What is monotonic classification? I read this about student surveys: 

Student surveys occupy a central place in the evaluation of courses at
  teaching institutions. At the end of each course, students are
  requested to evaluate various aspects such as activities, methodology,
  coordination or resources used. In addition, a final qualification is
  given to summarize the quality of the course. The prediction of this
  final qualification can be accomplished by using monotonic
  classification techniques.

Then it introduces the existence of a monotonic k-nearest neighbors algorithm (which I didn't even know it existed), but in a nutshell, what does it mean with monotonic classification? How does it differ from standard classification?
 A: I believe monotonic regression is used with Likert Scale information and so someone might refer to it as classification instead of regression because a Likert scale is categorical. Sort of like a Logistic regression is a classification method.
A: Definition
Monotonic classification is a classification where the dataset is monotonic.
From what I understood, I'll explain briefly what a monotonic dataset is.

Monotonic dataset
We can write any object $x$ of a dataset as a $n$-dimentional vector:
$x = (x_1, x_2, \dots, x_n)$ where all $x_{i<n}$ are the attributes and $x_n$ is the class of $x$.
A dataset $D$ will be monotonic if, for any $x, y \in D$, it follows that:
$$x_i \le y_i \Leftrightarrow x_n \le y_n \quad\forall i\small < n$$ 
That is, if all attributes of $x$ are less or equal than all correspondent attributes of $y$, then their classes will also be.

And what about the outliers?
Obviously there can be outliers in such dataset, for example, let $D$ be a dataset where each element $x$ stores the score of an student in $n-1$ exams and $x_n$ stores the mean. This dataset is clearly monotonic, given that if a student get greater scores than another student in all exams (which are the attributes), then the former's mean will also be greater than the latter's
Suppose $n=4$. Let $x=(\small 1,2,3,$ $2)$ and $y = (\small3,1,5,$ $3)$. We can't say that $x_i \le y_i$ and we can't say $y_i \le x_i$ completely, so we say these elements cannot be compared, although $x_n \le y_n$. This is an example of the behaviour of outliers in a monotonic dataset.

Example of monotonic classifier: Monotonic Nearest Neighbor
If a classification algorithm is able to deal with such datasets, it is a monotonic classifier.
An example is the Monotonic Nearest Neighbor. Given a monotonic dataset $D$, to classify an object $x$, it iterates through $D$ and computes:
$c_{min} = max\{y_n |\; y \in D \land y_i \le x_i\}$ $\quad \quad \quad$ (if $x$ and $y$ are not comparable, skip that $y$) 
$c_{max} = min\{y_n |\; y \in D \land y_i \ge x_i\}$ 
Then, it finds an element $z \in D$ such that $z_n \in [c_{min}, c_{max}]$ and the distance from $x$ to $z$ is minimum, that is, there will be no $y \in D$ with $y_n \in [c_{min}, c_{max}]$ whose distance to $x$ is smaller then the distance from $z$ to $x$.
Finally, $x$ will be classified as $z_n$.
