Fuzzy linear optimization in the presence of the fuzzy relation inequality constraints with max-min composition

Information Sciences

Volumn 178, Issue 2, 2008, Pages 501-519

  Ghodousian, A ^a   Khorram, E ^a  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Fuzzy compositions; Fuzzy relational equalities; Fuzzy relational inequalities; Linear objective function optimization; T norms

Indexed keywords

CONSTRAINT THEORY; OPTIMIZATION; PROBLEM SOLVING;

FUZZY COMPOSITIONS; FUZZY RELATIONAL EQUALITIES; FUZZY RELATIONAL INEQUALITIES; LINEAR OBJECTIVE FUNCTION OPTIMIZATION;

FUZZY SETS;

EID: 35348952037     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2007.07.022     Document Type: Article

References (58)

1. Bellman R.E., and Zadeh L.A. Decision-making in fuzzy environment. Management Science 17 (1970) 41-164
2. Chen L., and Wang P.P. Fuzzy relation equations(I): the general and specialized solving algorithms. Soft Computing 6 (2002) 428-435
3. Czogala E., Drewniak J., and Pedrycz W. fuzzy relation equations on a finite set. Fuzzy Sets and Systems 7 (1982) 89-101
4. Di Martino F., and Sessa S. Digital watermarking in coding/decoding processes with fuzzy relation equations. Soft Computing 10 (2006) 238 243
5. F. Di Martino, V. Loia, S. Sessa, A method in the compression/decompression of images using fuzzy equations and fuzzy similarities, in: Proceedings of Conference IFSA 2003, 29/6-2/7/2003, Istanbul, Turkey, 2003, pp. 524-527.
6. Di Nola A., Pedrycz W., and Sessa S. Some theoretical aspects of fuzzy relation equations describing fuzzy systems. Information Sciences 34 (1984) 241-264
7. Di Nola A., Pedrycz W., and Sessa S. Fuzzy relation equations and algorithms of inference mechanism in expert systems. In: Gupta M.M., Kandel A., Bandler W., and Kiszka J.B. (Eds). Approximate Reasoning in Expert System (1985), Elsevier Science Publishers (North Holland), Amsterdam 355-367
8. Di Nola A., Pedrycz W., Sessa S., and Sanchez E. Fuzzy relation equations theory as a basis of fuzzy modeling: an overview. Fuzzy Sets and Systems 40 (1991) 415-429
9. Di Nola A., and Russo C. Lukasiewicz transform and its application to compression and reconstruction of digital images. Information Sciences 177 (2007) 1481-1498
10. Di Nola A., Sessa S., Pedrycz W., and Sanchez E. Fuzzy Relation Equations and Their Applications to Knowledge Engineering (1989), Kluwer, Dordrecht
11. Dubois D., and Prade H. Fuzzy Sets and Systems: Theory and Applications (1980), Academic Press, New York
12. Fang S.C., and Li G. Solving fuzzy relational equations with a linear objective function. Fuzzy Sets and Systems 103 (1999) 107-113
13. Fernandez M.J., and Gil P. Some specific types of fuzzy relation equations. Information Sciences 164 (2004) 189-195
14. Guo F.F., and Xia Z.Q. An algorithm for solving optimization problems with one linear objective function and finitely many constraints of fuzzy relation inequalities. Fuzzy Optimization and Decision Making 5 (2006) 33-47
15. Guu S.M., and Wu Y.K. Minimizing a linear objective function with fuzzy relation equation constraints. Fuzzy Optimization and Decision Making 12 (2002) 1568-4539
16. Han S.C., Li H.X., and Wang J.Y. Resolution of finite fuzzy relation equations based on strong pseudo-t-norms. Applied Mathematics Letters 19 (2006) 752-757
17. Han S.C., and Li H.X. Notes on pseudo-t-norms and implication operators on a complete Brouwerian lattice and pseudo-t-norms and implication operators: direct products and direct product decompositions. Fuzzy Sets and Systems 153 (2005) 289-294
18. Higashi M., and Klir G.J. Resolution of finite fuzzy relation equations. Fuzzy Sets and Systems 13 (1984) 65-82
19. Hirota K., and Pedrycz W. Fuzzy relational compression. IEEE Transactions on Systems, Man and Cybernetics, Part B 29 3 (1999) 407-415
20. Hirota K., and Pedrycz W. Solving Fuzzy relational equations through logical filtering. Fuzzy Sets and Systems 81 (1996) 355-364
21. Hirota K., and Pedrycz W. Specificity shift in solving. Fuzzy Sets and Systems 106 (1999) 11-220
22. Klement E.P., Mesiar R., and Pap E. Triangular norms. Position paper I: Basic analytical and algebraic properties. Fuzzy Sets and Systems 143 (2004) 5-26
23. Klement E.P., Mesiar R., and Pap E. Triangular norms. Position paper II. Fuzzy Sets and Systems 145 (2004) 411-438
24. Klement E.P., Mesiar R., and Pap E. Triangular norms. Position paper III. Fuzzy Sets and Systems 145 (2004) 439-454
25. Klir G.J., and Yuan B. Fuzzy Sets and Fuzzy Logic: Theory and Applications (1995), Prentice-Hall, PTR, USA
26. Lee H.C., and Guu S.M. On the optimal three-tier multimedia streaming services. Fuzzy Optimization and Decision Making 2 1 (2002) 31-39
