zbMATH — the first resource for mathematics

New Pareto approach for ranking triangular fuzzy numbers. (English) Zbl 1418.90289
Laurent, Anne (ed.) et al., Information processing and management of uncertainty in knowledge-based systems. 15th international conference, IPMU 2014, Montpellier, France, July 15–19, 2014. Proceedings. Part II. Cham: Springer. Commun. Comput. Inf. Sci. 443, 264-273 (2014).
Summary: Ranking fuzzy numbers is an important aspect in dealing with fuzzy optimization problems in many areas. Although so far, many fuzzy ranking methods have been discussed. This paper proposes a new Pareto approach over triangular fuzzy numbers. The approach is composed of two dominance stages. In the first stage, mono-objective dominance relations are introduced and tested with some examples. In the second stage, a Pareto dominance is defined for multi-objective optimization and then applied to solve a vehicle routing problem (VRP).
For the entire collection see [Zbl 1385.68006].

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
03E72 Theory of fuzzy sets, etc.
Full Text: DOI
[1] Abbasbandy, S., Asady, B.: Ranking of fuzzy numbers by sign distance. Information Sciences 176(16), 2405-2416 (2006) · Zbl 1293.62008
[2] Boukezzoula, R., Galichet, S., Foulloy, L.: MIN and MAX operators for fuzzy intervals and their potential use in aggregation operators. IEEE Transactions on Fuzzy Systems 15(6), 1135-1144 (2007)
[3] Chen, S.: Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets and Systems 17(3), 113-129 (1985) · Zbl 0618.90047
[4] Cheng, C.: A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets and Systems 95(3), 307-317 (1998) · Zbl 0929.91009
[5] Chu, T., Tsao, C.: Ranking fuzzy numbers with an area between the centroid point and original point. Computers and Mathematics with Applications 43(1), 111-117 (2002) · Zbl 1113.62307
[6] Deb, K., et al.: A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization: NSGAII. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 849-858. Springer, Heidelberg (2000)
[7] Ezzati, R., Allahviranloo, T., Khezerloo, M.: An approach for ranking of fuzzy numbers. Expert Systems with Applications 43(1), 690-695 (2012)
[8] Bortolan, G., Degam, R.: A review of some methods for ranking fuzzy subsets. Fuzzy Sets Systems 15, 1-19 (1985) · Zbl 0567.90056
[9] Kaufmann, A., Gupta, M.: Fuzzy Mathematical Models in Engineering and Management Science. Elsevier Science, New York (1988) · Zbl 0683.90024
[10] Boulmakoul, A., Laarabi, M.H., Sacile, R., Garbolino, E.: Ranking Triangular Fuzzy Numbers Using Fuzzy Set Inclusion Index. In: Masulli, F. (ed.) WILF 2013. LNCS (LNAI), vol. 8256, pp. 100-108. Springer, Heidelberg (2013) · Zbl 06344562
[11] Limbourg, P., Daniel, E.S.: An Optimization Algorithm for Imprecise Multi-Objective Problem Functions. Evolutionary Computation 1, 459-466 (2005)
[12] Liefooghe, A., Basseur, M., Jourdan, L., Talbi, E.-G.: ParadisEO-MOEO: A Framework for Evolutionary Multi-objective Optimization. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T., et al. (eds.) EMO 2007. LNCS, vol. 4403, pp. 386-400. Springer, Heidelberg (2007)
[13] Paquet, L.F.: Stochastic Local Search algorithms for Multi-objective Combinatorial Optimization: A review. In: Handbook of Approximation Algorithms and Metaheuristics, vol. 13 (2007)
[14] Oumayma, B., Nahla, B.A., Talbi, E.G.: A Possibilistic Framework for Solving Multi-objective Problems under Uncertainty. In: IPDPSW, pp. 405-414. IEEE (2013)
[15] Solomon, M.M.: Algorithms for the vehicle Routing and Scheduling Problem with Time Window Constraints. Operations Research 35(2), 254-265 (1987) · Zbl 0625.90047
[16] Talbi, E.-G.: Metaheuristics: from design to implementation, vol. 74, pp. 309-373. John Wiley & Sons (2009)
[17] Teich, J.: Pareto Front Exploration with Uncertain Objectives. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 314-328. Springer, Heidelberg (2001)
[18] Toth, P., Vigo, D.: The vehicle routing problem, vol. 9. Siam (2002) · Zbl 0979.00026
[19] Wang, Y.: Centroid defuzzification and the maximizing set and minimizing set ranking based on alpha level sets. Computers and Industrial Engineering 57(1), 228-236 (2009)
[20] Yao, J., Wu, K.: Ranking fuzzy numbers based on decomposition principle and signed distance. Fuzzy Sets and Systems 116(2), 275-288 (2000) · Zbl 1179.62031
[21] Zadeh, L.A.: Fuzzy Sets. Information and Control 8(3), 338-353 (1965) · Zbl 0139.24606
[22] Zitzler, E., Laumans, M., Thiele, L.: SPEA2: Improving the strength Pareto evolutionary algorithm (2001)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.