Membership functions and operational law of uncertain sets
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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.
KeywordsUncertainty theory Uncertain set Uncertain measure Membership function
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- Gao, Y. (2012). Uncertain inference control for balancing inverted pendulum. Fuzzy Optimization and Decision Making (To be published).Google Scholar
- Kolmogorov A. N. (1933) Grundbegriffe der Wahrscheinlichkeitsrechnung. Julius Springer, BerlinGoogle Scholar
- Liu B. (2009) Some research problems in uncertainty theory. Journal of Uncertain Systems 3(1): 3–10Google Scholar
- Liu B. (2010a) Uncertain set theory and uncertain inference rule with application to uncertain control. Journal of Uncertain Systems 4(2): 83–98Google Scholar
- Liu B. (2010b) Uncertainty theory: A branch of mathematics for modeling human uncertainty. Springer, BerlinGoogle Scholar
- Liu B. (2011) Uncertain logic for modeling human language. Journal of Uncertain Systems 5(1): 3–20Google Scholar
- Liu B. (2012) Why is there a need for uncertainty theory?. Journal of Uncertain Systems 6(1): 3–10Google Scholar
- Peng, Z. X., & Chen, X. W. (2012) Uncertain systems are universal approximators. http://orsc.edu.cn/online/100110.pdf.