Aggregation Functions as a Base for Decision Making

When making the decision in various fields, the following types of uncertainties are frequently encountered: ignorance of the phenomenon; imprecision of measurement; the vagueness of language; subjective assessment. Combining information from different sources in a single important output is a crucial task of numerous investigations, mostly based on powerful computers. The paper presents the mathematical models based on aggregation functions for these uncertainties such as probability theory and statistics (by copulas), and newer mathematical methods such as the theory of fuzzy sets and fuzzy logics, and non-additive measures and integrals based on them. A generalization of the utility theory is given based on pseudo-additive measures.