Fuzzy Sets and Possibility Theory - Information Fusion in Signal and Image Processing - page 150

These operators are generally not associative; the medians are the only ones that
are, where m ( x, y ) is the median value of x , y and a parameter α in [0 , 1]:

⎧
⎨

≤ ≤ ≤ ≤

x if y x α or α x y

m ( x, y )= med ( x, y, α )= y if x ≤ y ≤ α or α ≤ y ≤ x [8.69]

⎩

α if y ≤ α ≤ x or x ≤ α ≤ y

Figure 8.7 illustrates a few median operators.

α

Figure 8.7. Three examples of medians, for equal to 0.1, 0.5 and 0.8, respectively