"A rating is the evaluation or assessment of something, in terms of quality (as with a critic rating a novel), quantity (as with an athlete being rated by his or her statistics), or some combination of both" (Wikipedia).
The "rating" and "valuation" tags refer to the same concept: "valuation" is the process of assigning numbers, scores, or ranks to options or outcomes to reflect relative preferences or to create a composite score.
Problems that involve the optimization of multiple criteria must make trade-offs between having more of one characteristic and less of another. A "valuation" or "value function" quantifies those trade-offs. Either a valuation is made explicit in order to solve the problem or else it will be implicit in any solution.
Examples include
Deciding between a product that has a high average user rating based on only a few reviews and another product with a lower average rating based on many reviews.
Determining the worth of players on a team or some group of experts based on multiple skills.
Identifying optimal investments based on expected return and volatility.
Creating an "index" for a market or other collection of varied objects, especially when they might not be directly comparable.
See Wikipedia at Multiple-criteria decision analysis for a general overview.
