Satisfying optimization method based on goal programming for fuzzy multiple objective optimization problem

This paper proposes a satisfying optimization method based on goal programming for fuzzy multiple objective optimization problem. The aim of this presented approach is to make the more important objective achieving the higher desirable satisfying degree. For different fuzzy relations and fuzzy importance, the reformulated optimization models based on goal programming is proposed. Not only the satisfying results of all the objectives can be acquired, but also the fuzzy importance requirement can be simultaneously actualized. The balance between optimization and relative importance is realized. We demonstrate the efficiency, flexibility and sensitivity of the proposed method by numerical examples.

[1]  Y. D. Hu,et al.  An interactive algorithm for multicriteria decision making: the attainable reference point method , 2001, IEEE Trans. Syst. Man Cybern. Part A.

[2]  Jian-Bo Yang,et al.  Normal vector identification and interactive tradeoff analysis using minimax formulation in multiobjective optimization , 2002, IEEE Trans. Syst. Man Cybern. Part A.

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

[4]  Bijay Baran Pal,et al.  A goal programming procedure for solving problems with multiple fuzzy goals using dynamic programming , 2003, Eur. J. Oper. Res..

[5]  Shaoyuan Li,et al.  Fuzzy goal programming with multiple priorities via generalized varying-domain optimization method , 2004, IEEE Trans. Fuzzy Syst..

[6]  R. Narasimhan.  GOAL PROGRAMMING IN A FUZZY ENVIRONMENT , 1980 .

[7]  Liang-Hsuan Chen,et al.  Fuzzy goal programming with different importance and priorities , 2001, Eur. J. Oper. Res..

[8]  Onur Aköz,et al.  A fuzzy goal programming method with imprecise goal hierarchy , 2007, Eur. J. Oper. Res..

[9]  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..

[10]  Chang-Chun Lin,et al.  A weighted max-min model for fuzzy goal programming , 2004, Fuzzy Sets Syst..

[11]  E. Hannan.  Linear programming with multiple fuzzy goals , 1981 .

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

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

[14]  Jian-Bo Yang,et al.  Minimax reference point approach and its application for multiobjective optimisation , 2000, Eur. J. Oper. Res..

[15]  D. A. Conway.  Management Goals and Accounting for Control , 1966 .

[16]  Pratyush Sen,et al.  Preference modelling by estimating local utility functions for multiobjective optimization , 1996 .

[17]  Baoding Liu,et al.  Theory and Practice of Uncertain Programming , 2003, Studies in Fuzziness and Soft Computing.

[18]  N. Dopuch,et al.  Management Goals and Accounting for Control. , 1967 .

[19]  R. Tiwari,et al.  Priority structure in fuzzy goal programming , 1986 .

[20]  Yacov Y. Haimes,et al.  Multiobjective Decision Making: Theory and Methodology , 1983 .

[21]  Masatoshi Sakawa,et al.  An interactive fuzzy satisficing method for multiobjective nonconvex programming problems with fuzzy numbers through coevolutionary genetic algorithms , 2001, IEEE Trans. Syst. Man Cybern. Part B.

[22]  Shaoyuan Li,et al.  Enhanced Interactive Satisfying Optimization Approach to Multiple Objective Optimization with Preemptive Priorities , 2006, Int. J. Inf. Technol. Decis. Mak..

[23]  Masatoshi Sakawa,et al.  An Interactive Fuzzy Satisficing Method for Multiobjective Linear-Programming Problems and Its Application , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[24]  C. Hwang,et al.  Fuzzy Multiple Objective Decision Making: Methods And Applications , 1996 .

[25]  Marc Despontin,et al.  Multiple Criteria Optimization: Theory, Computation, and Application, Ralph E. Steuer (Ed.). Wiley, Palo Alto, CA (1986) , 1987 .

[26]  Wynn C. Stirling,et al.  A theory of satisficing decisions and control , 1998, IEEE Trans. Syst. Man Cybern. Part A.

[27]  A. Charnes,et al.  Management Models and Industrial Applications of Linear Programming , 1961 .

[28]  R. Tiwari,et al.  Fuzzy goal programming- an additive model , 1987 .