Decision criteria under uncertainty using fuzzy concept

Abstract

Summary form only given. A minimax decision philosophy dictates that attention must be focused only on the most damaging outcomes in order to limit the damage as much as possible. Using a sequence of intervals of confidence instead of a sequence of ordinary numbers will give more reliable results. Therefore, in the case of fuzziness, triangular fuzzy numbers are very appropriate to use instead of those single possible outcomes. The Hurwicz criterion can be used for those situations in which the decision maker feels neither extremely pessimistic or optimistic. The degree of optimism is established by using a coefficient which is called an index of optimism. The Hurwicz criterion is criticized due to the difficulty of assigning a particular value to the index of optimism. In the case of fuzziness, a triangular fuzzy number for the index of optimism can also be used. In other words, the degree of optimism can be given as a membership function. In the fuzzy minimax regret criterion, the minimax regret rule is based on the assumption that a decision maker wants to avoid any regret or at least to minimize the maximum regret about a choice. To use the criterion, first a regret matrix is developed by finding out the maximum payoff for each state. Second, each payoff in the column is subtracted from the maximum payoff that has been recognized, and this process is reiterated for each column. Finally, the alternative that minimizes the maximum regret is then selected.