Stability of a mixed type additive-quadratic functional equation with a parameter in matrix intuitionistic fuzzy normed spaces

The purpose of this paper is first to introduce the notation of matrix intuitionistic fuzzy normed spaces, and then by virtue of this notation to study the Hyers-Ulam stability results concerning the mixed type additive-quadratic functional equation

$$\begin{gathered} 2k[f(x+ky)+f(kx+y)]=k(1-s+k+ks+2k^2)f(x+y) \\ +k(1-s-3k+ks+2k^2)f(x-y) \\ +2kf(kx)+2k(s+k-ks-2k^2)f(x)+2(1-k-s)f(ky)+2ksf(y) \end{gathered}$$

in the setting of matrix intuitionistic fuzzy normed spaces by applying two different methods, where $s$ is a parameter, $k>1$ and $s\ne 1-2k$. Moreover, the interdisciplinary relation between the theory of matrix intuitionistic fuzzy normed spaces and the theory of functional equations are also presented in this paper.