Recently, many researchers studied the degenerate multi-special polynomials as degenerate versions of the multi-special polynomials and obtained some identities and properties of the those polynomials. The aim of this paper was to introduce the degenerate multi-poly-Changhee polynomials arising from multiple logarithms and investigate some interesting identities and properties of these polynomials that determine the relationship between multi-poly-Changhee polynomials, the Stirling numbers of the second kind, degenerate Stirling numbers of the first kind and falling factorial sequences. In addition, we investigated the phenomenon of scattering the zeros of these polynomials.

For any positive integer $r$, the $r$-truncated (or $r$-associated) Stirling number of the second kind $S_2^{(r)}(n,k)$ enumerates the number of partitions of the set $\{1,2,3,\dots ,n\}$ into $k$ non-empty disjoint subsets, such that each subset contains at least $r$ elements. We introduce the degenerate $r$-truncated Stirling numbers of the second kind and of the first kind. They are degenerate versions of the $r$-truncated Stirling numbers of the second kind and of the first kind, and reduce to the degenerate Stirling numbers of the second kind and of the first kind for $r=1$. Our aim is to derive recurrence relations for both of those numbers.

Recently, probabilistic versions of certain special polynomials have been introduced, leading to the discovery of many interesting properties of these polynomials by many researchers. In this paper, we define the probabilistic degenerate Daehee polynomials, denoted by $D_{n,\lambda }^Y(x)$, and explore their properties along with several notable identities. We demonstrate that $D_{n,\lambda }^Y(x)$ and related special numbers can be expressed in terms of (degenerate) Stirling numbers of the first and second kinds, as well as falling factorial sequences.