Below is another method concerning multicriteria decision support. The formal aspect was presented in the works of Orlovsky [3], [4], and partially also in others [1], [5], [6].
When choosing a logistics service provider, as with many other selection problems, the goal is to achieve the maximum possible benefit resulting from this choice. The word “possible” reminds us of the ever-existing constraints to which the decision-maker must submit. “Maximum benefit” emphasizes the existing direction of action and the assumption that the decision-maker is able, based on a certain assessment of the degree of fulfillment of a previously defined goal, to indicate which of the decisions is considered better.
The results of actions can be evaluated from many points of view. In such cases, choosing the decision that yields maximum benefits is usually very difficult, as an optimal decision from one point of view does not have to be so from another. The degree of difficulty encountered when indicating the best decision also depends on how the set of admissible decisions, the functions assigning evaluations to decisions according to individual criteria, and the preference relations enabling optimal choice are defined and what properties they have. It is obvious that every economic entity operates under specific conditions, in a certain economic environment. This environment is always associated with a system of limiting conditions. A decision (plan, alternative) that takes into account all constraints, and thus one that can be considered, is called an admissible decision.
According to W. Findeisen and E. S. Quade, a criterion is “a certain rule or norm by which variants are ordered according to their merits”. From a mathematical point of view, it is a function that assigns to each admissible decision a certain value (not necessarily numerical), called a benefit. Criteria should enable the assessment of the quality of various variants. In many situations, choosing a single criterion is very difficult, and often impossible. Attempts are then made to make decisions based on several different criteria. We then speak of multicriteria decision-making. Most often, the choice is then made on the basis of a certain “intermediate”, “general” criterion, derived from many taken into account.
Of particular interest is the part of multicriteria analysis that combines the standard approach to decision support problems with the theory of fuzzy sets. The foundations for today’s knowledge on this subject were laid in 1965 by Lofti Zadeh, who introduced the concept of a fuzzy set. The use of fuzzy sets in the case of decision-making optimization consists in the fact that both goals and constraints imposed on decisions, as well as their evaluations, can be fuzzy sets (in particular, fuzzy numbers). Also, the relations allowing for an optimal choice in many decision problems can have a fuzzy character. This approach is worth noting especially when it is impossible or disadvantageous to clearly indicate the better of the alternatives. This situation often occurs when we are dealing with a choice based on many criteria or based on the assessments of many experts.
The article presents a procedure for determining an optimal alternative using fuzzy preference relations. The shown method also includes the possibility of differentiating the relative importance of individual criteria. A proposal for applying the discussed procedure to the multicriteria selection of a logistics service provider is also presented.