Abstract

In real life we have to deal with uncertainty, imprecision and vagueness. Many ideas were introduced and studied in detail to manage with these problems. Now we briefly expose the main formal concepts which describe non-ideal situations, i.e. Probability, Statistics and Fuzzy Logic. Probability has recent origins with respect to other branches of mathematics which have deep roots in the past, like geometry or algebra.We may say all this started with Antoine Gombaud, Chevalier de Méré, who asked Blaise Pascal about gambling with dice. The correspondence between Pierre de Fermat and Blaise Pascal, which began in 1654, initially on these questions, led to the introduction of basic concepts, i.e. probability and expectation. Only in 1657, Christian Huygens in "De Ratiociniis in ludo aleae" proposed a first systematic study of the new branch of mathematics. However, the need of an axiomatic construction of the theory of probability arose to analyze more general and complex situations than gambling. A strong formalization was supplied by the monograph "Foundations of the theory of probability" by Andrey Nikolaevich Kolmogorov.Statistics represent the most popular application of probability theory, providing research tools in several areas, including physical and natural sciences, technology, psychology, economics and medicine. Statistics are the bridge that connects experimental data to the mathematical theory behind itself.Fuzzy logic, sometime confused with probability, wants to express and formalize all the sentences which are not true or false at all; the philosophical idea is that "everything is a matter of degree".