Granularity and Entropy of Intuitionistic Fuzzy Information and Their Applications

A granular structure of intuitionistic fuzzy (IF) information presents simultaneously the similarity and diversity of samples. However, this structural representation has rarely displayed its technical capability in data mining and information processing due to the lack of suitable constructive meth...

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Bibliographic Details
Published in:IEEE transactions on cybernetics 2022-01, Vol.52 (1), p.192-204
Main Authors: Tan, Anhui, Shi, Suwei, Wu, Wei-Zhi, Li, Jinjin, Pedrycz, Witold
Format: Article
Language:English
Subjects:
Algorithms
Attribute reduction
Data Mining
Data processing
Data reduction
Entropy
Entropy (Information theory)
Fuzzy Logic
granular structure
granularity
Information entropy
Information systems
intuitionistic fuzzy (IF) relation
Measurement uncertainty
Sea measurements
Similarity
Uncertainty
uncertainty measure
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Summary:A granular structure of intuitionistic fuzzy (IF) information presents simultaneously the similarity and diversity of samples. However, this structural representation has rarely displayed its technical capability in data mining and information processing due to the lack of suitable constructive methods and semantic interpretation for IF information with regard to real data. To pursue better performance of the IF-based technique in real-world data mining, in this article, we examine information granularity, information entropy of IF granular structures, and their applications to data reduction of IF information systems. First, several types of partial-order relations at different hierarchical levels are defined to reveal the granularity of IF granular structures. Second, the granularity invariance between different IF granular structures is characterized by using relational mappings. Third, Shannon's entropies are generalized to IF entropies and their relationships with the partial-order relations are addressed. Based on the theoretical analysis above, the significance of intuitionistic attributes using the information measures is then introduced and the information-preserving algorithm for data reduction of IF information systems is constructed. Finally, by inducing substantial IF relations from public datasets that take both the similarity/diversity between the samples from the same/different classes into account, a collection of numerical experiments is conducted to confirm the performance of the proposed technique.
ISSN:2168-2267
2168-2275
DOI:10.1109/TCYB.2020.2973379