zbMATH — the first resource for mathematics

Minimizing a linear function under a fuzzy max-min relational equation constraint. (English) Zbl 1074.90057
Summary: We investigate the problem of minimizing a linear objective function subject to a fuzzy relational equation constraint. A necessary condition for optimal solution is proposed. Based on this necessary condition, we propose three rules to simplify the work of computing an optimal solution. Numerical examples are provided to illustrate the procedure. Experimental results are reported showing that our new procedure systematically outperforms our previous work.

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C47 Minimax problems in mathematical programming
Full Text: DOI
[1] Adamopoulos, G.I.; Pappis, C.P., Some results on the resolution of fuzzy relation equations, Fuzzy sets syst., 60, 83-88, (1993) · Zbl 0794.04005
[2] Baets, B.D., Analytical solution methods for fuzzy relational equations, (), 291-340 · Zbl 0970.03044
[3] Baets, B.D.; Tsiporkova, E.; Mesiar, R., Conditioning in possibility theory with strict order norms, Fuzzy sets syst., 106, 221-229, (1999) · Zbl 0985.28015
[4] Chen, L.; Wang, P.P., Fuzzy relation equations (I)the general and specialized solving algorithms, Soft comput., 6, 428-435, (2002) · Zbl 1024.03520
[5] Czogala, E.; Drewniak, J.; Pedrycz, W., Fuzzy relation equations on a finite set, Fuzzy sets syst., 7, 89-101, (1982) · Zbl 0483.04001
[6] Di Nola, A.; Sessa, S.; Pedrycz, W.; Sanchez, E., Fuzzy relational equations and their applications in knowledge engineering, (1989), Kluwer Academic Press Dordrecht
[7] Fang, S.-C.; Li, G., Solving fuzzy relation equations with a linear objective function, Fuzzy sets syst., 103, 107-113, (1999) · Zbl 0933.90069
[8] Guu, S.-M.; Wu, Y.-K., Minimizing a linear objective function with fuzzy relation equation constraints, Fuzzy optim. decision making, 1, 4, 347-360, (2002) · Zbl 1055.90094
[9] Higashi, M.; Klir, G.J., Resolution of finite fuzzy relation equations, Fuzzy sets syst., 13, 65-82, (1984) · Zbl 0553.04006
[10] Klir, G.J.; Folger, T.A., Fuzzy sets, uncertainty, and information, (1988), Prentice-Hall NJ · Zbl 0675.94025
[11] Klir, G.J.; Yuan, B., Fuzzy sets and fuzzy logictheory and applications, (1995), Prentice-Hall PTR, Englewood Cliffs, NJ
[12] Lee, H.-C.; Guu, S.-M., On the optimal three-tier multimedia streaming services, Fuzzy optim. decision making, 2, 31, 31-39, (2002)
[13] Loetamonphong, J.; Fang, S.-C., Optimization of fuzzy relational equations with MAX-product composition, Fuzzy sets syst., 118, 509-517, (2001) · Zbl 1044.90533
[14] Loetamonphong, J.; Fang, S.-C.; Young, R.E., Multi-objective optimization problems with fuzzy relation equation constraints, Fuzzy sets syst., 127, 141-164, (2002) · Zbl 0994.90130
[15] Lu, J.; Fang, S.-C., Solving nonlinear optimization problems with fuzzy relation equations constraints, Fuzzy sets syst., 119, 1-20, (2001)
[16] Luoh, L.; Wang, W.-J.; Liaw, Y.-K., Matrix-pattern-based computer algorithm for solving fuzzy relation equations, IEEE trans. fuzzy syst., 11, 1, 100-108, (2003)
[17] Miyakoshi, M.; Shimbo, M., Sets of solution-set-invariant coefficient matrices of simple fuzzy relation equations, Fuzzy sets syst., 21, 59-83, (1987) · Zbl 0649.04003
[18] Pappis, C.P.; Adamopoulos, G.I., A computer algorithm for the solution of the inverse problem of fuzzy systems, Fuzzy sets syst., 39, 279-290, (1991) · Zbl 0727.93029
[19] Pappis, C.P.; Adamopoulos, G.I., A software routine to solve the generalized inverse problem of fuzzy systems, Fuzzy sets syst., 47, 319-322, (1992) · Zbl 0850.93447
[20] Pappis, C.P.; Sugeno, M., Fuzzy relation equations and the inverse problem, Fuzzy sets syst., 15, 79-90, (1985) · Zbl 0561.04003
[21] Peeva, K., Fuzzy linear systems, Fuzzy sets syst., 49, 339-355, (1992) · Zbl 0805.04005
[22] Sanchez, E., Resolution of composite fuzzy relation equations, Inform. control, 30, 38-48, (1976) · Zbl 0326.02048
[23] Sanchez, E., Solutions in composite fuzzy relation equations, (), 221-234
[24] Stamou, G.B.; Tzafestas, S.G., Resolution of composite fuzzy relation equations based on Archimedean triangular norms, Fuzzy sets syst., 120, 395-407, (2001) · Zbl 0979.03042
[25] Wang, H.-F., A multi-objective mathematical programming problem with fuzzy relation constraints, J. multi-criteria decision anal., 4, 23-35, (1995) · Zbl 0843.90131
[26] Wang, S.; Fang, S.-C.; Nuttle, H.L.W., Solutions sets of interval-valued fuzzy relational equations, Fuzzy optim. decision making, 2, 1, 41-60, (2003) · Zbl 1178.03071
[27] Wang, P.Z.; Zhang, D.Z.; Sanchez, E.; Lee, E.S., Latticized linear programming and fuzzy relation inequalities, J. math. anal. appl., 159, 1, 72-87, (1991) · Zbl 0746.90081
[28] Wu, Y.-K.; Guu, S.-M.; Liu, J.Y.-C., An accelerated approach for solving fuzzy relation equations with a linear objective function, IEEE trans. fuzzy syst., 10, 4, 552-558, (2002)
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.