Fuzzy Logic Operators in Decision-making

The fuzzy logic operators are used to decide the following multicriteria decision-making problem. A finite set of alternatives is evaluated by a set of fuzzy criteria, i.e., fuzzy relations, which may be either fuzzy preference, or similarity, or likeness relations. The problem is to construct an evaluation procedure to compare the set of alternatives according to the whole set of criteria, i.e., to aggregate the private fuzzy relations in order to get the union relation as a fuzzy one, enhancing to solve the ranking, choice, or cluster problem. Some properties of these operators, required to decide the ranking, choice, or cluster problems and depending on the properties of the private relations, are proved. A numerical example is given as well.