Algorithm for interval linear programming involving interval constraints

In real optimization, we always meet the criteria of useful outcomes increasing or expenses decreasing and demands of lower uncertainty. Therefore, we usually formulate an optimization problem under conditions of uncertainty. In this paper, a new method for solving linear programming problems with fuzzy parameters in the objective function and the constraints based on preference relations between intervals is investigated. To illustrate the efficiency of the proposed method, a numerical example is presented.

[1]  M. K. Luhandjula Fuzzy optimization: an appraisal , 1989 .

[2]  Heinrich Rommelfanger,et al.  Fuzzy Decision Support-Systeme , 1994 .

[3]  Bing-Yuan Cao Programming with Fuzzy Variables , 2002 .

[4]  I. Alolyan,et al.  A NEW METHOD FOR COMPARING CLOSED INTERVALS , 2011 .

[5]  D. Dubois,et al.  Systems of linear fuzzy constraints , 1980 .

[6]  H. Ishibuchi,et al.  Multiobjective programming in optimization of the interval objective function , 1990 .

[7]  Ralph E. Steuer Algorithms for Linear Programming Problems with Interval Objective Function Coefficients , 1981, Math. Oper. Res..

[8]  M. Vila,et al.  A general model for fuzzy linear programming , 1989 .

[9]  G. Bitran Linear Multiple Objective Problems with Interval Coefficients , 1980 .

[10]  Eldon Hansen,et al.  Global optimization using interval analysis , 1992, Pure and applied mathematics.

[11]  Anju Vyas Print , 2003 .

[12]  H. Rommelfanger,et al.  Linear programming with fuzzy objectives , 1989 .

[13]  Masahiro Inuiguchi,et al.  Minimax regret solution to linear programming problems with an interval objective function , 1995 .

[14]  Ronald R. Yager,et al.  A procedure for ordering fuzzy subsets of the unit interval , 1981, Inf. Sci..

[15]  S. Chanas,et al.  Multiobjective programming in optimization of interval objective functions -- A generalized approach , 1996 .

[16]  Luc Jaulin,et al.  Applied Interval Analysis , 2001, Springer London.

[17]  Didier Dubois,et al.  Ranking fuzzy numbers in the setting of possibility theory , 1983, Inf. Sci..

[18]  Stanislaw Heilpern,et al.  Representation and application of fuzzy numbers , 1997, Fuzzy Sets Syst..

[19]  Huibert Kwakernaak,et al.  Rating and ranking of multiple-aspect alternatives using fuzzy sets , 1976, Autom..

[21]  G. Alefeld,et al.  Introduction to Interval Computation , 1983 .

[22]  Mitsuo Gen,et al.  Genetic algorithms and engineering design , 1997 .

[23]  Mashaallah Mashinchi,et al.  Linear programming with fuzzy variables , 2000, Fuzzy Sets Syst..

[24]  Z. Kulpa DIAGRAMMATIC REPRESENTATION FOR A SPACE OF INTERVALS , 1997 .

[25]  R. Yager,et al.  On ranking fuzzy numbers using valuations , 1999 .

[26]  Debjani Chakraborty,et al.  Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming , 2001, Fuzzy Sets Syst..

[27]  Yozo Nakahara,et al.  On the linear programming problems with interval coefficients , 1992 .