Abstract
The material in this section is taken from [36].
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References
Adamo, J.H., Fuzzy decision trees, Fuzzy Sets and Systems, 4 (1980) 207–219.
Behzad, M., Chartrand, G., and Lesniak-Foster, L., Graphs and Diagraphs, Wadsworth International, Belmont, CA, 1979.
Bellman, R. and Klaba R., On kth best policies, J. of Siam. 8 (1960) 582–585.
Bollabas, B., Random Graphs, Academic Press, London, 1985.
Bonissone, P.P., Summarizing and propogating uncertain information with triangular norms, Internat. J. Approximate Reasoning, 1 (1987) 71–101.
Bortolan, G. and Degani, R., A review of some methods for ranking fuzz subsets, Fuzzy Sets and Systems, 16 (1985), 1–19.
Carrayway, R. and Morin, T., Monotonicity, preference structures and principles of optimality, Computational Combinatorics, URI Technical Report CC-86–3, Purdue University, West Lafayette, In, 1986.
Chanas, S., Fuzzy optimization in networks, In: Operation Models Using Fuzzy Sets and Possibility Theory, Eds.: J. Kacprzyk and S.A. Orlovski, D. Reidel Publishing Co., 1987, 303–327.
Chanas, S. and Kamburowski, The use of variables in PERT, Fuzzy Sets and Systems, 5 (1981) 11–19.
Chanas, S. and Kolodziejczynk, W., Maximum flow in a network with fuzzy arc capacities, Fuzzy Sets and Systems, 8 (1982) 165–173.
Chanas, S. and Kolodziejczynk, W., Integer flows in networks with fuzzy capacity constraints, Inst. of Management, Tech. Univ. of Wroclaw, Report 368 (1982).
Chanas, S. and Kolodziejczynk, W., Real-valued flows in a network with fuzzy arc capacities, Fuzzy Sets and Systems, 13 (1984) 139–151.
Chanas, S. and Kolodziejczynk, W., Integer flows in network with fuzzy capacity constraints, Networks, 16 (1986) 17–32.
Delgado, M., Verdegay, J. L., and Vila, M. A., On fuzzy tree definition, European J. Oper. Res., 22 (1985) 243–249.
Delgado, M., Verdegay, J.L,. and Vila, M.A., El problema del arbol generador minimal para grafos disusos, Trabajos de Investigacion Operativa, 2 (1987) 3–20.
Delgado, M., Verdegay, J.L., and Vila, M.A., Fuzzy transportation problems: A general analysis, in J. Kacprzyk and S. Orlovski (eds.), Optimization Models Using Fuzzy Sets and Possibility Theory, P. Reidel, Dordrecht, The Netherlands, 1987, 342–358.
Delgado, M., Verdegay, J. L. and Vila, M. A., On valuation and optimization problems in fuzzy graphs: a general approach and some particular cases, ORSA J. Comput., 2 (1990) 74–83.
Dubois, D. and Prade, H., Algorithmes de plus court chemins pour trater des donnees flous, R.A.I.R.O. Recherche Operationelle/Operational Research, 12 (1978) 214–227.
Dubois, D. and Prade, H., Fuzzy Sets and System, Academic Press, New York 1980.
Dubois, D., Farreny, H. and Prade, H., Combinatorial search with fuzzy estimates, in J. Kacprzyk and S. Orlovski (eds.), Optimization Models Using Fuzzy Sets and Possibility Theory, P. Reidel, Dordrecht, The Netherlands, 1987, 171–185.
Fujishige, S., Submodular systems and related topics, Math. Programming Study, 22 (1984) 113–131.
Garey, M.R. and Johnson, D.S., Computers and Interactability: A Guide to the Theory of NP-Completéness, Freeman, San Francisco, CA, 1979.
Gonzalez, A., Metodso Subjetivos para la Comparacion de Numeros Difusos, Ph. D. Thesis, University of Granada, 1987.
Gonzalez, A. and Vila, M.A., A discrete method to study indifference and order relations between fuzzy numbers, Inform. Sci., 56 (1991) 245–258.
Gonzalez, A. and Vila, M.A., Dominance relation on fuzzy numbers, submitted to Inform. Sci., 64 (1992) 1–16.
Händler, W., Multiprocessors: Efficiency and fault tolerance, in: Architektur and Betrieb von Rechensystemen (NTG-Fachberichte 92, VDE-Verlag, Berlin-Offenbach, 1986), 7–29 (in German).
