Document Type : Research Paper


1 Department of Mathematics, Quchan Institute of Engineering and Technology, Iran,

2 Department of Mathematics, Ferdowsi University of Mashhad, Iran,


The objective of this paper is to deal with the fuzzy conic program-
ming problems. The aim here is to derive weak and strong duality theorems
for a general fuzzy conic programming. Toward this end, The convexity-like
concept of fuzzy mappings is introduced and then a speci c ordering cone is
established based on the parameterized representation of fuzzy numbers. Un-
der this setting, duality theorems are extended from crisp conic optimization
problems to fuzzy ones.


[1] C. R. Bector and S. Chandra,On duality in linear programming under fuzzy environment,Fuzzy Sets and Systems,125 (2002), 317{325.
[2] J. Brito, J. A. Moreno and J. L. Verdegay,Transport route planning Models based on fuzzy approach, Iranian Journal of Fuzzy Systems, 9 (2012), 141{158.
[3] K. L. Chew and E. U. Choo,Pesudolinearity and ecienc, Mathematical Programming,28(1984), 226{239.
[4] D. Dubois and H. Prade,Operations on fuzzy numbers, Int. J. Systems Sci., 9 (1978), 613{626. 
[5] P. Fortemps and M. Roubens,Ranking and defuzzi cation methods based on area compensation, Fuzzy Sets and Systems, 82 (1996), 319{330.
[6] N. Furukawa,Convexity and local Lipschitz continuity of fuzzy-valued mappings, Fuzzy Sets and Systems,93 (1998), 113{119.
[7] R. Goestschel and W. Voxman,Elementary fuzzy calculus, Fuzzy Sets and Systems, 18 1986),31{43. 
[8] N. Javadian, Y. Maali and N. Mahdavi-Amiri,Fuzzy linear programming with grades of satisfaction in constraints, Iranian Journal of Fuzzy Systems, 6 (2009), 17{35.
[9] V. Jeykumar and X. Q. Yang,On characterizing the solution sets of pesudolinear programs,J. O. T. A.,87(1995), 747{755.
[10] A. Kaufmann and L. A. Zadeh,Theory of fuzzy subsets, New York, San Francisco, London,1975. 
[11] D. Luenberger,Optimization by vector space methods, New York, Wiley, 1969.
[12] N. Mahdavi-Amiri and S. H. Nasseri,Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables Sets and Systems, 158(2007),1961{1978.
[13] S. K. Mishra, S. Y. Wang and K. K. Lai,Explicitly B-preinvex fuzzy mappings, Int. J.Computer Math.,83 (2006), 39{47.
[14] S. Nanda and K. Kar,Convex fuzzy mapping, Fuzzy Sets and Systems, 48 (1992), 129{132.
[15] J. Ramik,Duality theory in fuzzy linear programming: some new concepts and results, Fuzzy Optim. and Decision Making,4 (2005), 25{39.
[16] W. Rodder and H. J. Zimmermann,Duality in fuzzy linear programming, In: Internat. Symp.on Extremal Methods and Systems Analysis, University of Texas at Austin, (1977), 415{427.
[17] Y. R. Syau,Generalization of preinvex and B-vex fuzzy mappings, Fuzzy Sets and Systems,120(2001), 533{542.
[18] Y. R. Syau, L. Jia and E. S. Lee,-1􀀀concavity and fuzzy multiple objective decision making,Computers and Mathematics with Applications,55 (2008), 1181{1188.
[19] J. L. Verdegay,A dual approach to solve the fuzzy linear programming problems, Fuzzy Sets and systems,14 (1984), 131{141.
[20] H. C. Wu,Duality theory in fuzzy linear programming problems with fuzzy coecients, Fuzzy Optim. and Decision Making,2(2003), 61{73.
[21] C. Zalinescu,Convex analysis in general vector spaces, Word Scienti c, 2002.
[22] C. Zhang, X. H. Yuan and E. S. Lee,Duality theory in fuzzy mathematical programming problems with fuzzy coecien, Computers and Mathematics with Applications, 49(2005),1709{1730.