I have a list of 20 yes\no product attributes matching 20 questions of preference on a 5-point likert scale (strongly dislike to strongly like the attribute). I would like to score or rank a list of 100 products based on the customer's preferences. Some attributes can occur simultaneously and others cannot (it can be big and shinny but not blue and red at the same time).
What kind of analysis does this require? Are there an R package that would facilitate analysis of this or even more varied datasets?
If I were attempting this in R it seems like I could change the likert scale to -2 - +2 and multiply each answer with each product's binary yes/no answer. The sum could end up being somewhat useful.
It seems like it might make sense to identify similar groups of attributes and to compare the variation within each group to determine how important that category of attributes may be to the customer. Maybe that makes a 7-point scale more useful as well. Any guidance would be greatly appreciated.