The uncertain investment decision-making methods based on uncertain selected utility functions and their applications

The uncertain investment decision-making methods based on uncertain utility functions provide effective approaches to solving uncertain investment problems in complex environments. However, the ranking criteria of existing methods are limited. They consider only the uncertain expected utility value to assess the average return but fail to incorporate the uncertain variance utility value to measure the stability of returns. Furthermore, the uncertain utility functions in existing methods are directly specified and applied to the uncertain investment decision-making model without sufficient comparative analysis. To overcome these limitations, this paper makes the following contributions: First, we use numerical examples to verify the effectiveness of adopting the uncertain variance utility value as a ranking criterion. Second, based on a thorough comparative analysis, we construct three new uncertain utility functions by combining composite functions with uncertain variables. Third, we propose two new decision-making methods: one is a single method based on the uncertain variance utility value, and the other is a comprehensive method that introduces a risk preference coefficient and combines the uncertain expected utility value with the variance utility value. Based on these three new uncertain utility functions, the feasibility of the two methods is verified respectively through numerical examples. Finally, based on these three new uncertain utility functions, the feasibility and effectiveness of the proposed methods are verified through a case study of the water saving management contract.