Abstract
Vector optimization problems over a fuzzy combinatorial set of permutations are investigated. Based on the properties of the convex hull of a fuzzy combinatorial set of permutations, modifications of multicriteria choice methods are developed and substantiated for a fuzzy feasible combinatorial set. Mathematical models of some application problems are presented.
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References
L. A. Zadeh, “Fuzzy sets,” Inform. and Control, 8, 338–353 (1965).
V. V. Podinovskii and V. D. Nogin, Pareto-Optimal Solutions of Multicriteria Problems [in Russian], Nauka, Moscow (1982).
I. V. Sergienko and V. P. Shilo, Discrete Optimization Problems: Challenges, Solution Techniques, and Investigations [in Russian], Naukova Dumka, Kyiv (2003).
N. V. Semenova and L. N. Kolechkina, Vector Discrete Optimization Problems Over Combinatorial Sets: Methods of the Analysis and Solution, [in Ukrainian], Naukova Dumka, Kyiv (2009).
T. T. Lebedeva, N. V. Semenova, and T. I. Sergienko, “Optimality and solvability conditions in linear vector optimization problems with convex feasible sets,” Dop. NAN Ukrainy, No. 10, 80–85 (2003).
N. V. Semenova, L. N. Kolechkina, and A. N. Nagirna, “An approach to solving discrete vector optimization problems over a combinatorial set of permutations,” Cybern. Syst. Analysis, 44, No. 3, 441–451 (2008).
N. V. Semenova, L. N. Kolechkina, and A. N. Nagornaya, “Solution and investigation of vector problems of combinatorial optimization on a set of polypermutations,” J. Autom. Inform. Sci., Vol. 40, Issue 12, 27–42 (2008).
N. V. Semenova, “Optimality conditions in vector combinatorial optimization problems,” Teoriya Optim. Rishen’, No. 7, 153–160 (2008).
N. V. Semenova, L. N. Kolechkina, and A. M. Nagirna, “Solving multicriteria optimization problems over a set of polypermutations,” Dop. NAN Ukrainy, No. 2, 41–48 (2009).
A. N. Averkin, I. Z. Batyrshin, A. F. Blishun, et al., D. A. Pospelov (ed.), Fuzzy Sets in Models of Control and Artificial Intelligence [in Russian], Nauka, Moscow (1986).
S. A. Orlovskii, Problems of Decision Making under Fuzzy Initial Information [in Russian], Nauka, Moscow (1981).
A. N. Borisov, A. V. Alekseev, G. V. Merkur’eva, et al., Processing Fuzzy Information in Decision Making Systems [in Russian], Radio i Svyaz’, Moscow (1989).
I. V. Sergienko and M. F. Kaspshitskaya, Models and Methods for the Computer Solution of Combinatorial Optimization Problems [in Russian], Naukova Dumka, Kyiv (1981).
V. A. Emelichev, M. M. Kovalev, and M. K. Kravtsov, Polyhedra, Graphs, and Optimization [in Russian], Nauka, Moscow (1981).
Yu. G. Stoyan and S. V. Yakovlev, Mathematical Models and Optimization Methods of Geometric Design [in Russian], Naukova Dumka, Kyiv (1986).
O. O. Emets and O. O. Emets, “Some operations and relations over fuzzy numbers,” Nauk. Visti NTUU “KPI,” No. 5, 39–46 (2008).
E. Takeda and T. Nishida, “Multiple criteria decision problems with fuzzy domination structures,” Fuzzy Sets and Syst., 3, 123–136 (1980).
E. Jaquet Lagreze, “Applying fuzzy relations to estimate the preferability of distributed quantities,” in: Statistical Models and Multicriteria Decision-Making Problems [in Russian], Statistika, Moscow (1979), pp. 168–183.
A. V. Andreichikov and O. N. Andreichikova, Analysis, Synthesis, and Planning of Economic Decisions [in Russian], Finansy i Statistika, Moscow (2001).
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Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 88–99 March–April 2011.
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Semenova, N.V., Kolechkina, L.N. & Nagirna, A.M. Vector optimization problems with linear criteria over a fuzzy combinatorial set of alternatives. Cybern Syst Anal 47, 250–259 (2011). https://doi.org/10.1007/s10559-011-9307-5
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DOI: https://doi.org/10.1007/s10559-011-9307-5