Fuzzy linear programming under interval uncertainty based on IFS representation

Fuzzy Sets and Systems

Volumn 188, Issue 1, 2012, Pages 68-87

  Dubey, Dipti ^a   Chandra, Suresh ^a   Mehra, Aparna ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY DELHI   (India)

Author keywords

Fuzzy linear programming; Interval uncertainty; Intuitionistic fuzzy goals; Intuitionistic fuzzy sets; S shaped membership function

Indexed keywords

FUZZY LINEAR PROGRAMMING; INTERVAL UNCERTAINTY; INTUITIONISTIC FUZZY; INTUITIONISTIC FUZZY SETS; S-SHAPED;

COMPUTER PROGRAMMING; LINEAR PROGRAMMING; MEMBERSHIP FUNCTIONS;

FUZZY SETS;

EID: 80955131791     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2011.09.008     Document Type: Article

References (48)

1. P.P. Angelov Optimization in an intuitionistic fuzzy environment Fuzzy Sets Syst. 86 1997 299 306 (Pubitemid 127683583)
2. K.T. Atanassov Intutionistic fuzzy sets Fuzzy Sets Syst. 20 1986 87 96
3. K.T. Atanassov Intuitionistic Fuzzy Sets: Theory and Applications 1999 Physica-Verlag Heidelberg
4. K.T. Atanassov Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prades paper: terminological difficulties in fuzzy set theory - the case of intuitionistic fuzzy sets Fuzzy Sets Syst. 156 2005 496 499
5. K.T. Atanassov, G. Pasi, and R.R. Yager Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making Int. J. Syst. Sci. 36 2005 859 868 (Pubitemid 43149045)
6. K.T. Atanassov, 25 years of intuitionistic fuzzy sets, or the most important results and mistakes of mine, in: 7th International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets, Warsaw, Poland, 2008 〈 http://ifigenia.org/w/images/4/49/7IWIFSGN-Atanassov.pdf 〉.
7. K.T. Atanassov, and G. Gargov Interval valued intuitionistic fuzzy sets Fuzzy Sets Syst. 31 1989 343 349
8. C.R. Bector, and S. Chandra Fuzzy Mathematical Programming and Fuzzy Matrix Games, Studies in Fuzziness and Soft Computing vol. 169 2005 Springer
9. R.E. Bellman, and L.A. Zadeh Decision making in fuzzy environment Manage. Sci. 17 1970 B-141 B-164
10. H. Bustince, J. Kacprzyk, and V. Mohedano Intuitionistic fuzzy generators application to intuitionistic fuzzy complementations Fuzzy Sets Syst. 114 2000 485 504
11. B. Choi, and F.C. Rhee Interval type-2 fuzzy membership function generation methods for pattern recognition Inf. Sci. 179 2009 2102 2122
12. C. Cornelis, G. Deschrijver, and E.E. Kerre Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application Int. J. Approximate Reasoning 35 2004 55 95
13. S.K. De, R. Biswas, and A.R. Roy An application of intuitionistic fuzzy sets in medical diagonsis Fuzzy Sets Syst. 117 2001 209 213
14. G. Deschrijver, C. Cornelis, and E.E. Kerre On the representation of intuitionistic fuzzy t-norms and t-conorms IEEE Trans. Fuzzy Syst. 12 2004 45 61
15. G. Deschrijver, and E.E. Kerre On the relationship between some extensions of fuzzy set theory Fuzzy Sets Syst. 133 2003 227 235
16. G. Deschrijver, and E.E. Kerre On the position of intuitionistic fuzzy set theory in the framework of theories modelling imprecision Inf. Sci. 177 2007 1860 1866 (Pubitemid 46176955)
17. G. Deschrijver, O. Arielie, C. Cornelis, and E.E. Kerre A bilattice-based framework for handling graded truth and imprecision Int. J. Uncertainty Fuzziness Knowl.-Based Syst. 15 2007 13 41 (Pubitemid 46339166)
18. D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk, and H. Prade Terminological difficulties in fuzzy set theory - the case of intuitionistic fuzzy sets Fuzzy Sets Syst. 156 2005 485 491 (Pubitemid 41475504)
19. D. Dubois, and H. Prade An introduction to bipolar representations of information and preference Int. J. Intell. Syst. 23 2008 866 877
20. D. Dubois, and H. Prade An overview of the asymmetric bipolar representation of positive and negative information in possibility theory Fuzzy Sets Syst. 160 2009 1355 1366
21. S. Freson, B. De Baets, and H. De Meyer Linear optimization with bipolar max-min constraints Inf. Sci. 2011 doi: 10.1016/j.ins.2011.06.009
