Decision Making

Decision making is a complex and also a fundamental process for human beings. Several authors claim that decision making is one of the most important features to distinguish human beings from animals. Everyday, we face situations in which there are different alternatives and, usually, we must decide which one is the best or which one should be acomplished. In Decision Making we can find two different areas: (i) The selection of alternatives, whose aim is to find the best alternative or set of alternatives that can solve a decision problem, and (ii) the consensus, that measures the degree of agreement among the experts who take part in a group decision making problem.
A classic decision making problem has the following elements:

  1. A set of alternatives or possible decisions.
  2. A set of states of the nature that defines the context of the problem.
  3. A set of utility values, each one is related to a pair of elements, the first one is an alternative and the second one to a state of the nature.
  4. A function that establishes the experts' preferences over the possible results.

In Decision Making there exist different decision situations depending on the context of the problem:

  1. Environments with certainty: the utility of each alternative is known exactly and with precision..
  2. Environments with risk: the knowledge about the alternatives consists of their probability distribution.
  3. Environments with uncertainty: In this situation we do not know the probability of the alternatives. The utility of each one is characterized in an approximate way.

Decision making is applied to different areas such as social sciences, economy, engineering, psychology, etc. This wide range of application fields implies the need of different decision making models. These needs gave rise to the Decision Theory. The Classic Decision Theory provides a great number of models that can be applied to the aforementioned situations. However, not always the classic models are suitable for all the decision situations such us uncertainty, i.e., in problems with vague and imprecise information. These situations are known as Decision Making Problems in a Fuzzy Context or Fuzzy Decision Making. Therefore, depending on the experts' knowledge about the alternatives of the problem, the definition context; the decision model could be different.

The preference modelling plays a key role in the Decision Making too. Due to the fact that it will define the nature and the organization of the information that the experts will use to express their knowledge, tastes, preferences, etc. In contexts with certainty and risk, where experts assess quantitative aspects, the use of numerical crisp or interval-valued information is suitable. However in context with uncertainty, that are the type of problems we focus on, in which qualitative aspects must be assessed the use of the Fuzzy Linguistic Approach [Zad75] based on the Fuzzy sets Theory [Zad65] has provided successful results.

In the literature can be distinguished two different processes in Decision Making Problems: the selection of alternatives and the consensus.

  1. The selection of alternatives: it looks for a solution set of alternatives that are the most suitable ones for the Decision Making Problem.
  2. Consensus: it may that happen that solves a Decision Making problem with multiple experts by using a selection process of the alternatives produces that several experts don't agree with the obtained solution. For this reason, the study of the consensus has become a very important research field within the Decision Making. Consensus can be defined as an iterative process for a group of experts that are discussing each other to reach an agreement. The group is coordinated by a chairperson that assists the experts with the aim of making their opinions closer.

In this topic we have developed several decision models to deal with problems in context with uncertainty by using linguistic modelling of information as well as models for managing non_homogeneous information. Additionally, some consensus models have been designed with the aim of automating human tasks of these processes and dealing with vague and uncertain information.