By Ali M. Abbasov (auth.), Ronald R. Yager, Ali M. Abbasov, Marek Z. Reformat, Shahnaz N. Shahbazova (eds.)
This e-book is a tribute to Lotfi A. Zadeh, the daddy of fuzzy common sense, at the get together of his 90th Birthday. The e-book gathers unique medical contributions written by way of most sensible scientists and offering the newest theories, functions and new tendencies within the interesting and tough box of sentimental computing.
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Extra info for Soft Computing: State of the Art Theory and Novel Applications
A (xn ), νA (xn ), πA (xn )), (μB (xn ), νB (xn ), πB (xn ))] which correspond to the membership values, non-memberships values and hesitation margins of the A-IFSs A and B defined on X, then the correlation coefficient rA−IFS (A, B) is given by Definition 2. Definition 2. The correlation coefficient rA−IFS (A, B) between two A-IFSs, A and B in X, is (Szmidt and Kacprzyk ): 1 rA−IFS (A, B) = (r1 (A, B) + r2(A, B) + r3 (A, B)) 3 (11) 44 E. Szmidt, J. Kacprzyk, and P. 5 n i=1 1 n n ∑ μB (xi ), νA = i=1 1 n n ∑ νA (xi ), i=1 νB = 1 n n ∑ νB (xi ), i=1 ∑ πB (xi ), i=1 The proposed correlation coefficient (11) depends on two factors: the amount of information expressed by the membership and non-membership degrees (12)–(13), and the reliability of information expressed by the hesitation margins (14).
62 petal width 1 Table 6. 7 petal width 1 Table 7. 61 petal width 1 Table 8. 64 petal width 1 Table 9. 86 petal width 1 The Kendall Rank Correlation between Intuitionistic Fuzzy Sets 51 Table 10. 89 petal width 1 Table 11. 61 petal width 1 Table 12. 78 petal width 1 Table 13. 76 petal width 1 The Kendall correlation coefficient (15) – Table 4 is the biggest between petal length and petal width, and does not count only between sepal length and sepal width. The results concerning the Iris Versicolor data are in Tables 5 – 8.
In our quest for doing the above, we have already discussed in detail the Pearson correlation coefficient r (Szmidt and Kacprzyk , and the Spearman rank correlation coefficient rs in (Szmidt and Kacprzyk ). This paper is a continuation of our work  on the Kendall τ correlation coefficient. We have proposed the concept of the Kendall correlation coefficient for the A-IFSs which is a generalization of the Kendall correlation coefficient for crisp sets as it fulfills the same properties.