Multi-goal Programming Including Fractional Goal in Consideration of Fuzzy Solutions

Abstract

Various types of formulations of solving methods have been proposed with fuzzy multigoal programming, but most of them exclusively take linear functions as objectives. However among the elements exhibited as goals, some goals that can be expressed with a ratio equation are available. Therefore, thus 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 notwithstanding that vague numerical values are considered. However since the elements composing problems are given by vague numerical values, the solutions should depend on the degree of the vagueness. Accordingly it is natural that the solutions themselves are calculated as vague numerical values. As one of the solutions based upon such an idea, Kono et al.'s method is recommendable. However, even the said method cannot handle the fractional goal.In this study, a method that expands Kono et al.'s method and allows also the fraction-al goal to be complied with si proposed in consideration of such a situation mentioned above.