A theoretical development on information measures of $ n $-polygonal interval-value fuzzy sets

Xue Zhao; Lili Zhang; Chunfeng Suo; Xue Zhao; Lili Zhang; Chunfeng Suo

doi:10.3934/math.20261365

AIMS Mathematics

2026, Volume 11, Issue 10: 35070-35118. doi: 10.3934/math.20261365

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Research article

A theoretical development on information measures of $ n $-polygonal interval-value fuzzy sets

School of Mathematics and Statistics, Beihua University, Jilin, 132000, China

Received: 13 July 2026 Revised: 11 September 2026 Accepted: 21 October 2026 Published: 27 October 2026
MSC : 90B50, 91A35

$ n $-polygonal interval-valued fuzzy sets are a very effective means for describing fuzzy information. How to handle the uncertain information is the key issue. In this paper, we generalized the recent results on the entropy and similarity measures of $ n $-polygonal interval-valued fuzzy sets based on abstract functions that meet specific conditions. Our main contribution is two formulas that derive to create various new entropies and similarity measures by the use of given functions. Meanwhile, we utilized the similarity measure function to construct the cross-entropy function, which can be understood as a dual relationship from the mathematical structure. Besides, we also proved that entropy and similarity measures for $ n $-polygonal interval-valued fuzzy sets can be transformed by each other in a general way. Finally, a multi-attribute decision-making (MADM) method in the light of the newly proposed entropy and cross-entropy were designed to solve practical problems. The experimental results demonstrate the effectiveness of the novel method in solving practical problems in decision-making.
- $ n $-polygonal interval-valued fuzzy set,
- entropy,
- similarity measure,
- cross-entropy
Citation: Xue Zhao, Lili Zhang, Chunfeng Suo. A theoretical development on information measures of $ n $-polygonal interval-value fuzzy sets[J]. AIMS Mathematics, 2026, 11(10): 35070-35118. doi: 10.3934/math.20261365

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Abstract

$ n $-polygonal interval-valued fuzzy sets are a very effective means for describing fuzzy information. How to handle the uncertain information is the key issue. In this paper, we generalized the recent results on the entropy and similarity measures of $ n $-polygonal interval-valued fuzzy sets based on abstract functions that meet specific conditions. Our main contribution is two formulas that derive to create various new entropies and similarity measures by the use of given functions. Meanwhile, we utilized the similarity measure function to construct the cross-entropy function, which can be understood as a dual relationship from the mathematical structure. Besides, we also proved that entropy and similarity measures for $ n $-polygonal interval-valued fuzzy sets can be transformed by each other in a general way. Finally, a multi-attribute decision-making (MADM) method in the light of the newly proposed entropy and cross-entropy were designed to solve practical problems. The experimental results demonstrate the effectiveness of the novel method in solving practical problems in decision-making.

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