Me and my simple questions: Can I do this in FPGA?

Tricky now that you mentioned, I'm not that sure that the input should be decimal, but I'm quite sure that in the end I have to reflect somehow results in decimal (for showing purpose).

This is for a project in my course, I'm working with a hypothetical FPGA system that read a black and white picture in which every pixel has a different pixel intensity ranging from 0 to 99, those values are loaded into a list, that I have to cluster according to "Membership value" of every pixel into only 3 groups.

Each pixel should be processed by 1 PE to calculate "membership" as shown equation in my OP. (Then, each PE will communicate each other so they can "update" membership, but that's another story).

This equation includes Adding, subtraction, multiply and dividing. One big issue is that factional values (example: 0.0002) are generated in the process, (it also generates real periodic numbers like 0.1416.........., but I will keep them limited to a certain fixed number).

My work doesn't include how to catch the pixel intensity numbers, I will just take the values from a list, so I think you are right, maybe I can consider the list originally in binary, and in the end I cluster them in groups by binary also, without needing decimals ever.

Do you think doing divisions and multiplications of fractional values is any easy or feasible? My intention is to make this as simple as possible. Thanks so much!