Oriented fuzzy numbers are a convenient tool to manage an investment portfolio as they enable the inclusion of uncertain and imprecise information about the financial market in a portfolio analysis. This kind of portfolio analysis is based on the discount factor. Thanks to this fact, this analysis is simpler than a portfolio analysis based on the return rate. The present value is imprecise due to the fact that it is modelled with the use of oriented fuzzy numbers. In such a case, the expected discount factor is also an oriented fuzzy number. The main objective of this paper is to conduct a portfolio analysis consisting of the instruments with the present value estimated as a trapezoidal oriented fuzzy number. We consider the portfolio elements as being positively and negatively oriented. We test their discount factor. Due to the fact that adding oriented fuzzy numbers is not associative, a weighted sum of positively oriented discount factors and a weighted sum of negatively oriented factors is calculated and consequently a portfolio discount factor is obtained as a weighted addition of both sums. Also, the imprecision risk of the obtained investment portfolio is estimated using measures of energy and entropy. All theoretical considerations are illustrated by an empirical case study.

中文翻译：

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梯形定向模糊数在投资组合分析中的应用

定向模糊数是管理投资组合的便捷工具，因为它们能够在投资组合分析中包含关于金融市场的不确定和不精确的信息。这种投资组合分析基于贴现因子。由于这一事实，这种分析比基于回报率的投资组合分析更简单。现值是不精确的，因为它是使用定向模糊数建模的。在这种情况下，预期折扣因子也是一个有向模糊数。本文的主要目的是进行投资组合分析，由工具组成，现值估计为梯形模糊数。我们认为投资组合元素是积极和消极的。我们测试他们的折扣因子。由于加法模糊数不具有关联性，计算了正向贴现因子的加权和和负向因子的加权和，从而得到投资组合贴现因子作为两个和的加权加法。此外，使用能量和熵的度量来估计所获得的投资组合的不精确风险。所有的理论考虑都通过一个经验案例研究来说明。