Linear programming with a possibilistic objective function |
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| Affiliation: | 1. Federal University of Santa Catarina/LabPlan, Florianópolis, Brazil;2. INESC P&D, Santos, Brazil;3. MINES ParisTech, PSL-Research University, CMA-Centre de Mathématiques Appliquées, France;1. School of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai 264005, Shandong, China;2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;3. School of Electrical Engineering, Computing, and Mathematical Sciences, Curtin University, Perth 6845, Australia;4. Coordinated Innovation Center for Computable Modeling in Management Science, Tianjin University of Finance and Economics, Tianjin 300222, China;1. School of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai 264005, Shandong, China;2. School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, China;3. Department of Mathematics and Statistics, Curtin University, Perth 6845, Australia |
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| Abstract: | This paper proposes some ways for dealing with a linear program when the coefficients of the objective function are subject to possibilistic imprecision, i.e. they are characterized by fuzzy restrictions. Emphasis is placed upon a passive approach that yields a satisfying solution via an appropriate semi-infinite program, and an active one that allows to reach a solution with a high possibility level of optimality. Extensions to the possibilistic constraints case and to the case of multiple-objective programming problems with possibilistic coefficients are also hinted. We end up with some concluding remarks and indicate axes for further developments. |
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