Classification of possibilistic uncertainty and information functions.

*(English)*Zbl 0637.94027The U-uncertainty introduced by Higashi and Klir is proved to be of the form
\[
V(p_ 1,...,p_ n)=z(p_ 1)\log n+(z(p_ 2)-z(p_ 1))\log (n-1)+(z(p_ 3)-z(p_ 2))\log (n-2)+...
\]
where \(p_ 1\leq p_ 2\leq..\). is an ordered possibility distribution and \(z: [0,1]\to [0,1]\), \(z(0)=0\), \(z(1)=1\) and z monotonic. It is proved that any other form of U-uncertainty is a particular form of the above and some properties are derived. A related paper is by G. J. Klir and M. Mariano [ibid. 24, 197-219 (1987; Zbl 0632.94039)]. Here, the authors prove that the uniqueness is related to the assumption of linearity of V, i.e. \(V(a+b,1)=V(a,1)+V(b,1).\)

Reviewer: H.Teodorescu

##### MSC:

94D05 | Fuzzy sets and logic (in connection with information, communication, or circuits theory) |

94A17 | Measures of information, entropy |

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\textit{A. Ramer} and \textit{L. Lander}, Fuzzy Sets Syst. 24, 221--230 (1987; Zbl 0637.94027)

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##### References:

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