Open Journal Systems

FROM LINGUISTIC REPRESENTATION TO FUZZY MATHEMATICS IN GROWN UP PEOPLE

Maria Antonietta Lepellere, Livio Clemente Piccinini, Mario Taverna

Abstract

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.

Keywords

Infinity; Grossone; Bak-Sneppen model; Conceptual granularity and translation; Lloyd’s problem of clustering; Probabilistic delusions

Full Text:

PDF

References

Aurenhammer, F. (1991). Voronoi diagrams—A survey of a fundamental geometric data structure. ACM Comput. Surv., 23, 345– 405.

Bak, P. & Sneppen , K. (1993). Punctuated equilibrium and criticality in a simple model of evolution. Physical Review Letters, 71(24), 4083-4086.

Boyer, C.B. (1968). A history of Mathematics. John Wiley & Sons.

Chang, T.F.M. & Iseppi, L. (2011), Specialization versus Diversification in EU Economies: a Challenge for Agro-food? Transition Studies Review, Volume 18, n. 1, 16-37. DOI: 10.1007/s11300-011-0196-0.

Chang, T.F.M. & Iseppi, L. (2012), EU Agro-Food Chain and Vertical Integration Potentiality: a Strategy for Diversification? Transition Studies Review, Volume 19, n. 1, 107-130. DOI: 10.1007/s11300-011-0196-0.

Chang, T.F.M., Piccinini, L.C., Iseppi, L. & Lepellere, M.A. (2013) The Black Box of Economic Interdependence in the Process of Structural Change. EU and EA on the Stage. Italian Journal of Pure and Applied Mathematics, 31, 285-306.

Chang, T.F.M., Droli, M. & Iseppi L. (2014), Does Smart Agriculture Go Downstream in the Supply Chain? Italian Journal of Food Science, 26, 4, 451-457.

Chang, T.F.M., Iseppi, L., & Droli, M. (2015), Extra-core production and capabilities: where is the Food Industry going? International Food and Agribusiness Management Review, Volume 18, Issue 1, 105-126.

Chang, T.F.M., Droli, M. & Iseppi L. (2015) The black box of economic interdependence in the process of structural change. The International Food and Agribusiness Management Review, 2015/2, 18(1), 105-126.

Du, Q., Emelianenko, M. & Ju, L. (2006). Convergence of the Lloyd algorithm for computing centroidal Voronoi tessellations. Siam J., 44, 1, 102–119.

Eco, U. (1975). A Theory of Semiotic. Indiana University Press.

Eco, U.(2003). Dire quasi la stessa cosa. Milano, Bompiani.

Freudenthal, H. (1991). Revisiting Mathematical Education. China Lectures. Dordrecht: Kluwer Academic Publishers. Sect. 2.3.

Gordon, P. (2004). Numerical cognition without words: Evidence from Amazonia. Science 306 (215), 496-499.

Hotelling, H. (1929). Stability in Competition. Economic Journal, 39, 31-57.

Margenstern, M. (2011) Using grossone to count the number of elements of infinite sets and the connexion with bijections p-Adic Number. Ultrametric Analysis and Applications, 3(3); 196-204.

Métivier, M. (1968). Notions fondamentales de la théorie des probabilités, Paris, Dunod page 12.

Pica, P., Lemer, C., Izard, V. & Dehaene (2004). Exact and approximate arithmetic in an Amazonia ideigene group. Science, 306 (15) 499-503.

Piccinini, L.C. & Indelli P. (1980-1981). Matematica per gli anni ’90, Vol. 1-2-3, Liguori Editore, Napoli

Piccinini, L.C. & Chang, T.F.M., (2007). An exact method for triangularizing input-output matrixes, Italian Journal of Pure and Applied Mathematics, 21, 45-62.

Piccinini, L.C., Lepellere, M. A. & Chang, T.F.M. (2013). Utopias of Perfection and their dystopias. Society, Integration, Education. Proceedings of the International Scientific Conference, v. 3, 189-200.

Piccinini, L.C; & Lepellere, M. A.: & Chang, T.F.M: & Iseppi, L. (2014). Partitioned Frames in Bak Sneppen Models. Italian Journal of Pure and Applied Mathematics, 33, 461-488.

Piccinini, L.C., Taverna, M., Chang, T.F.M. & Tubaro, G. (2015). Perception, Connotation, Translation of Numbers. Society, Integration, Education. Proceedings of the International Scientific Conference, Rezekne.

Piccinini, L.C., Lepellere, M. A., Chang, T. F. M & Iseppi, L.(2016) Structured Knowledge in the Frame of Bak-Sneppen Models. Italian Journal of Pure and Applied Mathematics, 36, 703-718.

Sergeyev, Ya.D. (2015). Un semplice metodo per trattare le grandezze infinite e infinitesime, La matematica nella società e nella cultura, 8, 111-147.

Sergeyev, Ya.D. (2008). A new applied approach for executing computations with infinite and infinitesimal quantities. Informatica, 19, 567-596.

Sergeyev, Ya.D. (2013). Arithmetic of Infinity Cosenza, Edizioni Orizzonti Meridionali.

Voronoi, M.G. (1908). Nouvelles applications des parametres continus a la theorie des formes quadratiques. J. Reine Angew. Math. 134, 198-287.

DOI: http://dx.doi.org/10.17770/sie2018vol1.3314

Refbacks

There are currently no refbacks.