The paper presents an adaptation of Interval valued intuitionistic fuzzy number. The arithmetic operation of interval-valued intuitionistic fuzzy number (IVIFN) is addressed here. The differentiability of IVIFN valued function is also addressed here. Demonstration of intuitionistic fuzzy solutions of differential equation is carried out with the said numbers. Additionally, a illustrative application is also undertaken with the useful graph for usefulness for attained to the proposed approaches.
ZadehL.A., Fuzzy sets, Information and Control8 (1965), 338–353.
2.
ChangS.S.L. and ZadehL.A., On fuzzy mappings and control, IEEE Trans Syst Man Cybernet2 (1972), 30–34.
3.
AtanassovK.T., Intuitionistic fuzzy sets, VII ITKR’s Session, Sofia, Bulgarian, 1983.
4.
AtanassovK.T., Intuitionistic fuzzy sets, Fuzzy Sets and Systems20 (1986), 87–96.
5.
ZhangX., YueG. and TengZ., Possibility Degree of Interval-valued Intuitionistic Fuzzy Numbers and its Application, Proceedings of the 2009 International Symposium on Information Processing (ISIP’09) Huangshan, P.R. China, 2009, pp. 033–036.
6.
BroumiS. and SmarandacheF., New operations over interval valued intuitionistic hesitant fuzzy set, Mathematics and Statistics2(2) (2014), 62–71.
7.
KumarG. and BajajR.K., On solution of interval valued intuitionistic fuzzy assignment problem using similarity measure and score function, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering8(4) (2014).
8.
MaoyingT. and JingL., Some aggregation operators with interval-valued intuitionistic trapezoidal fuzzy numbers and their application in multiple attribute decision making, Advanced Modeling and Optimization15(2) (2013).
9.
GouX., XuZ. and LiaoH., Exponential operations of interval-valued intuitionistic fuzzy numbers, Int J Mach Learn & Cyber (2015).
10.
WuJ., CaoQ. and LiH., An Approach for MADM Problems with Interval-Valued Intuitionistic fuzzy sets Based on Nonlinear Functions, Technological and Economical Development of Economy, 2013.
11.
WangL. and GuoS., New results on multiple solutions for intuitionistic fuzzy differential equations, Journal of Systems Science and Information4(6) (2016), 560–573.
12.
PedersonS. and SambandhamM., Numerical solution of hybrid fuzzy differential equation IVP by characterization theorem, Inform Sci179 (2009), 319–328.
13.
BedeB., Note on “Numerical solution of fuzzy differential equations by predictor corrector method”, Information Sciences178 (2008), 1917–1922.
14.
BedeB. and GalS.G., Solutions of fuzzy differential equations based on generalized differentiability, Commun Math Anal9 (2010), 22–41.
15.
NietoJ.J., KhastanA. and IvazK., Numerical solution of fuzzy differential equations under generalized differentiability, Nonlinear Analysis: Hybrid System3 (2009), 700–707.
16.
AllahviranlooT. and SalahshourS., Euler method for solving hybrid fuzzy differential equation, Soft Comput15 (2011), 1247–1253.
17.
NguyenH.T., A note on the extension principle for fuzzy set, Journal Mathematical Analysis and Applications64 (1978), 369–380.
18.
BassaneziR.C. and de BarrosL.C. and TonelliP.A., Attractors and asymptotic stability for fuzzy dynamical systems, Fuzzy Sets and Systems113 (2000), 473–483.
19.
MondalS.P. and RoyT.K., First order linear homogeneous ordinary differential equation in fuzzy environment based on laplace transform, Journal of Fuzzy Set Valued Analysis2013 (2013), 1–18.
