Random walk - fuzzy aspects

• Autorzy: Frič R. , Papčo M.
• Języki publikacji: EN

Abstrakty

EN

Some beautiful and powerful mathematical ideas are hard to present to students because of the involved abstract language (notation, definitions, theorems, proofs, formulas) and lack of time. Animation and “mathematical experiments” provide a remedy. In the field of stochastics, the Galton board experiment presents several fundamental stochastic notions: a random event, independent random events, the binomial distribution, limit distribution, normal distribution, interpretation of probability, and leads to their better understanding. Random walk is a natural generalization of the Galton board. We use random walks as a motivation and presentation of basic principles of fuzzy random events and fuzzy probability. Fuzzy mathematics and fuzzy logic generalize classical (Boolean) mathematics and logic, reflect everyday experience and decision making and have broader applications. Experimenting with random walks also sheds light on the transition from classical to fuzzy probability.

Słowa kluczowe

EN

random walk; fuzzy probability; experiment; stochastics

PL

spacery losowe; prawdopodobieństwo rozmyte; eksperyment; stochastyka

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2011
• Tom: Vol. 16
• Strony: 205--212
• Opis fizyczny: Bibliogr. 4 poz., rys.

Twórcy

autor

Frič R.

• Mathematical Institute, Slovak Academy of Sciences Grešákova 6, 040 01 Košice, Slovak Republic
• Catholic University in Ružomberok Hrabovská cesta 1, 034 01 Ružomberok, Slovak Republic

autor

Papčo M.

• Catholic University in Ružomberok Hrabovská cesta 1, 034 01 Ružomberok, Slovak Republic
• Mathematical Institute, Slovak Academy of Sciences Štefánikova 49, 814 73 Bratislava, Slovak Republic

Bibliografia

• [1] R. Frič, M. Papčo. Fuzzification of crisp domains. Kybernetika, 46, 1009-1024, 2010.
• [2] R. Frič, M. Papčo. Random variable as a network of pipelines. Usta ad Albim Bohemica, 1, 33-38, 2010.
• [3] R. Frič, M. Papčo. Statistical maps and generalized random walks. (Preprint).
• [4] S. Gudder. Fuzzy probability theory. Demonstratio Math., 31, 235-254, 1998.