Formulation of the decision-making problem
The decision-making problem consists of forming a set of possible alternatives that resolve a problem situation under existing constraints, and selecting among these alternatives a single best one or several preferred alternatives that satisfy the requirements imposed upon them. Formally, the decision-making problem D can be written in the following generalized form:
D = ⟨F, A, X, G, P⟩
Where:
F is the formulation of the decision-making problem, which includes a substantive description of the problem at hand and, if necessary, its model representation, the definition of the goal or goals to be achieved, and requirements for the form of the final result;
A is the set of possible alternatives from which the choice is made. These may be actually existing alternatives, which, depending on the context of the problem, take the form of objects, candidates, ways of achieving the goal, actions, decisions, and the like, or a hypothetical set of all theoretically possible alternatives, which may even be infinite. A choice arises only when there are at least two possible alternatives for solving the problem;
X is the set of attributes (features, parameters) describing the alternatives and their distinguishing characteristics. Attributes include, first, objective indicators that characterize certain properties inherent in the alternatives and that, as a rule, can be measured; and second, subjective assessments that are usually given according to specially selected or constructed criteria reflecting features of the alternatives that are important to the participants in the choice;
G is the set of conditions that constrain the domain of admissible alternatives for solving the problem. Constraints may be described either substantively or specified in the form of certain formal requirements for alternatives and/or their attributes. For example, these may be constraints on the values of a given attribute, or varying degrees of the attribute's relevance (expressiveness) for different alternatives, or the impossibility of simultaneously combining certain attribute values for actually existing alternatives;
P represents the preferences of one or several decision-makers (DMs), which serve as the basis for evaluating and comparing possible alternatives for solving the problem, selecting admissible alternatives, and finding the best or acceptable alternative. Quite often, to simplify the formulation of the decision-making problem, part of the information describing the DM's preferences is converted into constraints.
The factors characterizing a problem situation are conventionally divided into two groups: controllable and uncontrollable.
- Controllable factors, the choice of which depends on the DM, are in essence the goals set, the alternatives for achieving them, the subjective assessments of alternatives, and the degree of goal attainment.
- Uncontrollable factors do not depend on the DM. They determine the objective attributes of alternatives and partly establish constraints on the choice of possible alternatives.
Factors are also subdivided into:
- deterministic, with known and/or predetermined exact characteristics;
- probabilistic, or stochastic, with known and/or predetermined random characteristics;
- uncertain, or unknown, with vaguely defined and/or unknown characteristics, but sometimes with a known range of variation of their values.