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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.

Triangular structures and duality

Frič R., Papčo P.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2007

Vol. 12

23-28

We introduce and study the category AFD the objects of which are generalized convergence D-posets (with more than just one greatest element) of maps into a triangle object T and the morphisms of which are sequentially continuous D-homomorphisms. The category AFD can serve as a base category for antagonistic fuzzy probability theory. AFD-measurable maps can be considered as generalized random variables and ADF-morphisms, as their dual maps, can be considered as generalized observables.

Observables in fuzzy probability theory

Gudder S.

Demonstratio Mathematica

1998

Vol. 31, nr 3

573-586

Properties of observables in a recently formulated fuzzy probability theory are investigated. After a review of definitions and terminology, we compare observables to probability kernels (or Markov kernels) and statistical maps which have been studied previously. We then discuss the spectrum of an observable and a spectral mapping theorem is proved. Finally, a special type of observable called an apparatus is introduced and its properties are studied.

Fuzzy probability theory

Gudder S.

Demonstratio Mathematica

1998

Vol. 31, nr 1

235-254

A basic theory of fuzzy pr