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An algorithm for solving optimization problems with fuzzy relational inequality constraints. (English) Zbl 1330.90139
Summary: An algorithm for solving a kind of optimization problems with fuzzy relational inequalities was proposed by F.-F. Guo and Z.-Q. Xia [Fuzzy Optim. Decis. Mak. 5, No. 1, 33–47 (2006; Zbl 1176.90675)]. However, it is too expensive to verify the optimal condition. In this paper, some rules for reducing these problems are proposed and the relationship between minimal solutions and FRI paths is also given. These lead to a new algorithm for solving this kind of problems. Numerical experiments are presented for illustrating the efficiency of the proposed algorithm.

MSC:
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
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[1] Czogala, E.; Predrycz, W., On identification in fuzzy systems and its applications in control problems, Fuzzy Sets and Systems, 6, 73-83, (1981)
[2] Di Martino, F.; Loia, V.; Sessa, S., Fuzzy transforms for compression and decompression of color videos, Information Sciences, 180, 20, 3914-3931, (2010)
[3] Fang, S.-C.; Li, G., Solving fuzzy relation equations with a linear objective function, Fuzzy Sets and Systems, 103, 107-113, (1999) · Zbl 0933.90069
[4] Ghodousian, A.; Khorram, E., An algorithm for optimizing the linear function with fuzzy relation equation constraints regarding MAX-prod composition, Applied Mathematics and Computation (New York), 178, 2, 502-509, (2006) · Zbl 1105.65067
[5] Ghodousian, A.; Khorram, E., Fuzzy linear optimization in the presence of the fuzzy relation inequality constraints with MAX-MIN composition, Information Sciences, 178, 501-519, (2008) · Zbl 1149.90189
[6] Guo, F.-F.; Xia, Z.-Q., An algorithm for solving optimization problems with one linear objective function and finitely many constraints of fuzzy relation inequalities, Fuzzy Decision Making and Optimization, 5, 33-47, (2006) · Zbl 1176.90675
[7] Khorram, E.; Hassanzadeh, R., Solving nonlinear optimization problems subjected to fuzzy relation equation constraints with MAX-average composition using a modified genetic algorithm, Computers and Industrial Engineering, 55, 1, 1-14, (2008)
[8] Khorram, E.; Ghodousian, A.; Molai, A. A., Solving linear optimization problems with MAX-star composition equation constraints, Applied Mathematics and Computation, 179, 2, 654-661, (2006) · Zbl 1103.65067
[9] Lee, H. C.; Guu, S. M., On the optimal three-tier multimedia streaming services, Fuzzy Optimization and Decision Making, 2, 31-39, (2002)
[10] Li, G.-Z.; Fang, S.-C., Solving interval-valued fuzzy relation equations, IEEE Transactions on Fuzzy Systems, 6, 2, 321-324, (1998)
[11] Li, J.-X., A new algorithm for minimizing a linear objective function with fuzzy relation equation constraints, Fuzzy Sets and Systems, 159, 2278-2298, (2008) · Zbl 1180.90382
[12] Li, P.; Fang, S.-C., On the resolution and optimization of a system of fuzzy relational equations with sup-T composition, Fuzzy Optimization and Decision Making, 7, 169-214, (2008) · Zbl 1169.90493
[13] Li, P.; Fang, S.-C., A survey on fuzzy relational equations, part I: classification and solvability, Fuzzy Optimization and Decision Making, 8, 179-229, (2009) · Zbl 1180.03051
[14] Loetamonphong, J.; Fang, S.-C., Optimization of fuzzy relation equations with MAX-product composition, Fuzzy Sets and Systems, 118, 509-517, (2001) · Zbl 1044.90533
[15] Loetamonphong, J.; Fang, S.-C.; Young, R. E., Multi-objective optimization problems with fuzzy relation equation constraints, Fuzzy Sets and Systems, 127, 141-164, (2002) · Zbl 0994.90130
[16] Loia, V.; Sessa, S., Fuzzy relation equations for coding/decoding processed of images and videos, Information Sciences, 171, 145-172, (2005) · Zbl 1078.68815
[17] Lu, J.-J.; Fang, S.-C., Solving nonlinear optimization problems with fuzzy relation equation constraints, Fuzzy Sets and Systems, 119, 1-20, (2001)
[18] Luo, C.-Z., Introduction of fuzzy sets, (1980), Beijing Normal University Press Beijing
