A new method for solving fully fuzzy linear Bilevel programming problems

In this paper, a new method is proposed to find the fuzzy optimal solution of fully fuzzy linear Bilevel programming (FFLBLP) problems by representing all the parameters as triangular fuzzy numbers. In the proposed method, the given FFLBLP problem is decomposed into three crisp linear programming (CLP) problems with bounded variables constraints, the three CLP problems are solved separately and by using its optimal solutions, the fuzzy optimal solution to the given FFLBLP is obtained. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of FFLBLP occurring in real life situations.

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

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

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

[4]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[5]  Jagdeep Kaur,et al.  SOLVING FULLY FUZZY LINEAR PROGRAMMING PROBLEMS WITH INEQUALITY CONSTRAINTS , 2010 .

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

[7]  Jagdeep Kaur,et al.  Fuzzy Optimal Solution of Fully Fuzzy Linear Programming Problems with Equality Constrains , 2016 .

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

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

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

[11]  Hans-Jürgen Zimmermann,et al.  Fuzzy mathematical programming , 1983, Comput. Oper. Res..

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

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

[14]  S. H. Nasseri,et al.  A fuzzy primal simplex algorithm and its application for solving flexible linear programming problems , 2010 .

[15]  Jagdeep Kaur,et al.  FUZZY LINEAR PROGRAMMING PROBLEMS WITH FUZZY PARAMETERS , 2010 .