Journal
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS
Volume 28, Issue 2, Pages 591-604Publisher
IOS PRESS
DOI: 10.3233/IFS-141338
Keywords
Picture fuzzy sets; Atanassov's intuitionistic fuzzy sets; correlation coefficient; bidirectional approximate reasoning system; cluster analysis
Categories
Funding
- European Social Fund
- state budget of the Czech Republic
- Education for Competitiveness Operational Programme [CZ.1.07/2.3.00/30.0004]
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Picture fuzzy sets are extension of Atanassov's 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.
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