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2 Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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Fuzzified probability : from Kolmogorov to Zadeh and beyond

Frič R., Papčo M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2014

Vol. 19

179--188

We discuss the fuzzification of classical probability theory. In particular, we point out similarities and differences between the so-called fuzzy probability theory and the so-called operational probability theory.

Random walk - fuzzy aspects

Frič R., Papčo M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2011

Vol. 16

205--212

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.