\bibitem{2} G. Bahr, J. Kereiakes, H. Horwitz, R. Finnery, J. Calvin and
K. Goode, {\it The method of linear programming applied to
radiation treatment planning}, Radiology, {\bf 91} (1968), 686-693.
\bibitem{salmani ref1} J. Chiang, {\it Fuzzy linear programming based on statistical confidence interval and
interval-valued fuzzy set}, European Journal of
Operational Research, {\bf 129} (2001), 65-86.
\bibitem{8} C. Cotrutz, M. Lahanas, C. Kappas and D. Baltas, {\it A
multiobjective gradient based dose optimization algorithm for
external beam conformal radiotherapy}, Physics in Medicine and Biology, {\bf 46} (2001), 2161-2175.
\bibitem{CERR} J. Deasy, A. Blanco and V. Clark, {\it Cerr: a computational environment for radiotherapy research}, Medical Physics, {\bf 30} (2003), 979-985.
\bibitem{Dubois} D. Dubois and H. Prade, {\it Fuzzy sets and systems: theory and application},
Academic Press, New York, 1980.
\bibitem{Hamacher} H. W. Hamacher and K. H. Kufer, {\it Inverse radiation therapy planninng - a multiple objective optimization
approach}, Discrete Applied Mathematics, {\bf 118} (2002), 145-161.
\bibitem{15} C. L. Lawson and R. J. Hanson, {\it Solving least squares problems}, SIAM, (1995), 160-165.
\bibitem{mixed integer} E. Lee, T. Fox and I. Crocker, {\it Integer programming applied to intensity
modulated radiation therapy treatment planning}, Annals of
Operations Research, {\bf 119} (2003), 165-181.
\bibitem{IMRT1} M. S. Merritt, {\it A sensitivity-driven greedy approach to fluence map
optimization in intensity-modulated radiation therapy}, Ph. D. thesis, Department of Computational and Applied Mathematics,
Rice University, April 2006.
\bibitem{26} S. Morrill, R. Lane, J. Wong and I. Rosen, {\it Dose-volume
considerations with linear programming optimization}, Medical Physics, {\bf 18} (1991), 1201-1210.
\bibitem{Preciado} F. Preciado-Walters, M. Langer, R. Rardin and V. Thai, {\it A coupled column generation, mixed-integer
approach to optimal planning of intensity modulated therapy for
cancer}, Mathematical Programming, {\bf 101} (2004), 319-338.
\bibitem{Romeijn} H. E. Romeijn, R. K. Ahuja, J. F. Dempsey, A. Kumar and G. J. Li, {\it Novel linear programming approach
to fluence map optimization for intensity modulated radiation
therapy treatment planning}, Physics in Medicine and Biology, {\bf 48} (2003), 3521-3542.
\bibitem{30} H. E. Romeijn, J. F. Dempsey and J. G. Li, {\it A unifying framework for multi
criteria fluence map optimization models}, Physics in Medicine and Biology, {\bf 49} (2004), 1991-2013.
\bibitem{34} S. V. Spirou and C. Chui, {\it A gradient inverse planning algorithm with dose-volume constraints}, Medical Physics, {\bf 25} (1998), 321-333.
\bibitem{Yao wu} J. Yao and K. Wu, {\it Ranking fuzzy numbers based on decomposition principle and signed
distance}, Fuzzy Sets and Systems, {\bf 116} (2000), 275-288.
\bibitem{Yin Zhang} Y. Zhang and M. Merrit, {\it Dose-volume-based IMRT fluence optimization: a fast
leastsquares approach with differentiability}, Linear Algebra and
its Applications, {\bf 428} (2008), 1365-1387.
\bibitem{zimerman} H. J. Zimmermann, {\it Fuzzy set theory and its applications},
second ed., Kluwer Academic Publishers, Boston, 1991.