Fuzzy mean-variance approach to strategic decision in agricultural management

When we decide the production of each agricultural product in the uncertain circumstance where its sell price, climate, consumers' preference and so on are not known previously, we should take its risk as well as the best expected selling volume or its interest into consideration. In this paper we employ fuzzy mean-variance analysis to decide the optimal solution in agricultural management which minimizes the risk and maximizes the expected selling volume. The mean-variance analysis is proposed by H. Markowitz and widely employed in stock investment. Nevertheless, it is also hard to treat an aspiration beheld by a decision-maker, because the formulation given by H. Markowitz is written using rigid values. In this paper a fuzzy number is employed to deal with a vague aspiration level and a fuzzy goal given by a decision-maker, that is, the fuzzy mean-variance analysis enables us to obtain the best solution which is realized within a vague aspiration level and a fuzzy goal. In the method, the decision maker defines a necessity level and a sufficient level for each of expected interest rate and risk. The effectiveness of our method is shown using a numerical example.