Artificial Intelligence

    

The Information Volume of Uncertain Information: (2) Fuzzy Membership Function

Authors: Jixiang Deng, Yong Deng

In fuzzy set theory, the fuzzy membership function describes the membership degree of certain elements in the universe of discourse. Besides, Deng entropy is a important tool to measure the uncertainty of an uncertain set, and it has been wildly applied in many fields. In this paper, firstly, we propose a method to measure the uncertainty of a fuzzy MF based on Deng entropy. Next, we define the information volume of the fuzzy MF. By continuously separating the BPA of the element whose cardinal is larger than $1$ until convergence, the information volume of the fuzzy sets can be calculated. When the hesitancy degree of a fuzzy MF is $0$, information volume of the fuzzy membership function is identical to the Shannon entropy. In addition, several examples and figures are expound to illustrated the proposed method and definition.

Comments: 18 Pages.

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Submission history

[v1] 2020-06-04 13:35:02

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