Soft Computing: State of the Art Theory and Novel by Ali M. Abbasov (auth.), Ronald R. Yager, Ali M. Abbasov,

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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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 [37]): 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 [37], and the Spearman rank correlation coefficient rs in (Szmidt and Kacprzyk [38]). This paper is a continuation of our work [39] 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.

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