On fuzzy random multiobjective quadratic programming

In this paper, a multiobjective quadratic programming problem having fuzzy random coefficients matrix in the objective and constraints and the decision vector are fuzzy pseudorandom variables is considered. First, we show that the efficient solutions of fuzzy quadratic multiobjective programming problems are resolved into series-optimal-solutions of relative scalar fuzzy quadratic programming. Some theorems are proved to find an optimal solution of the relative scalar quadratic multiobjective programming with fuzzy coefficients, having decision vectors as fuzzy variables. At the end, numerical examples are illustrated in the support of the obtained results.

[1]  Kim-Fung Man,et al.  A real-coding jumping gene genetic algorithm (RJGGA) for multiobjective optimization , 2007, Inf. Sci..

[2]  N. Huang,et al.  A new class of interval projection neural networks for solving interval quadratic program , 2008 .

[3]  Matthias Ehrgott,et al.  Multicriteria Optimization , 2005 .

[4]  EkelPetr Ya.,et al.  Algorithms of discrete optimization and their application to problems with fuzzy coefficients , 2006 .

[5]  C. Carlsson,et al.  A parametric approach to fuzzy linear programming , 1986 .

[6]  Fred W. Glover,et al.  Solving the maximum edge weight clique problem via unconstrained quadratic programming , 2007, Eur. J. Oper. Res..

[7]  Yian-Kui Liu,et al.  A class of fuzzy random optimization: expected value models , 2003, Inf. Sci..

[8]  Wang Guangyuan,et al.  Linear programming with fuzzy random variable coefficients , 1993 .

[9]  S. Czerwik,et al.  Stability of the quadratic functional equation in Lipschitz spaces , 2004 .

[10]  Peter Schlattmann,et al.  Theory and Algorithms , 2009 .

[11]  H. Ishibuchi,et al.  Identification of possibilistic linear systems by quadratic membership functions of fuzzy parameters , 1990 .

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

[13]  Deng-Feng Li,et al.  An approach to fuzzy multiattribute decision making under uncertainty , 2005, Inf. Sci..

[14]  Madan M. Gupta,et al.  On fuzzy stochastic optimization , 1996, Fuzzy Sets Syst..

[15]  Masatoshi Sakawa,et al.  An interactive fuzzy satisficing method for multiobjective linear programming problems with random variable coefficients through a probability maximization model , 2004, Fuzzy Sets Syst..

[16]  Riccardo Cambini,et al.  On Generalized Linearity of Quadratic Fractional Functions , 2004, J. Glob. Optim..

[17]  Yian-Kui Liu,et al.  Fuzzy random programming with equilibrium chance constraints , 2005, Inf. Sci..

[18]  Z. Qiao,et al.  On solutions and distribution problems of the linear programming with fuzzy random variable coefficients , 1993 .

[19]  M. K. Luhandjula Fuzziness and randomness in an optimization framework , 1996, Fuzzy Sets Syst..

[20]  Masaaki Ida,et al.  Efficient solution generation for multiple objective linear programming based on extreme ray generation method , 2005, Eur. J. Oper. Res..

[21]  Tapan Kumar Pal,et al.  On comparing interval numbers , 2000, Eur. J. Oper. Res..

[22]  Jiafu Tang,et al.  An interactive approach based on a genetic algorithm for a type of quadratic programming problems with fuzzy objective and resources , 1997, Comput. Oper. Res..

[23]  Yinzhen Li,et al.  The fuzzy quadratic assignment problem with penalty: New models and genetic algorithm , 2006, Appl. Math. Comput..

[24]  Kok Lay Teo,et al.  Some properties on quadratic infinite programs of integral type , 2007, Appl. Math. Lett..

[25]  Wang Guangyuan,et al.  On fuzzy random linear programming , 1994 .

[26]  Lotfi A. Zadeh,et al.  Toward a generalized theory of uncertainty (GTU)--an outline , 2005, Inf. Sci..

[27]  Petr Ekel,et al.  Algorithms of discrete optimization and their application to problems with fuzzy coefficients , 2006, Inf. Sci..

[28]  Aníbal Ollero,et al.  Fuzzy Methodologies for Interactive Multicriteria Optimization , 1980, IEEE Transactions on Systems, Man, and Cybernetics.

[29]  Xiaofeng Liao,et al.  Tabu search for fuzzy optimization and applications , 2004, Inf. Sci..

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

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

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