Fuzzy Optimization and Decision Making

, Volume 11, Issue 4, pp 387–410 | Cite as

Membership functions and operational law of uncertain sets



Uncertain set is a set-valued function on an uncertainty space, and attempts to model “unsharp concepts” that are essentially sets but their boundaries are not sharply described. This paper will propose a concept of membership function and define the independence of uncertain sets. This paper will also present an operational law of uncertain sets via membership functions or inverse membership functions. Finally, the linearity of expected value operator is verified.


Uncertainty theory Uncertain set Uncertain measure Membership function 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Uncertainty Theory Laboratory, Department of Mathematical SciencesTsinghua UniversityBeijingChina

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