How to combine multiple indices?

Question

I'm trying to combine various risk indices e.g. flooding, fire, burglary and structural damage. These values are scored from 1-3. For instance, I could have measures for two different areas as follows:

    flooding | fire | burglary | structural |
            1|     2|         3|           1|
            2|     1|         1|           3|

My issue is that these values sum to the same score (7) despite the differences in the individual indices (flooding gets a 1 on the first row but a 2 on the second).

My end goal is to plot these values on a map. Thus, I would like a way to identify the unique combinations of each of these 4 scores. In this case I have 81 possible combinations ($3^4$).

I appreciate this is a little off topic, but I thought someone here could help.

Answer 1

I would like a way to identify the unique combinations of each of these 4 scores

Then map them to a four digit base 3 number.

$(a,b,c,d) \to (a-1)*3^3 + (b-1)*3^2 + (c-1)*3 + (d-1)$.

Each value gets mapped to a distinct number between $0$ and $80$.