A method for solving fuzzy goal programming problems based on MINMAX approach

Abstract Narasimhan incorporated fuzzy set theory within goal programming formulation in 1980. Since then numerous research has been carried out in this field. One of the well-known models for solving fuzzy goal programming problems was proposed by Hannan in 1981. In this paper the conventional MINMAX approach in goal programming is applied to solve fuzzy goal programming problems. It is proved that the proposed model is an extension to Hannan model that deals with unbalanced triangular linear membership functions. In addition, it is shown that the new model is equivalent to a model proposed in 1991 by Yang et al. Moreover, a weighted model of the new approach is introduced and is compared with Kim and Whang’s model presented in 1998. A numerical example is given to demonstrate the validity and strengths of the new models.

[1]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

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

[3]  J. Ignizio,et al.  Fuzzy programming with nonlinear membership functions: piecewise linear approximation , 1991 .

[4]  S. Chanas,et al.  Fuzzy goal programming - one notion, many meanings , 2002 .

[5]  S. B. Sinha,et al.  Fuzzy goal programming in multi-criteria decision systems: A case study in agricultural planning , 1988 .

[6]  Jong Soon Kim,et al.  A tolerance approach to the fuzzy goal programming problems with unbalanced triangular membership function , 1998, Eur. J. Oper. Res..

[7]  Mehrdad Tamiz,et al.  Goal Programming in the Period 1990–2000 , 2003 .

[8]  Mehrdad Tamiz,et al.  Goal programming for decision making: An overview of the current state-of-the-art , 1998, Eur. J. Oper. Res..

[9]  Jean-Marc Martel,et al.  Incorporating the Decision-maker's Preferences in the Goal-programming Model , 1990 .

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

[11]  Kirk R. Karwan,et al.  A chance-constrained goal programming model to evaluate response resources for marine pollution disasters. Research report , 1979 .

[12]  Jong Soon Kim,et al.  A tolerance approach for unbalanced economic development policy-making in a fuzzy environment , 2002, Inf. Sci..

[13]  Mehrdad Tamiz,et al.  A note on article "A tolerance approach to the fuzzy goal programming problems with unbalanced triangular membership function" , 2007, Eur. J. Oper. Res..

[14]  Shinji Suzuki,et al.  Multiobjective trajectory optimization by goal programming with fuzzy decisions , 1994 .

[15]  Jean-Marc Martel,et al.  Diverse Imprecise Goal Programming Model Formulations , 1998, J. Glob. Optim..

[16]  Singiresu S Rao,et al.  A fuzzy goal programming approach for structural optimization , 1992 .

[17]  E. Hannan.  ON FUZZY GOAL PROGRAMMING , 1981 .

[18]  B. K. Mohanty,et al.  A preference structure on aspiration levels in a goal programming problem—a fuzzy approach , 1988 .

[19]  Carlos Romero,et al.  A general structure of achievement function for a goal programming model , 2004, Eur. J. Oper. Res..

[20]  Mehrdad Tamiz,et al.  A review of Goal Programming and its applications , 1995, Ann. Oper. Res..

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

[22]  H. Kunzi,et al.  Lectu re Notes in Economics and Mathematical Systems , 1975 .

[23]  M. Inuiguchi,et al.  Goal programming problems with interval coefficients and target intervals , 1991 .

[24]  M. Gen,et al.  Large-scale 0–1 fuzzy goal programming and its application to reliability optimization problem , 1993 .

[25]  Jean-Marc Martel,et al.  Incorporating the Decision-Maker’s Preferences in the Goal Programming Model with Fuzzy Goal Values: A new Formulation , 1996 .

[26]  Singiresu S Rao,et al.  Multiobjective decision making in a fuzzy environment with applications to helicopter design , 1990 .

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

[28]  R. Narasimhan,et al.  Fuzzy goal programming with nested priorities , 1984 .

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

[30]  Singiresu S. Rao,et al.  Fuzzy goal programming approach for structural optimization , 1992 .

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

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

[33]  Hsiao-Fan Wang,et al.  A generalization of fuzzy goal programming with preemptive structure , 1997, Comput. Oper. Res..

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

[35]  G. A. Chalam.  Fuzzy goal programming (FGP) approach to a stochastic transportation problem under budgetary constraint , 1994 .