. Nishida, and Y. Namasuya. 1981. “Stochastic Spanning Tree Problem.” Discrete Applied Mathematics 3 (4): 263–273.
  • Itoh, T., and H. Ishii. 1996. “An Approach based on Necessity Measure to the Fuzzy Spanning Tree Problems.” Journal of the Operations Research Society of Japan 39 (2): 247–257.
  • Janiak, A., and A. Kasperski. 2008. “The Minimum Spanning Tree Problem with Fuzzy Costs.” Fuzzy Optimization and Decision Making 7 (2): 105–118.
  • Kruskal, J. B. 1956. “On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem.” Proceedings of the American Mathematical Society 7 (1): 48–50.
  • Liu, B. 2002. Theory and Practice of Uncertain Programming. Heidelberg: Physica-Verlag.
  • Liu, B. 2004. Uncertainty Theory. Berlin: Springer-Verlag.
  • Liu, B., and Y.-K. Liu. 2002. “Expected Value of Fuzzy Variable and Fuzzy Expected Value Models.” IEEE Transactions on Fuzzy Systems 10 (4): 445–450.
  • Öncan, T. 2007. “Design of Capacitated Minimum Spanning Tree with Uncertain Cost and Demand Parameters.” Information Sciences 177 (20): 4354–4367.
  • Osteen, R. E., and P. P. Lin. 1974. “Picture Skeletons based on Eccentricities of Points of Minimum Spanning Trees.” SIAM Journal on Computing 3 (1): 23–40.
  • Prim, R. C. 1957. “Shortest Connection Networks and Some Generalizations.” Bell System Technical Journal 36 (6): 1389–1401.
  • Prüfer, H. 1918. “Neuer beweis eines satzes über permutation [A New Proof of a Theorem on Permutations].” Archives of Mathematical Physics 27: 742–744.
  • Swamy, C., and D. B. Shmoys. 2006. “Approximation Algorithms for 2-stage Stochastic Optimization Problems.” Association for Computing Machinery Special Interest Group on Algorithms and Computation Theory 37 (1): 33–46.
  • Syswerda, G. 1989. “Uniform Crossover in Genetic Algorithms.” In Proceedings of the Third International Conference on Genetic Algorithms, San Mateo, CA, 2–9.
  • Torkestani, J. A. 2012. “Degree-constrained Minimum Spanning Tree Problem in Stochastic Graph.” Cybernetics and Systems 43 (1): 1–21.
  • Torkestani, J. A., and M. R. Meybodi. 2012. “A Learning Automata-based Heuristic Algorithm for Solving the Minimum Spanning Tree Problem in Stochastic Graphs.” The Journal of Supercomputing 59 (2): 1035–1054.
  • Zadeh, L. A. 1978. “Fuzzy Sets as a Basis for a Theory of Possibility.” Fuzzy Sets and Systems 1: 3–28.
  • Zadeh, L. A. 1979. “A Theory of Approximate Reasoning.” Machine Intelligence 9: 149–194.
  • Zhou, G., and M. Gen. 1998. “An Effective Genetic Algorithm Approach to the Quadratic Minimum Spanning Tree Problem.” Computers and Operations Research 25 (3): 229–237.
  • Zhou, G., and M. Gen. 1999. “Genetic Algorithm Approach on Multi-criteria Minimum Spanning Tree Problem.” European Journal of Operational Research 114 (1): 141–152.
  • Zhou, J., F. Yang, and K. Wang. 2016. “Fuzzy Arithmetic on LR Fuzzy Numbers with Applications to Fuzzy Programming.” Journal of Intelligent & Fuzzy Systems. 30 (1): 71–87.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.