Fuzzy optimal solution of fully fuzzy linear programming problems using ranking function

In this paper, a new method is proposed to find the fuzzy optimal solution of fully fuzzy linear programming FFLP problems with mixed constraints. By using the proposed method the fuzzy optimal solution of FFLP problems with mixed constraints occurring in real life situations can be easily obtained. To illustrate the proposed method a numerical example is solved. The proposed method can be easily applied to find the fuzzy optimal solution of FFLP problems occurring in real life situations.

[1]  T. Allahviranloo,et al.  Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution , 2009 .

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

[3]  Lourdes Campos,et al.  Linear programming problems and ranking of fuzzy numbers , 1989 .

[4]  Nezam Mahdavi-Amiri,et al.  Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables , 2007, Fuzzy Sets Syst..

[5]  B. Werners An interactive fuzzy programming system , 1987 .

[6]  Heinrich J. Rommelfanger,et al.  A general concept for solving linear multicriteria programming problems with crisp, fuzzy or stochastic values , 2007, Fuzzy Sets Syst..

[7]  Ali Ebrahimnejad,et al.  Using complementary slackness property to solve linear programming with fuzzy parameters , 2009 .

[8]  K. Ganesan,et al.  Fuzzy linear programs with trapezoidal fuzzy numbers , 2006, Ann. Oper. Res..

[9]  M. Inuiguchi,et al.  A solution algorithm for fuzzy linear programming with piecewise linear membership functions , 1990 .

[10]  S. Chanas The use of parametric programming in fuzzy linear programming , 1983 .

[11]  James J. Buckley,et al.  Evolutionary algorithm solution to fuzzy problems: Fuzzy linear programming , 2000, Fuzzy Sets Syst..

[12]  H. Zimmermann Fuzzy programming and linear programming with several objective functions , 1978 .

[13]  Jaroslav Ramík,et al.  Duality in Fuzzy Linear Programming: Some New Concepts and Results , 2005, Fuzzy Optim. Decis. Mak..

[14]  Xinwang Liu,et al.  Measuring the satisfaction of constraints in fuzzy linear programming , 2001, Fuzzy Sets Syst..

[15]  José L. Verdegay,et al.  Using fuzzy numbers in linear programming , 1997, IEEE Trans. Syst. Man Cybern. Part B.

[16]  T. Allahviranloo,et al.  SOLVING FULLY FUZZY LINEAR PROGRAMMING PROBLEM BY THE RANKING FUNCTION , 2008 .

[17]  A. Kaufmann,et al.  Introduction to fuzzy arithmetic : theory and applications , 1986 .

[18]  Hideo Tanaka,et al.  On Fuzzy-Mathematical Programming , 1973 .

[19]  Jie Lu,et al.  Formulation of fuzzy linear programming problems as four-objective constrained optimization problems , 2003, Appl. Math. Comput..

[20]  Tofigh Allahviranloo,et al.  Fuzzy integer linear programming problems , 2007 .

[21]  Hamid Reza Maleki,et al.  RANKING FUNCTIONS AND THEIR APPLICATIONS TO FUZZY LINEAR PROGRAMMING , 2003 .

[22]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

[23]  Hsiao-Fan Wang,et al.  Linear programming with fuzzy coefficients in constraints , 1999 .

[24]  Seyed Hadi Nasseri A NEW METHOD FOR SOLVING FUZZY LINEAR PROGRAMMING BY SOLVING LINEAR PROGRAMMING , 2008 .

[25]  Amelia Bilbao-Terol,et al.  Linear programming with fuzzy parameters: An interactive method resolution , 2007, Eur. J. Oper. Res..

[26]  S. H. Nasseri,et al.  A primal-dual method for linear programming problems with fuzzy variables , 2010 .

[27]  Mao-Jiun J. Wang,et al.  Ranking fuzzy numbers with integral value , 1992 .

[28]  Ebrahim Nasrabadi,et al.  Fully fuzzified linear programming, solution and duality , 2006, J. Intell. Fuzzy Syst..

[29]  Amit Kumar,et al.  A new method for solving fully fuzzy linear programming problems , 2011 .