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Top1. Introduction
The fuzzy set theory is completely described by its membership function. A membership function of a standard fuzzy set assigns to each element of the universe of discourse a number from the interval 
to indicate the degree of belongingness to the set under consideration. The degree of non-membership is just automatically equal to 1 minus the membership degree. However, a human being who expresses the degree of membership of a given element in a fuzzy set very often does not express the corresponding degree of non-membership as the complement to “1”. This reflects a well-known psychological fact that linguistic negation does not always identify with logical negation. There may be some hesitation about the belongingness and non-belongingness. This missing data or hesitation is accomplished by a set known as an intuitionistic fuzzy set. Atanassov (1983) proposed the concept of intuitionistic fuzzy sets (IFSs) as an extension of fuzzy sets introduced by Zadeh (1965). Atanassov (1986) explored the idea of fuzzy set theory by intuitionistic fuzzy set (IFS) theory. Several applications in IFSs are presented in (Robinson J. P., & Jeeva S., 2019; Muthukumar, P. & Gangadharan, S. S. 2018; Robinson, J. P. & Jeeva, S. 2017; Shreevastava, S., Tiwari, A.K. & Som, T. 2018; Talukdar, P. & Dutta, P. 2019; Tripathy, B. K., Sooraj, T. R., Mohanty, R. K. & Panigrahi, A. 2018; Yu, G.-F., Li, D. F., Qiu, J. M., & Ye, Y. F. 2017; An, J. & Li, D. 2019; An, J., Li, D. &. Nan, J. 2017; Li, D. & Wan, S. P. 2017; Li, D. & Liu, J. 2015; Li, D. 2014; Li. D. 2011; Li, D. 2010; Ren, H., Chen, H., Fei, W. & Li, D. 2017; Wei, A., Li, D., Jiang, B. & Lin, P. 2019; Wan, S. P. & Li., D. 2015; Melliani, S., Castillo, O. 2019).
The concept of intuitionistic fuzzy differential equations was first introduced by S. Melliani and L. S. Chadli (2000). The first step which included applicable definitions of intuitionistic fuzzy derivative and the intuitionistic fuzzy integral was followed by introducing intuitionistic fuzzy differential equations and establishing sufficient conditions for the existence of unique solutions to these equations using different concepts (Ben Amma, B., Melliani, S., & Chadli, L. S. 2018,2019; Melliani, S., Elomari, M., Atraoui M., & Chadli, L. S. 2015).