Ph.D. Mellado-Cid, Cristhian

Interval numbers are widely used in many fields to provide information about different scenarios. This paper presents several new uncertain average formulations using the ordered weighted average, prioritized, probabilistic and induced operators. First, the work introduces the uncertain prioritized induced probabilistic ordered weighted average (UPIPOWA) operator that its main applicability is in complex group decision making problems. Also, a wide range of special cases and extensions using quasi-arithmetic means are presented, such is the case of the quasi-arithmetic UPIPOWA (QUPIPOWA) operator. The study analyzes the applicability of this new approach in economic variables, specifically are imports and exports. Particularly, the paper focuses on measuring the imports and exports for Latin America for 2017

Agricultural product prices are subject to various uncertainties, including unpredictable weather conditions, pest infestations, and market fluctuations, which can significantly impact agricultural yields and productivity. Accurately assessing and understanding price is crucial for farmers, policymakers, and stakeholders in the agricultural sector to make informed decisions and implement appropriate risk management strategies. This study used the ordered weighted average (OWA) operator and its extensions as mathematical aggregation techniques incorporating ordered weights to capture and evaluate the factors influencing price variation. By generating different vectors related to different inputs to the traditional formulation, it is possible to aggregate information to calculate and provide a new view of the outcomes. The results of this research can help enhance risk management practices in agriculture and support decision-making processes to mitigate the adverse effects of price.

The main practical problems that are faced by portfolio optimisation under the Markowitz model are (i) its lower out-of-sample performance than the naive 1=n rule, (ii) the resulting asset weights with extreme values, and (iii) the high sensitivity of those asset weights to small changes in the data. In this study, we aim to overcome these problems by using a computation method that shifts the smaller eigenvalues of the covariance matrix to the space that houses the eigenvalue spectrum of a random matrix. We evaluate this new method using a rolling sample approach. We obtain portfolios that show both more stable asset weights and better performance than the 1=n rule. We expect that this new computation method will be extended to several problems in portfolio management, thereby improving their consistency and performance.