Here I need an equation or ideas to narrow the left view on ranking and categorization system and to widen the right view on ranking and categorization system.
Could you please provide a more precise question? (Context of research?) What (I think) I see is: you are interested in 'category generation'. Have you read the tons of reinforcement learning books out there how categories are learned? Or the literature on 'category generation' models (e.g. SUSTAIN)? Or the "Bayesian approach" asking/formalizing where category hypotheses come from? (The last one looks like the answer to your question on a superficial level.)
I agree with you I need more and more research and digging about the subject before I conclude a theory. I ask a question before generating a theory because of the fabulous feedback and guidance that I got from researchgate researchers. I will start digging about category generation.