Do not loose your time with entropy, take the most general MOO technique.
MOO for many objectives and many variables
methods like ELECTRE and PROMETHEE compare 2 by 2 and are not good for many objectives.
AHP looks at dominating effects and comparisons and end finally with 2 super objectives to compare, very subjective.
For deficiencies of other methods see: Chakraborty 2011.
MOORA, extended to MULTIMOORA, used for Europe 2020, 22 objectives and the 27 countries as variables, but these numbers may increase without difficulties.