27. Loetamonphong J., Fang S.C., and Young R.E. Multi-objective optimization problems with fuzzy relation equation constraints. Fuzzy Sets and Systems 127 (2002) 41-164
28. Loetamonphong J., and Fang S.C. Optimization of fuzzy relation equations with max-product composition. Fuzzy Sets and Systems 118 (2001) 509-517
29. Loia V., and Sessa S. Fuzzy relation equations for coding/decoding processes of images and videos. Information Sciences 171 (2005) 145-172
30. Loia V., Pedrycz W., and Sessa S. Fuzzy relation calculus in the compression and decompression of fuzzy relations. International Journal of Image and Graphics 2 (2002) 1-15
31. Lu J., and Fang S.C. Solving nonlinear optimization problems with fuzzy relation equations constraints. Fuzzy Sets and Systems 119 (2001) 1-20
32. Markovskii A.V. On the relation between equations with max-product composition and the covering problem. Fuzzy Sets and Systems 153 (2005) 261-273
33. Nobuhara H., Pedrycz W., and Hirota K. A digital watermarking algorithm using image compression method based on fuzzy relational equations. Proceedings of FUZZ-IEEE 2002 vol. 2 (2002), IEEE Press 1568-1573
34. Nobuhara H., Hirota K., and Pedrycz W. Relational image compression: optimizations through the design of fuzzy coders and YUV colour space. Soft Computing 9 (2005) 471-479
35. Nobuhara H., Hirota K., Di Martino F., Pedrycz W., and Sessa S. Fuzzy relation equations for compression/decompression processes of colour images in the RGB and YUV colour spaces. Fuzzy Optimization and Decision Making 4 (2005) 235-246
36. Nobuhara H., Pedrycz W., and Hirota K. Fast solving method of fuzzy relational equation and its application to lossy image compression. IEEE Transactions on Fuzzy Systems 8 3 (2000) 325-334
37. Nobuhara H., Bede B., and Hirota K. On various eigen fuzzy sets and their application to image reconstruction. Information Sciences 176 (2006) 2988-3010
38. Pedrycz W. An approach to the analysis of fuzzy systems. International Journal on Control 34 (1981) 403-421
39. Pedrycz W. Fuzzy relational equations with generalized connectives and their applications. Fuzzy Sets and Systems 5 (1983) 185-201
40. Pedrycz W. On generalized fuzzy relational equations and their applications. Journal of Mathematical Analysis and Applications 107 (1985) 520-536
41. Pedrycz W. s-t fuzzy relational equations. Fuzzy Sets and Systems 59 (1993) 89-195
42. Pedrycz W. Inverse problem in fuzzy relational equations. Fuzzy Sets and Systems 36 (1990) 277-291
43. Pedrycz W., and Vasilakos A.V. Modularization of fuzzy relational equations. Soft Computing 6 (2002) 3-37
44. Peeva K., and Kyosev Y. Fuzzy Relational Calculus, Theory, Applications and Software (2004), World Scientific
45. Perfilieva I. Fuzzy function as an approximate solution to a system of fuzzy relation equations. Fuzzy Sets and Systems 147 (2004) 363-383
46. Perfilieva I., and Novak V. System of fuzzy relation equations model of I F-THEN rules. Information Sciences (2007) 10.1016/j.ins.2006.11.006
47. Sakawa M. Fuzzy Sets and Interactive Multi-Objective Optimization (1993), Plenum Press
48. Sanchez E. Solution in composite fuzzy relation equations: application to medical diagnosis in Brouwerian logic. In: Gupta M.M., Saridis G.N., and Games B.R. (Eds). Fuzzy Automata and Decision Processes (1977), North-Holland, New York 221-234
49. Wang S., Fang S.C., and Nuttle H.L.W. Solution sets of interval-valued fuzzy relational equations. Fuzzy Optimization and Decision Making 2 1 (2003) 1-60
50. Wang H.F. A multi-objective mathematical programming problem with fuzzy relation constraints. Journal of Multi-Criteria Decision Analysis 4 (1995) 23-35
51. Wang P.Z. Latticized linear programming and fuzzy relation inequalities. Journal of Mathematical Analysis and Applications 159 (1991) 72-87
52. Wang G.J. On the logic foundation of fuzzy reasoning. Information Sciences 117 1 (1999) 47-88
53. Wenstop F. Deductive verbal models of organizations. International Journal of Man-Machine Studies 8 (1976) 93-311
54. Wu Y.K., Guu S.M., and Liu Y.C. An accelerated approach for solving fuzzy relation equations with a linear objective function. IEEE Transactions on Fuzzy Systems 10 4 (2002) 552-558
55. 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
56. Wu Y.K., and Guu S.M. Minimizing a linear function under a fuzzy max min relational equation constraints. Fuzzy Sets and Systems 150 (2005) 147-162
57. Xiong Q.Q., and Wang X.P. Some properties of sup-min fuzzy relational equations on infinite domains. Fuzzy Sets and Systems 151 (2005) 93-402
58. Zimmermann H.J. Description and optimization of fuzzy systems. International Journal of General Systems 2 (1976) 209-215