Livio Clemente Piccinini

FROM LINGUISTIC REPRESENTATION TO FUZZY MATHEMATICS IN GROWN UP PEOPLE

The aim of this note is to give some critical examples where even the use of the same clustering rules lead to fuzziness. It starts from poor numerical systems and compares them with the expanded Sergeyev model, where the grossone is used, as an infinite terminal element. It can be compared with terminal elements of the ancient languages, such as the Greek myriad and the Chinese wan. On them some propositions that hold in the arithmetic of the grossone are similar, while they are not meaningful for the countable system of infinity. The note shows that both the upward and downward trend are actually present in human language and in conceptual arrangements. The note then goes on to sketch the model of evolution of Bak-Sneppen, showing two significant applications: the case of the evolution and study of foreign languages and, according to the model of Lloyd, the territorial analysis. In both cases it is highlighted how the Bak-Sneppen model becomes more stable when the universe is segmented, as already proven by the authors in previous works. The third part examines some cases of false probabilistic intuition due to incomplete perception of the phenomena, what could therefore be defined as hidden conditional probability. Interesting is the classic application of the theory of games to lotteries and ternary games, such as Chinese morra.

Discrete Exterior Measures and Their Meaning in Applications

E.De Giorgi uses to deliver very original lectures during his courses at Scuola Normale Superiore in Pisa. Among the many subjects he dealt with, we recall that the course of the academic year 1971–72 was mostly devoted to the theory of exterior measures. Some of it was collected in the “Quaderno della Scuola Normale” [2]; namely Chapter 3 contains the fundamentals of exterior measures (following mostly Caratheodory’s approach [1]), while chapter 4 contains the definition of an original geometric measure, used to solve problems of minimal surfaces with obstacles.