Linear fractional goal programming in consideration of fuzzy solution |
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| Institution: | 1. Département d’informatique et recherche opérationnelle, Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT), Université de Montréal, Montréal, QC, Canada;2. LAMIH UMR CNRS 8201 - Université de Valenciennes, Valenciennes Cedex 9, 59313, France;1. Department of Mathematics, University of Salerno, Via Giovanni Paolo II, 132, Fisciano 84084, SA, Italy;2. J.B. Speed School of Engineering, Industrial Engineering Department, University of Louisville, 132 Eastern Parkway, Louisville, Kentucky 40292, USA;1. Charles University, Faculty of Mathematics and Physics, Department of Applied Mathematics, Malostranské nám. 25, Prague 11800, Czech Republic;2. University of Economics, Faculty of Informatics and Statistics, nám. W. Churchilla 4, Prague 13067, Czech Republic |
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| Abstract: | Various types of formulations or solution methods have been proposed with fuzzy multi-goal programming, but most of them exclusively take linear functions as objective functions. However among the elements exhibited as goals, some goals that can be expressed with a ratio equation are available. Therefore, models that can handle such a fractional goal are preferable. On the other hand, most of the methods are of the type with which solutions can be obtained by crisp values. However since the elements composing problems are given by vague numerical values, the solutions should depend on the degree of vagueness. Accordingly it is natural that the solutions themselves are calculated as vague numerical values. As one of the models based upon such an idea, Kono et al.'s method is recommendable. However even this method cannot handle fractional goals. In this study, we propose a new method that expands Kono et al.'s method and allows also fractional goals. |
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