Fuzzy multi-objective linear programming applying to crop area planning

Crop area planning plays significant role in agricultural water management. During the planning, because of ambiguous or uncertain information caused by the vagueness of decision makers' subjective preference or the uncertainty of objective information, conventional multi-objective linear programming (MOLP) model is not suitable for such decision-making in such fuzzy environment. In this study, we proposed the fuzzy multi-objective linear programming (FMOLP) model with triangular fuzzy numbers and transformed the FMOLP model and its corresponding fuzzy goal programming (FGP) problem to crisp ones which can be solved by the conventional programming methods. The FMOLP model was applied to crop area planning of Liang Zhou region, Gansu province of northwest China, and then the optimal cropping patterns under different water-saving levels and satisfaction grades for water resources availability of the decision makers (DM) were obtained. Compared to the MOLP model, the FMOLP model itself expresses the fuzzy information effectively, and its solutions can represent the DMs satisfactory degree of the subjective preference and propose alternative solutions for better decision support when applied in the crop area planning.

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

[2]  Tien-Fu Liang,et al.  Application of fuzzy multi-objective linear programming to aggregate production planning , 2004, Comput. Ind. Eng..

[3]  Da Ruan,et al.  An α-Fuzzy Goal Approximate Algorithm for Solving Fuzzy Multiple Objective Linear Programming Problems , 2006, Soft Comput..

[4]  A. K. Lohani,et al.  Fuzzy Multiobjective and Linear Programming Based Management Models for Optimal Land-Water-Crop System Planning , 2006 .

[5]  Ruhul A. Sarker,et al.  Modelling a nationwide crop planning problem using a multiple criteria decision making tool , 2002 .

[6]  M. K. Luhandjula.  Multiple objective programming problems with possibilistic coefficients , 1987 .

[7]  Jaroslav Ramík.  Fuzzy goals and fuzzy alternatives in goal programming problems , 2000, Fuzzy Sets Syst..

[8]  C. Hwang,et al.  A new approach to some possibilistic linear programming problems , 1992 .

[9]  D. Kumar,et al.  Multicriterion decision making in irrigation planning , 1999 .

[10]  Hans-Jürgen Zimmermann,et al.  Applications of fuzzy set theory to mathematical programming , 1985, Inf. Sci..

[11]  K. Asai,et al.  Fuzzy linear programming problems with fuzzy numbers , 1984 .

[12]  Ichiro Nishizaki,et al.  An interactive fuzzy satisficing method for multiobjective stochastic linear programming problems through an expectation model , 2003, Eur. J. Oper. Res..

[13]  Zhang Chi,et al.  Optimization and evaluation of multi-objective crop pattern based on irrigation water resources allocation , 2007 .

[14]  Jacques-Eric Bergez,et al.  Estimating irrigation demand for water management on a regional scale: I. ADEAUMIS, a simulation platform based on bio-decisional modelling and spatial information , 2004 .

[15]  Tien-Fu Liang,et al.  Distribution planning decisions using interactive fuzzy multi-objective linear programming , 2006, Fuzzy Sets Syst..

[16]  S Vedula,et al.  Multireservoir System Optimization using Fuzzy Mathematical Programming , 2000 .

[17]  W Thomas Lin,et al.  A survey of goal programming applications , 1980 .

[18]  Jungji Kwon,et al.  The Air Pollution Constraints Considered Best Generation Mix Using Fuzzy Linear Programming , 2005, KES.

[19]  Masahiro Inuiguchi,et al.  Multiple Objective Linear Programming with Fuzzy Coefficients , 2005 .

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

[21]  A. Charnes,et al.  Goal programming and multiple objective optimizations: Part 1 , 1977 .

[22]  E. Xevi,et al.  A multi-objective optimisation approach to water management. , 2005, Journal of environmental management.

[23]  Didier Dubois,et al.  Ranking fuzzy numbers in the setting of possibility theory , 1983, Inf. Sci..

[24]  Mohammed Mainuddin,et al.  Optimal crop planning model for an existing groundwater irrigation project in Thailand , 1997 .

[25]  J. Ramík,et al.  Inequality relation between fuzzy numbers and its use in fuzzy optimization , 1985 .

[26]  Xiaodong Zhang,et al.  Optimal decision schemes for agricultural water quality management planning with imprecise objective , 2009 .

[27]  R. Harboe,et al.  Fuzzy multiple-criteria decision making for crop area planning in Narmada river basin. , 2000 .

[28]  Guangquan Zhang,et al.  A new approximate algorithm for solving multiple objective linear programming problems with fuzzy parameters , 2006, Appl. Math. Comput..