On the Use of Fuzzy Set Theory for Optimizing Portfolios of Power Generation Assets

Decision-making processes need the support of analytical methods that are able to adequately capture the complexity of reality. Welldeveloped and well-established theories, such as the modern portfolio theory introduced by Harry M. Markowitz in 1952, are often based on probability theory and widely used for both financial and real assets. However, a number of empirical studies have shown that the Markowitz approach captures reality only to a very limited extent. In this paper, we propose fuzzy set theory as an alternative to the classical probabilistic approach. More specifically, we investigate the usefulness of a fuzzy portfolio selection model, where an investor’s aspiration levels of a portfolio’s return and risk are taken into account and expressed by membership functions. We define portfolio risk as a downside risk measure and introduce a fuzzy semi-mean absolute deviation portfolio selection model that is applied in order to optimize mixes of power generation plants.