Faculty of Physics
M.V.Lomonosov Moscow State University
Regular Article

Foundations of possibility theory. Methods of optimal estimation and decision making. 4. Maximal extension of possibility

Yu.P. Pyt'ev

Moscow University Physics Bulletin 1998. 53. N 1. P. 1

  • Article

It is shown that a possibility $P(\cdot): \mathcal{A}\rightarrow[0,1]$ can always be extended from an arbitrary $\sigma$-algebra $\mathcal{A}$ of subsets of $X$ to the algebra $\mathcal{P}(X)$ of all subsets of $X$ with preservation of all properties of the possibility, and that a measure $p(\cdot): \mathcal{L}(X)\rightarrow[0,1]$ specifying a possibility of fuzzy events can be extended with preservation of its properties to the class of all functions $X\rightarrow[0,1]$.

Yu.P. Pyt'ev
Московский государственный университет имени М.В. Ломоносова, физический факультет, кафедра компьютерных методов физики. Россия, 119991, Москва, Ленинские горы, д. 1, стр. 2
Issue 1, 1998

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