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**Some information measures for interval-valued intuitionistic fuzzy sets.**
*(English)*
Zbl 1204.94055

Summary: A new information entropy measure of interval-valued intuitionistic fuzzy set (IvIFS) is proposed by using membership interval and non-membership interval of IvIFS, which complies with the extended form of Deluca-Termini axioms for fuzzy entropy. Then the cross-entropy of IvIFSs is presented and the relationship between the proposed entropy measures and the existing information measures of IvIFSs is discussed. Additionally, some numerical examples are given to illustrate the applications of the proposed entropy and cross-entropy of IvIFSs to pattern recognition and decision-making.

### MSC:

94A17 | Measures of information, entropy |

94D05 | Fuzzy sets and logic (in connection with information, communication, or circuits theory) |

### Keywords:

interval-valued intuitionistic fuzzy set; information measure; entropy; divergence measure; cross-entropy
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\textit{Q.-s. Zhang} et al., Inf. Sci. 180, No. 24, 5130--5145 (2010; Zbl 1204.94055)

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