Novel approximate solving algorithm for fuzzy relational equations

Mathematical and Computer Modelling

Volumn 52, Issue 1-2, 2010, Pages 303-308

  Luoh, Leh ^a   Liaw, Yi Ke ^a  

^a CHUNG HUA UNIVERSITY   (Taiwan)

Author keywords

Fuzzy relational equation; Genetic algorithm; Max product composition

Indexed keywords

APPROXIMATE SOLUTION; EXACT SOLUTION; FUZZY RELATIONAL EQUATION; FUZZY RELATIONAL EQUATIONS; MAX-PRODUCT COMPOSITION; PRACTICAL ENGINEERING PROBLEMS; RESEARCH TOPICS; SOLVING ALGORITHM; THEORETICAL RESULT;

GENETIC ALGORITHMS;

EID: 77953136873     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2010.02.046     Document Type: Article

References (39)

1. Sanchez E. Resolution of composite fuzzy relation equations. Information and Control 30 (1976) 38-48
2. Higashi M., and Klir G.J. Resolution of finite fuzzy relation equations. Fuzzy Sets and Systems 13 (1984) 65-82
3. Wang H.-F., and Chang Y.-C. Resolution of composite interval-valued fuzzy relation equations. Fuzzy Sets and Systems 44 (1991) 227-240
4. Sessa S. Some results in the setting fuzzy relation equations theory. Fuzzy Sets and Systems 14 (1984) 281-297
5. Sessa S. Finite fuzzy relation equations with unique solution in complete brouwerian lattices. Fuzzy Sets and Systems 29 (1989) 103-113
6. Lettieri A., and Liguori F. Characterization of some fuzzy relation equations provided with one solution on a finite set. Fuzzy Sets and Systems 13 (1984) 83-94
7. Baets B.D. Analytical solution methods for fuzzy relational equations. In: Dubois D., and Prade H. (Eds). Fundamentals of Fuzzy Sets. The Handbooks of Fuzzy Sets Series vol. 1 (2000), Kluwer, Norwell, MA 291-340
8. Klir G.J., and Yaun B. Fuzzy Sets and Fuzzy Logic: Theory and Applications (1995), Prentice-Hall, Upper Saddle River, NJ
9. Khorram E., Ghodousian A., and Molai A.A. Solving linear optimization problems with max-star composition equation constraints. Applied Mathematics and Computation 179 2 (2006) 654-661
10. Khorram E., and Zarei H. Multi-objective optimization problems with fuzzy relation equation constraints regarding max-average composition. Mathematical and Computer Modelling 49 5-6 (2009) 856-867
11. Kuo M.-S., Tzeng G.-H., and Huang W.-C. Group decision-making based on concepts of ideal and anti-ideal points in a fuzzy environment. Mathematical and Computer Modelling 45 3-4 (2007) 324-339
12. Nola A.D., Sessa S., Pedrycz W., and Sanchez E. Fuzzy Relation Equations and their Applications to Knowledge Engineering (1989), Kluwer, Norwell, MA
13. Pedrycz W., and Gomide F. An Introduction to Fuzzy Sets: Analysis and Design (1998), MIT Press, Cambridge, MA
14. Wang Y.M., and Fan Z.P. Group decision analysis based on fuzzy preference relations: logarithmic and geometric least squares methods. Applied Mathematics and Computation 194 1 (2007) 108-119
15. Wu W. Fuzzy reasoning and fuzzy relational equations. Fuzzy Sets and Systems 20 1 (1986) 67-78
16. 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 (2008) 352-362
17. Adamopoulos G.I., and Pappis C.P. Some results on the resolution of fuzzy relation equations. Fuzzy Sets and Systems 60 (1993) 83-88
18. Czogala E., Drewniak J., and Pedrycz W. Fuzzy relation equations on a finite set. Fuzzy Sets and Systems 7 (1982) 89-101
19. Li X., and Ruan D. Novel neural algorithms based on fuzzy δ rules for solving fuzzy relation equations: part III. Fuzzy Sets and Systems 109 (2000) 355-362
20. Li P., and Fang S.-C. A note on solution sets of interval-valued fuzzy relational equations. Fuzzy Optimization and Decision Making 8 1 (2009) 115-121
21. Perfilieva I., and Novák V. System of fuzzy relation equations as continuous model of IF-THEN rules. Information Sciences 177 (2007) 3218-3227
22. Shieh B.S. Solutions of fuzzy relation equations based on continuous t-norms. Information Sciences 177 (2007) 4208-4215
23. Shieh B.-S. Driving minimal solutions for fuzzy relation equations with max-product composition. Information Sciences 178 19 (2008) 3766-3774
24. Wang H.-F., and Hsu H.-M. An alternative approach to the resolution of fuzzy relation equations. Fuzzy Sets and Systems 45 (1992) 203-213
25. L.-X. Wang, Solving fuzzy relational equations through network training, in: Proc. 2nd IEEE Int. Conf., 1993, pp. 956-960.
26. Yeh C.-T. On the minimal solutions of max-min fuzzy relational equations. Fuzzy Sets and Systems 159 1 (2008) 23-39
27. Li P., and Fang S.-C. A survey on fuzzy relational equations, part I: classification and solvability. Fuzzy Optimization and Decision Making 8 2 (2009) 179-229
28. Molai A.A., and Khorram E. An algorithm for solving fuzzy relation equations with max-T composition operator. Information Sciences 178 (2008) 1293-1308
29. Pappis C.P., and Sugeno M. Fuzzy relational equations and the inverse problem. Fuzzy Sets and Systems 15 (1985) 79-90
30. Pappis C.P. Resolution of Cartesian products of fuzzy sets. Fuzzy Sets and Systems 26 (1988) 387-391
31. Pappis C.P., and Adamopoulos G.I. A computer algorithm for the solution of the inverse problem of fuzzy systems. Fuzzy Sets and Systems 39 (1991) 279-290
32. Pappis C.P., and Adamopoulos G.I. A software routine to solve the genearalized inverse problem of fuzzy relational equations. Fuzzy Sets and Systems 47 (1992) 319-322
33. Luoh L., Wang W.J., and Liaw Y.-K. New algorithms for solving fuzzy relation equations. Mathematics and Computers in Simulation 59 4 (2002) 329-333
34. Luoh L., Wang W.J., and Liaw Y.-K. Matrix-pattern-based computer algorithm for solving fuzzy relation equations. IEEE Transactions on Fuzzy Systems 11 2 (2003) 100-110
35. Imai H., Kikuchi K., and Miyakoshi M. Unattainable solutions of a fuzzy relation equation. Fuzzy Sets and Systems 99 (1998) 193-196
36. Pedrycz W. Numerical and applicational aspects of fuzzy relational equations. Fuzzy Sets and Systems 11 (1983) 1-18
37. Gottwald S., and Pedrycz W. Solvability of fuzzy relational equations and manipulation of fuzzy data. Fuzzy Sets and Systems 18 1 (1986) 45-65
38. G.J. Klir, Bo Yuan, Approximate solutions of systems of fuzzy relation equations, in: Conference on IEEE, 1994, pp. 1452-1457.
39. Lee L.H. An adaptive real-coded genetic algorithm. Applied Artificial Intelligence 16 6 (2002) 457-486