22. P. Grzegorzewski, and E. Mrowka Some notes on (Atanassovs) intuitionistic fuzzy sets Fuzzy Sets Syst. 156 2005 492 495 (Pubitemid 41475505)
23. A. Homaifar, and E. McCormick Simultaneous design of membership functions and rule sets for fuzzy controllers using genetic algorithms IEEE Trans. Fuzzy Syst. 3 1995 129 139
24. L. Hurwicz, A Criterion for Decision-Making Under Uncertainty, Technical Report 355, Cowels Commission, 1952.
25. D.-F. Li, and C.-T. Cheng New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions Pattern Recognition Lett. 23 2002 221 225
26. D.-F. Li Multiattribute decision making models and methods using intuitionistic fuzzy sets J. Comput. Syst. Sci. 70 2005 73 85
27. D.-F. Li Extension of the LINMAP for multiattribute decision making under Atanassovs intuitionistic fuzzy environment Fuzzy Optim. Decision Making 7 2008 17 34
28. D.-F. Li, G.-H. Chen, and Z.-G. Huang Linear programming method for multiattribute decision making using IF sets Inf. Sci. 180 2010 1591 1609
29. D.-F. Li TOPSIS-based nonlinear-programming methodology for multiattribute decision making with interval-valued intuitionistic fuzzy sets IEEE Trans. Fuzzy Syst. 18 2010 299 311
30. D.-F. Li Linear programming method for MADM with interval-valued intuitionistic fuzzy sets Expert Syst. Appl. 37 2010 5939 5945
31. D.-F. Li Multiattribute decision making method based on generalized OWA operators with intuitionistic fuzzy sets Expert Syst. Appl. 37 2010 8673 8678
32. T.W. Liao, A.K. Celmins, and R.J. Hammell II A fuzzy c-means variant for the generation of fuzzy term sets Fuzzy Sets Syst. 135 2003 241 257
33. C.C. Lin, and A.P. Chen Generalization of Yang et al.s method for fuzzy programming with piecewise linear membership function Fuzzy Sets Syst. 132 2002 347 352
34. LINGO Super 12.0: Optimization Modeling with LINGO, 6th ed., Lindo Systems, Inc., Chicago, 2009.
35. H.W. Liu, and G.J. Wang Multi-criteria decision making methods based on intuitionistic fuzzy sets Eur. J. Oper. Res. 179 2007 220 233
36. M. Makrehchi, O. Basir, and M. Kamel Generation of fuzzy membership function using information theory measures and genetic algorithm Lecture Notes in Computer Science vol. 275 2003 603 610 (Pubitemid 36892446)
37. S. Medasani, J. Kim, and R. Krishnapuram An overview of membership function generation techniques for pattern recognition Int. J. Approx. Reason. 19 1998 391 417 (Pubitemid 128426488)
38. H.T. Nguyen, V. Kreinovich, and Q. Zuo Interval-valued degree of belief: application of interval computations to expert systems and intelligent control International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 5 1997 317 358 (Pubitemid 127530908)
39. T.-S. Shih, H.-M. Lee, and J.-S. Su Fuzzy multiple objective programming based on interval-valued sets Eighth International Conference on Intelligent Systems Design and Applications 2008 IEEE Computer Society Taiwan 397 402
40. A. Tversky, and D. Kahneman Advances in prospect theory: cumulative representation of uncertainty J. Risk Uncertainty 5 1992 297 323
41. I.K. Vlachos, and G.D. Sergiadis Intuitionistic fuzzy information - applications to pattern recognition Pattern Recognition Lett. 28 2007 197 206 (Pubitemid 44716402)
42. Z. Wang, K.W. Li, and W. Wang An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights Inf. Sci. 179 2009 3026 3040
43. Z. Xu, J. Chen, and J. Wu Clustering algorithm for intuitionistic fuzzy sets Inf. Sci. 178 2008 3775 3790
44. R.R. Yager Some aspects of intuitionistic fuzzy sets Fuzzy Optim. Decision Making 8 2009 67 90
45. T. Yang, J.P. Ignizio, and H.J. Kim Fuzzy programming with nonlinear membership functions: piecewise linear approximation Fuzzy Sets Syst. 41 1991 39 53 (Pubitemid 21727001)
46. L.A. Zadeh Fuzzy sets Inf. Control 8 1965 338 353
47. L.A. Zadeh The concept of a linguistic variable and its application to approximate reasoning - I Inf. Sci. 8 1975 199 249
48. H.-J. Zimmermann Fuzzy programming and linear programming with several objective functions Fuzzy Sets Syst. 1 1978 45 55