  Given an indeterminate string pattern $p$ and an indeterminate string text
$t$, the problem of order-preserving pattern matching with character
uncertainties ($\mu$OPPM) is to find all substrings of $t$ that satisfy one of
the possible orderings defined by $p$. When the text and pattern are
determinate strings, we are in the presence of the well-studied exact
order-preserving pattern matching (OPPM) problem with diverse applications on
time series analysis. Despite its relevance, the exact OPPM problem suffers
from two major drawbacks: 1) the inability to deal with indetermination in the
text, thus preventing the analysis of noisy time series; and 2) the inability
to deal with indetermination in the pattern, thus imposing the strict
satisfaction of the orders among all pattern positions. This paper provides the
first polynomial algorithm to answer the $\mu$OPPM problem when indetermination
is observed on the pattern or text. Given two strings with length $m$ and
$O(r)$ uncertain characters per string position, we show that the $\mu$OPPM
problem can be solved in $O(mr\lg r)$ time when one string is indeterminate and
$r\in\mathbb{N}^+$. Mappings into satisfiability problems are provided when
indetermination is observed on both the pattern and the text, and results
concerning the general problem complexity are presented as well, with $\mu$OPPM
problem proved to be NP-hard in general.
