Fuzzy Optimization and Decision Making

, Volume 13, Issue 3, pp 259–271 | Cite as

Uncertainty distribution and independence of uncertain processes

  • Baoding Liu


Uncertain process is a sequence of uncertain variables indexed by time. This paper presents a concept of uncertainty distribution for describing uncertain process. Some sufficient and necessary conditions are also proved for uncertainty distribution and inverse uncertainty distribution of uncertain process. Finally, this paper proposes an independence definition of uncertain processes and shows some mathematical properties of it.


Uncertainty theory Uncertain process Uncertainty distribution 



This work was supported by National Natural Science Foundation of China Grants No. 61273044 and No. 91224008.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingChina

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