Minimization of linear objective functions under the constraints expressed by a system of fuzzy relation equations

Information Sciences

Volumn 178, Issue 17, 2008, Pages 3482-3490

  Qu, Xiao Bing ^a   Wang, Xue Ping ^b  

^a LESHAN NORMAL UNIVERSITY   (China)

^b SICHUAN NORMAL UNIVERSITY   (China)

Author keywords

Fuzzy optimization; Fuzzy relation equation; Max product composition; Minimal solution; Optimal solution

Indexed keywords

AEROSPACE APPLICATIONS; COMPUTER NETWORKS; EIGENVALUES AND EIGENFUNCTIONS; FUNCTION EVALUATION; FUZZY SYSTEMS; INTEGER PROGRAMMING; LINEAR EQUATIONS; MATHEMATICAL MORPHOLOGY; NUMERICAL METHODS; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION; STRUCTURE (COMPOSITION);

(PL) PROPERTIES; ELSEVIER (CO); FUZZY RELATION EQUATIONS; LINEAR OBJECTIVE FUNCTIONS; MAX PRODUCT COMPOSITION; MINIMAL SOLUTIONS; NUMERICAL EXAMPLES; OPTIMAL SOLUTIONS; OPTIMIZ ATION PROBLEMS; ORIGINAL PROBLEM;

FUZZY LOGIC;

EID: 45849083206     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2008.04.004     Document Type: Article

References (19)

1. Adamopoulos G.I., and Pappis C.P. Some results on the resolution of fuzzy relation equations. Fuzzy Sets and Systems 60 (1993) 83-88
2. Bourke M.M., and Fisher D.G. Solution algorithms for fuzzy relation equations with max-product composition. Fuzzy Sets and Systems 94 (1998) 61-69
3. Czogola E., Drewniak J., and Pedrycz W. Fuzzy relation equations on a finite set. Fuzzy Sets and Systems 7 (1982) 89-101
4. Dubois D., and Prade H. New results about properties and semantics of fuzzy set-theoretic operators. In: Wang P.P., and Chang S.K. (Eds). Fuzzy Sets (1986), Plenum Press, New York 59-75
5. Fang S.-C., and Li G. Solving fuzzy relation equations with a linear objective function. Fuzzy Sets and Systems 103 (1999) 107-113
6. Ghodousian A., and Khorram E. An algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max-prod composition. Applied Mathematics and Computation 178 (2006) 502-509
7. Guu S.-M., and Wu Y.-K. Minimizing a linear objective function with fuzzy relation equation constraints. Fuzzy Optimization and Decision Making 1 (2002) 347-360
8. Higashi M., and George J.K. Resolutions of finite fuzzy relation equations. Fuzzy Sets and Systems 13 (1984) 65-82
9. Imai H., Miyakoshi M., and Da-Te T. Some properties of minimal solutions for a fuzzy relation equation. Fuzzy Sets and Systems 90 (1997) 335-340
10. Loetamonphong J., and Fang S.-C. An efficient solution procedure for fuzzy relational equations with max-product composition. IEEE Transactions on Fuzzy Systems 7 (1998) 441-445
11. Loetamonphong J., and Fang S.-C. Optimization of fuzzy relation equations with max-product composition. Fuzzy Sets and Systems 118 (2001) 65-82
12. Markovskii A.V. On the relation between equations with max-product composition and the covering problem. Fuzzy Sets and Systems 153 (2005) 261-273
13. Molai A.A., and Khorram E. A modified algorithm for solving the proposed models by Ghodousian and Khorram and Khorram and Ghodousian. Applied Mathematics and Computation 190 (2007) 1161-1167
14. Sanchez E. Resolution of composite fuzzy relation equations. Information and Control 30 (1976) 38-48
15. Shieh B.S. Solutions of fuzzy relation equations based on continuous t-norms. Information Sciences 177 (2007) 4208-4215
16. Wang X.-P. A method to solve a fuzzy relational equation in a lattice [0,1]. Applied Mathematics Journal: Chinese University Series A 15 (2000) 127-133 (in Chinese)
17. Wu Y.-K., and Guu S.-M. A note on fuzzy relation programming problems with max-strict-t-norm composition. Fuzzy Optimization and Decision Making 3 (2004) 271-278
18. Xiong Q.-Q., and Wang X.-P. Some properties of sup-min fuzzy relational equations on infinite domains. Fuzzy Sets and Systems 151 (2005) 393-402
19. Zimmermann H.-J. Fuzzy set theory and its applications (1991), Kluwer Academic Publishers, Boston