Correlation coefficients for picture fuzzy sets

Picture fuzzy sets are extension of Atanassovs intuitionistic fuzzy sets. Picture fuzzy set based models may be adequate in situations when we face human opinions involving more answers of types: yes, abstain, no, refusal. It can be considered as a powerful tool represent an uncertain information in...

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Bibliographic Details
Published in:Journal of intelligent & fuzzy systems 2015, Vol.28 (2), p.591-604
Main Author: Singh, Pushpinder
Format: Article
Language:English
Subjects:
Approximation
Correlation coefficients
Fuzzy
Fuzzy logic
Fuzzy set theory
Human
Pictures
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Summary:Picture fuzzy sets are extension of Atanassovs intuitionistic fuzzy sets. Picture fuzzy set based models may be adequate in situations when we face human opinions involving more answers of types: yes, abstain, no, refusal. It can be considered as a powerful tool represent an uncertain information in the process of cluster analysis. In this paper, we present a geometrical interpretation of picture fuzzy sets. We propose correlation coefficients for picture fuzzy sets which considers the degree of positive membership, degree of neutral membership, degree of negative membership and the degree of refusal membership. Effectiveness of the proposed correlation coefficient has been established in a bidirectional approximate reasoning systems. We apply the correlation coefficient to clustering analysis under picture fuzzy environments. Advantages of proposed correlation coefficients and drawbacks of existing correlation coefficients have been discussed.
ISSN:1064-1246
DOI:10.3233/IFS-141338