Hearn, D.W., Lawphongpanich, S., and Ventura J.A., Restricted simplicial decomposition: Computation and extensions, Math. Programming Study, 31 (1987) 99–118.
Ignizio, J. and Daniels, S., Fuzzy multicriteria integer programming via fuzzy generalized networks, Fuzzy Sets and Systems, 10 (1983) 261–270.
Itakura, H. and Nishikawa, Y., Fuzzy network technique for technological forecasting, Fuzzy Sets and Systems, 14 (1984) 99–113.
Jensen, P. and Barnes, J., Network Flow Programming, John Wiley and Sons, New York, 1980.
Katsumata Y., Tsuda E. and Yamashita H., Fuzzy clustering and ordering. Instructional Analysis Applying Fuzzy Graphs, preprints of International Workshop on Fuzzy Systems Applications, Fukuoka, Japan, 1988.
Katsumata, Y., Tsuda, E. and Yamashita, H., The difference of two fuzzy graphs, preprints of International Workshop on Fuzzy Systems Applications, Fukuoka, Japan, 1988.
Kaufman, A., Introduction to the Theroy of Fuzzy Sets, Vol. 1, Academic Press, New York, 1975.
Kauffman, A., Introduction a la Theorie des Sousensambles, Vol 1. Flous, Masson et Cie, Paris, France, 1977.
Kim, K.H. and Roush, F.W., Fuzzy flows on networks, Fuzzy Sets and Systems, 8 (1982) 35–38.
Klein, C. M., Fuzzy shortest paths, Fuzzy Sets and Systems, 39 (1991) 27–41.
Klein, C., A model for transportation of hazardous waste, Department of Industrial Engineering, University of Missouri-Columbia, working paper series #1210388 (1988).
Klein, C.M. and Yeralan, S., Network flow models with fuzzy auxilary edge and vertex attributes, in J.L. Chameau and J. Yao, Eds, Proc. of Nafips Workship, Purdue University, West Lafayette, IN (May 5–7, 1987) 431–444.
Koczy L.T., Fuzzy trees in distributed systems design, preprints of International Workshop on Fuzzy Systems Applications, Fukuoka, Japan, 1988.
Lawler, E., Combinatorial Optimization; Networks and Matroids, Holt Reinhart and Winston, New York 1976.
Lovász, D. L., Submodular functions and convexity in: A. Bachem, M. Grötschel and B. Korte, Eds., Mathematical Programming the State of the Art-Bonn 1982 (Springer-Verlag, New York, 1983) 235–257.
Mares, M. and Horak, J., Fuzzy quantities in networks, Fuzzy Sets and Systems, 10 (1988) 123–134.
McAllister, M., Fuzzy matrices and diagraphs, Communications of First I.F.S.A Congress, Mallorca, Spain, 1985.
Morioka, M. and Yamasita, H., Extraction method of difference between fuzzy graphs, preprints of IFAC Symposium on Fuzzy Information, Knowledge Representation and Decision Analysis, (Marseille, France) E. Sanchez and M.M. Gupta (eds.), Pergamon Press, New York, 1983.
Nair, P.S., Extension principle revisited, JCIS’98, Vol. II, (1998) 11–14.
Rosenfeld, A., Fuzzy graphs, In: Zadeh, L.A., Fu, K.S., Tanaka, K., and Shimura, M., eds, Fuzzy Sets and Their Applications to Cognitive and Decision Processes, Academic Press, New York, 1975, 75–95.
Takeya M., A clustering method for a fuzzy diagraph based on connectedness and its applications to instructional evaluation, preprints of IFAC Symposium on Fuzzy Information, Knowledge Repsentaion and Decision Analysis, (Marseille, France) E. Sanchez and M. M. Gupta (eds.), Pergamon Press, New York, 1983.
Ventura, J.A. and Klein, C. M., An algorithm for certain convex network problems, AMSE Rev., 8 (1988) 31–42.
Yager R., Paths of least resistence in possibilistic production systems, Fuzzy Sets and Systems, 19 (1986) 121–132.
Yeh R.T. and Bang S.Y., Fuzzy relations, fuzzy graphs, and their applications to clustering analysis, In: Zadeh, L.A., Fu, K.S., Tanaka, K., and Shimura, M., eds., Fuzzy Sets and Their Applications to Cognitive Decision Processes, Academic Press, London, 1975, 125–150.
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Malik, D.S., Mordeson, J.N. (2000). Fuzzy Graphs and Shortest Paths. In: Fuzzy Discrete Structures. Studies in Fuzziness and Soft Computing, vol 58. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1838-3_4
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