Linear fractional goal programming in consideration of fuzzy solution

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.