uncertain entropy as a risk measure in multi-objective portfolio optimization

As we are looking for knowledge of stock future returns in portfolio optimization, we are practically faced with two principal concepts: uncertainty and information about variables. this paper attempts to introduce a pragmatic bi-objective invest-ment model based on uncertainty, instead of probability space and information theory, instead of variance and other moments as a risk measure for portfolio optimization. not only is uncertainty space expected to be more in line with in-vestment theory, but also, applying and learning this approach seems more straightforward and practical for novice investors. the proposed model simulta-neously maximizes the uncertain mean of stock returns and minimizes uncertain entropy as a measure of portfolio risk. the uncertain zigzag distribution has been used for variables to avoid the complexity of fitting distributions for data. this uncertain mean-entropy portfolio optimization (umepo) has been solved by three meta-heuristic methods of multi-objective optimization: nsga-ii, mopso, and moica. finally, it was observed that the optimal portfolio obtained from the proposed model has a higher return and a lower entropy as a risk measure com-pared to the same model in the probability space.