### Abstract

An axiomatic derivation of the U-uncertainty that is simpler than the standard proof which covers the case of sub-normal possibility distributions is presented. The standard deviation uses an extremely complex branching axiom which is equivalent to the branching axiom presented. While the terminology used is possibility theory, a fuzzy set can be considered as an unordered and sub-normal possibility distribution. As a consequence the correct measure of uncertainty for a fuzzy set is U(A) = ∫_{0}^{h(A)} log_{2}|^{α}A|+(1-h(A))log_{2}|s(A)|.

Original language | English |
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Pages (from-to) | 313-316 |

Number of pages | 4 |

Journal | Unknown Journal |

State | Published - 1999 |

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### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Media Technology

### Cite this

*Unknown Journal*, 313-316.

**Uncertainty and subnormal possibility distributions.** / Wierman, Mark J.

Research output: Contribution to journal › Article

*Unknown Journal*, pp. 313-316.

}

TY - JOUR

T1 - Uncertainty and subnormal possibility distributions

AU - Wierman, Mark J.

PY - 1999

Y1 - 1999

N2 - An axiomatic derivation of the U-uncertainty that is simpler than the standard proof which covers the case of sub-normal possibility distributions is presented. The standard deviation uses an extremely complex branching axiom which is equivalent to the branching axiom presented. While the terminology used is possibility theory, a fuzzy set can be considered as an unordered and sub-normal possibility distribution. As a consequence the correct measure of uncertainty for a fuzzy set is U(A) = ∫0h(A) log2|αA|+(1-h(A))log2|s(A)|.

AB - An axiomatic derivation of the U-uncertainty that is simpler than the standard proof which covers the case of sub-normal possibility distributions is presented. The standard deviation uses an extremely complex branching axiom which is equivalent to the branching axiom presented. While the terminology used is possibility theory, a fuzzy set can be considered as an unordered and sub-normal possibility distribution. As a consequence the correct measure of uncertainty for a fuzzy set is U(A) = ∫0h(A) log2|αA|+(1-h(A))log2|s(A)|.

UR - http://www.scopus.com/inward/record.url?scp=0032591493&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032591493&partnerID=8YFLogxK

M3 - Article

SP - 313

EP - 316

JO - Nuclear Physics A

JF - Nuclear Physics A

SN - 0375-9474

ER -