Document Type : Research Paper

Authors

1 Department of Mathematics, Statistics and Computer Science, University of Agriculture, P.M.B. 2327, Makurdi-Nigeria.

2 Department of Computer Science, University of Agriculture, P.M.B. 2373, Makurdi, Nigeria.

Abstract

The concept of correlation coefficient of intuitionistic fuzzy sets is a reliable tool in information theory with numerous applications in diverse areas. Correlation coefficients of intuitionistic fuzzy sets have been studied through two-way approach by many researchers. This approach inappropriately discarded the hesitation margins of the concerned intuitionistic fuzzy sets, which makes the results of such experiments unreliable. In this paper, we modified the correlation coefficient of intuitionistic fuzzy sets of Thao et al. [36] in a three-way approach by including the hesitation margins in the computational process to enhance reliable output through an algorithmic method. We show that the modified correlation coefficient of intuitionistic fuzzy sets is more reasonable with precise outputs than correlation coefficient method. In terms of application, we demonstrate an analysis of medical diagnosis on some selected patients via an algorithm of the novel approach coded with JAVA programming language.

Keywords

Main Subjects

[1]   Zadeh, L. A. (1965). Fuzzy sets. Information and control8(3), 338-353.
[2]   Atanassov, K. T. (1994). New operations defined over the intuitionistic fuzzy sets. Fuzzy sets and systems61(2), 137-142.
[3]   Atanassov, K. (1999). Intuitionistic fuzzy sets: theory and applications, physica-verlag, heidelberg.  International journal of advanced computer science and applications, 14-17.
[4]   Davvaz, B., & Hassani Sadrabadi, E. (2016). An application of intuitionistic fuzzy sets in medicine. International journal of biomathematics9(03), 1650037.
[5]   De, S. K., Biswas, R., & Roy, A. R. (2001). An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy sets and systems117(2), 209-213.
[6]   Ejegwa, P. A., & Onasanya, B. O. (2019). Improved intuitionistic fuzzy composite relation and its application to medical diagnostic process. Note IFS25(1), 43-58.
[7]   Szmidt, E., & Kacprzyk, J. (2001, October). Intuitionistic fuzzy sets in some medical applications. International conference on computational intelligence (pp. 148-151). Springer, Berlin, Heidelberg.
[8]   Szmidt, E., & Kacprzyk, J. (2004). Medical diagnostic reasoning using a similarity measure for intuitionistic fuzzy sets. Note on IFS10(4), 61-69.
[9]   Todorova, L., Atanassov, K., Hadjitodorov, S., & Vassilev, P. (2007). On an intuitionistic fuzzy approach for decision making in medicine: part 1. International journal bioautomation6, 92.
[10]    Todorova, L., Atanassov, K., Hadjitodorov, S., & Vassilev, P. (2007). On an intuitionistic fuzzy approach for decision making in medicine: part 2. International journal bioautomation7, 64-69.
[11]    Boran, F. E., & Akay, D. (2014). A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition. Information sciences255, 45-57.
[12]    Hatzimichailidis, A. G., Papakostas, G. A., & Kaburlasos, V. G. (2012). A novel distance measure of intuitionistic fuzzy sets and its application to pattern recognition problems. International journal of intelligent systems27(4), 396-409.
[13]    Wang, W., & Xin, X. (2005). Distance measure between intuitionistic fuzzy sets. Pattern recognition letters26(13), 2063-2069.
[14]    Ejegwa, P. A., Akubo, A. J., & Joshua, O. M. (2014). Intuitionistic fuzzy set and its application in career determination via normalized Euclidean distance method. European scientific journal10(15).
[15]    Ejegwa, P. A., Akubo, A. J., & Joshua, O. M. (2014). Intuitionistic fuzzy sets in career determination. J. of Inform. and Computing Sci9(4), 285-288.
[16]    Ejegwa, P. A., & Onyeke, I. C. (2018). An object oriented approach to the application of intuitionistic fuzzy sets in competency based test evaluation. Ann. Commun. Math1(1), 38-47.
