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I have a general problem in going from a problem that is described in english to it being described in mathematics and then solving it to find the solution.

Take, for example, that I have a set of "houses" with features such as {bedrooms, build_quality, noise_pollution (lower is better), air_quality (higher is better), price_per_sqft}

Then I want to find the house that has the higher number of bedrooms, lowest noise pollution, highest air_quality and lowest price_per_sqft. How would I describe this using the language of mathematics? (can I say how do I model this problem mathematically?) and then how would I go about actually solving it? Can I describe the problem in some function and then try and minimise it? What about normalization as air_quality and bedrooms could be vastly different?

Many thanks

Asaf Karagila
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hairybear
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    You need to create a measure that is a weighted function of these variables. Yes, you will need to balance the weightings to account for different scales (and different directions) but also to account for the relative importance of the different variables to your users. Once you have your measure, it is fairly easy to find an optimum value. – tomi Aug 20 '21 at 17:31
  • if you have two houses one with better air quality and the other with better price surely you can't have the lowest of both, what you can do is defining a function which takes into account the interaction between the variables. Obviously an house with an unbreathable air can't be a good choice almost independently from its price :) – Tortar Aug 20 '21 at 17:40

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