I have a dataset consisting of ordinal variables on a Likert scale from 1 to 5. I intend to use triangular membership function and transform each factor data value for all the variables to a defined fuzzy set in R.
For example, I have a dataset with 5 variables say V1 to V5 which I measured through my survey items of a questionnaire on scale 1 to 5 from 1 being strongly disagreed to 5 being strongly agreed. Likert values are nothing but perceptions of respondents so they can be transformed into a fuzzy set. So, a score of 1 can be transformed into a triangular membership function of (0,1,2) and so on. Once derived, I wish to cluster or perform PCA on these variables.
I am confused about how to transform my variables entries to the fuzzy set and then perform the above-mentioned analysis. Any suggestions or references are welcome.