[19] Miyagi, H.; Kinjo, I.; Fan, Y., Qualified decision-making using the fuzzy relation inequalities, Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, 2, 2014-2018, (1998)
[20] Molai, A. A.; Khorram, E., An algorithm for solving fuzzy relation equations with MAX-T composition operator, Information Sciences, 178, 5, 1293-1308, (2008) · Zbl 1136.03330
[21] Molai, A.-A.; Khorram, E., Another modification from two papers of Ghodousian and khorram and khorram et al., Applied Mathematics and Computation, 197, 2, 559-565, (2008) · Zbl 1141.65045
[22] Molai, A. A.; Khorram, E., A modified algorithm for solving the proposed models by ghodousian and khorram and khorram and Ghodousian, Applied Mathematics and Computation, 190, 2, 1161-1167, (2007) · Zbl 1227.90049
[23] Nobuhara, H.; Pedrycz, W., Fast solving method of fuzzy relational equation and it application to lossy image compression/reconstruction, IEEE Transactions on Fuzzy Systems, 8, 3, 325-334, (2000)
[24] Pedrycz, W., Proceeding in relational structures: fuzzy relational equations, Fuzzy Sets and Systems, 40, 77-106, (1991) · Zbl 0721.94030
[25] Qu, X.-B.; Wang, X.-P., Minimization of linear objective functions under the constraints expressed by a system of fuzzy relation equations, Information Sciences, 178, 17, 3482-3490, (2008) · Zbl 1190.90300
[26] Sanchez, E., Resolution of composite fuzzy relation equations, Information and Control, 30, 38-48, (1976) · Zbl 0326.02048
[27] Shieh, B., Solutions of fuzzy relation equations based on continuous t-norms, Information Sciences, 177, 19, 4208-4215, (2007) · Zbl 1122.03054
[28] Su, C.-H.; Guo, F.-F., Solving interval-valued fuzzy relation equations with a linear objective function, Proceedings of the Six International Conference on Fuzzy Systems and Knowledge Discovery, 4, 380-385, (2009)
[29] Wang, P.-Z.; Zhang, D.-Z.; Sanchez, E.; Lee, E.-S., Lattecized linear programming and fuzzy relation inequalities, Journal of Mathematics Analysis and Applications, 159, 72-87, (1991) · Zbl 0746.90081
[30] Wang, H.-F.; Wang, C.-H., A fixed charge model with fuzzy inequality constraints composed by MAX-product operator, Computer Mathematics and Applications, 36, 7, 23-29, (1998) · Zbl 0935.90048
[31] Wu, Y.-K.; Guu, S.-M.; Liu, J. Y.-C., An accelerated approach for solving fuzzy relation equations with a linear objective function, IEEE Transactions on Fuzzy Systems, 10, 4, 552-558, (2002)
[32] Wu, Y.-K.; Guu, S.-M., Minimizing a linear function under a fuzzy MAX-MIN relational equation constraint, Fuzzy Sets and Systems, 150, 147-162, (2005) · Zbl 1074.90057
[33] Wu, Y.-K., Optimizing the geometric programming problem with single-term exponents subject to MAX-MIN fuzzy relational equation constraints, Mathematical and Computer Modelling, 47, 3-4, 352-362, (2008) · Zbl 1171.90572
[34] Y.-K. Wu, W.-W. Yang, Optimization of fuzzy relational equations with a linear convex combination of max-min and max-average compositions, in: 2007 IEEE International Conference on Industrial Engineering and Engineering Management, 2007, pp. 832-836.
[35] Wu, Y.-K., Optimization of fuzzy relational equations with MAX-av composition, Information Sciences, 177, 1, 4216-4229, (2007) · Zbl 1140.90523
[36] Y.-K. Wu, S.-M. Guu, Minimizing a linear objective function under a max-t-norm fuzzy relational equation constraint, in: 2006 IEEE International Conference on Fuzzy Systems, 2006, pp. 1604-1610.
[37] Wu, Y.-K.; Guu, S.-M., A note on fuzzy relation programming problems with MAX-strict-t-norm composition, Fuzzy Optimization and Decision Making, 3, 3, 271-278, (2004) · Zbl 1091.90087
[38] Yeh, C.-T., On the minimal solutions of MAX-MIN fuzzy relational equations, Fuzzy Sets and Systems, 159, 23-39, (2008) · Zbl 1176.03040
[39] Zadeh, L. A., Is there a need for fuzzy logic?, Information Sciences, 178, 2751-2779, (2008) · Zbl 1148.68047
[40] Zadeh, L. A., Toward a generalized theory of uncertainty (GTU) - an outline, Information Sciences, 172, 1-40, (2005) · Zbl 1074.94021
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