Context
I am building a game that have numerical imprecisions. It has two stores that does not have accurate information about their inventory. This inaccuracy is represented by the imprecision percentage (e.g. 100±20% items). The inventory can assume negative values when there is demands and no items in the store's inventory. Further, the stores can send items between them. So, if there is less demand in one store, it can send more items to the other that has more demands.
I'm using Intervals to represent inaccurate numeric information in my game. There, I represent an inaccurate number as being any number in an interval. For example: $100\pm20\%$ imprecision is represented by an interval $[80, 120]$.
The problem I am facing is with the Interval operations. When I add two intervals using the Wikipedia Interval operations formulas I am always able to maintain the same $20\%$ imprecision. For example with $100\pm20\% + 20\pm20\%$:
$[80,120] + [16,24] = [96,144] \text{ which is } 120\pm20\%$.
Problem
When I subtract two intervals using the following formula:
$[x_1,x_2]-[y_1,y_2] = [x_1-y_2, x_2-y_1]$
I get a different imprecision percentage.
$[80,120] - [16,24] = [56, 104] \text{ which is } 80\pm30\%$.
I noticed that the $80\pm20\%$ could be achieved by doing:
$[x_1,x_2]-[y_1,y_2] = [x_1-y_1, x_2-y_2]$
But I am not sure this would be mathematically correct.
Question
Am I using the correct operation for my problem? Should I be using something else other than intervals?
ps: All my intervals have the same imprecision. All $20\%$, or all $15\%$, or all $10\%$.