[17]    Liu, P., & Chen, S. M. (2016). Group decision making based on Heronian aggregation operators of intuitionistic fuzzy numbers. IEEE transactions on cybernetics47(9), 2514-2530.
[18]    Chiang, D. A., & Lin, N. P. (1999). Correlation of fuzzy sets. Fuzzy sets and systems102(2), 221-226.
[19]    Hung, W. L., & Wu, J. W. (2002). Correlation of intuitionistic fuzzy sets by centroid method. Information sciences144(1-4), 219-225.
[20]    Murthy, C. A., Pal, S. K., & Majumder, D. D. (1985). Correlation between two fuzzy membership functions. Fuzzy sets and systems17(1), 23-38.
[21]    Ejegwa, P. A. (2020). Modified and generalized correlation coefficient between intuitionistic fuzzy sets with applications. Retrieved from https://www.researchgate.net/profile/Ejegwa_Paul_Augustine/publication/341902780_Modified_and_generalized_correlation_coefficient_between_intuitionistic_fuzzy_sets_with_applications/links/5ed8d821299bf1c67d3bdf10/Modified-and-generalized-correlation-coefficient-between-intuitionistic-fuzzy-sets-with-applications.pdf
[22]    Mitchell, H. B. (2004). A correlation coefficient for intuitionistic fuzzy sets. International journal of intelligent systems19(5), 483-490.
[23]    Xuan Thao, N. (2018). A new correlation coefficient of the intuitionistic fuzzy sets and its application. Journal of intelligent & fuzzy systems35(2), 1959-1968.
[24]    Xu, Z., Chen, J., & Wu, J. (2008). Clustering algorithm for intuitionistic fuzzy sets. Information sciences178(19), 3775-3790.
[25]    Hong, D. H., & Hwang, S. Y. (1995). Correlation of intuitionistic fuzzy sets in probability spaces. Fuzzy sets and systems75(1), 77-81.
[26]    Zeng, W., & Li, H. (2007). Correlation coefficient of intuitionistic fuzzy sets. Journal of industrial engineering international, 3(5), 33-40.
[27]    Gerstenkorn, T., & Mańko, J. (1991). Correlation of intuitionistic fuzzy sets. Fuzzy sets and systems, 44(1), 39-43.
[28]    Hung, W. L. (2001). Using statistical viewpoint in developing correlation of intuitionistic fuzzy sets. International journal of uncertainty, fuzziness and knowledge-based systems, 9(4), 509-516.
[29]    Hung, W. L., & Wu, J. W. (2002). Correlation of intuitionistic fuzzy sets by centroid method. Information sciences, 144(1-4), 219-225.
[30]    Park, J. H., Lim, K. M., Park, J. S., & Kwun, Y. C. (2009). Correlation coefficient between intuitionistic fuzzy sets. Fuzzy information and engineering Volume 2 (pp. 601-610). Springer, Berlin, Heidelberg.
[31]    Bustince, H., & Burillo, P. (1995). Correlation of interval-valued intuitionistic fuzzy sets. Fuzzy sets and systems74(2), 237-244.
[32]    Liu, B., Shen, Y., Mu, L., Chen, X., & Chen, L. (2016). A new correlation measure of the intuitionistic fuzzy sets. Journal of intelligent & fuzzy systems, 30(2), 1019-1028.
[33]    Garg, H., & Kumar, K. (2018). A novel correlation coefficient of intuitionistic fuzzy sets based on the connection number of set pair analysis and its application. Scientia Iranica. Transaction E, industrial engineering, 25(4), 2373-2388.
[34]    Garg, H. (2018). Novel correlation coefficients under the intuitionistic multiplicative environment and their applications to decision-making process. Journal of industrial & management optimization, 14(4), 1501.
[35]    Garg, H., & Rani, D. (2019). A robust correlation coefficient measure of complex intuitionistic fuzzy sets and their applications in decision-making. Applied intelligence, 49(2), 496-512.
[36]    Thao, N. X., Ali, M., & Smarandache, F. (2019). An intuitionistic fuzzy clustering algorithm based on a new correlation coefficient with application in medical diagnosis. Journal of intelligent & fuzzy systems, 36(1), 189-198.
[37]  Atanassov, K. T. (1994). New operations defined over the intuitionistic fuzzy sets. Fuzzy sets and systems, 61(2), 137-142.