Models for dealing with uncertainty in decision-making

Abstract

[eng] All aspects of life revolve around making decisions. From the very basic, such as choosing each morning what clothes to wear, to the most transcendental, as might be deciding what bachelor’s degree to study. Also, all decisions are subject to different types and degrees of uncertainties. In recent decades, major theoretical advances have taken place in the field of decision-making under uncertainty. Moreover, a large variety of applications. However, there are still outstanding research gaps. Some of these unresolved problems have been successfully addressed in this doctoral thesis, under the title of “Models for dealing with uncertainty in decision-making”. Specifically, the applicability of Yager’s ordered weighted averaging (OWA) operator in issues related to retirement and the need of new comparative tools for particular and complex situations.

This doctoral thesis is divided into five chapters. Chapter 1 gives an introduction, discusses the objectives, explains the followed methodology, and provides information regarding the structure of the thesis work.

Chapter 2 offers a comprehensive review of mathematical methods for decision-making under uncertain environments, particularly of the OWA operator. The OWA operator is a nonlinear function for aggregating information that has gained much popularity. Also, a bibliometric analysis is conducted in order to quantitatively explore a large volume of publications related to the OWA operator. This is done by using the Web of Science (WoS) Core Collection data source and the Visualization of Similarities (VOS) viewer software. Likewise, the main theoretical concepts of pensions as well as the knowledge domain are described.

Chapter 3 presents a compendium of five significant research contributions related to the general objective of the doctoral thesis. Two of these contributions show new aggregation operators based on the OWA operator, the adequacy coefficient, the linguistic variable, and the interval number. These novel aggregation operators are proven to be very useful in real-life decision-making problems under a high degree of uncertainty, particularly when the decision maker wants to compare different alternatives with an ideal but without giving any penalty or reward in the case that the ideal levels are exceeded. Two extensive illustrative examples are offered, one regarding business internationalization and another one regarding human resource practices in football.

The three remaining research contributions explore the use of the OWA operator and some of its prime extensions in pension decision-making. One contribution measures the future average pension adjusted for inflation for all autonomous communities of Spain. Similarly, the same index is calculated in a further contribution but in this case for each state of the United States (U.S.). Another contribution designs two algorithms to choose the most suitable product for supplementing the public pension when a person retires and develops a practical example for a better understanding. These three research contributions seek to positively impact the lives of the current and future retirees by making available practical tools for pension decision-making.

Chapter 4 points out the final conclusions, limitations, and future research opportunities of this thesis work.

Finally, Chapter 5 includes as an annex an additional research contribution, where basic uncertain information (BUI) is used to assess different types of enterprise risks, as it allows to effectively model uncertainty. Then the BUI assessments are aggregated through an extension of the OWA operator, thus facilitating the prioritization of the identified risks.