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Conditional uncertain set and conditional membership function

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Abstract

The uncertain set, as a generation of uncertain variable, is a set-valued function on an uncertainty space. The conditional uncertain set, derived from an uncertain set restricted to a conditional uncertainty space given an uncertain event, plays a crucial role in uncertain inference systems. This paper studies conditional uncertain sets and their membership functions, and gives a sufficient condition for an uncertain set having a conditional membership function. In addition, when the uncertain set is conditioned on an independent event, this paper finds the analytic expression of the conditional membership function based on the original membership function.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 61403360), the Special Funds for Science and Education Fusion of University of Chinese Academy of Sciences, and the Open Project of Key Laboratory of Big Data Mining and Knowledge Management of Chinese Academy of Sciences.

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Correspondence to Kai Yao.

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Yao, K. Conditional uncertain set and conditional membership function. Fuzzy Optim Decis Making 17, 233–246 (2018). https://doi.org/10.1007/s10700-017-9271-2

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  • DOI: https://doi.org/10.1007/s10700-017-9271-2

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