If a decision problem is not multiple criteria one, it is not a real-world problem
Foreword
This blog is dedicated to problem solving. Every day we choose between multitude of the options, mostly unconsciously, and we base our decisions on a number of criteria that oftencontradict each other. Every time we do this we solve multiple criteria problem. Our team developed the methodology for solving this kind of a problem, here's my attempt to describe it with extremely non-serious example. I'm going to omit many details for brevity sake, please reach out if you want to learn more!
Multiple Criteria Decision Making in a nutshell
Case study: Buying a cat
Let us consider a problem of cat shopping. With all the breeds and cat personalities out there, it's not a trivial choice.So let's try to approach this consciously. We can come up with some criteria hierarchy, something like this:
- Fuzziness. Cat's fur can be described by its length
- Weight
- Activity. Some pet owners prefer animals not that different from the stuffed toys, others love to play with their cats. Activity is a quite vague notion, so let's separate it into two different parameters:
- Playfulness. Let's just measure it on a scale from 0 (absolutely inert creature) to 10 (twister with a tail)
- Hours a day sleeping
Suppose we like fuzzy animals, so "Fuzziness" is our top priority. We can say that "Fuzziness" is essentially more important than "Activity" and considerably more important than "Weight". On the other hand, we would like to have a playful cat, so "Activity" considerably more important than "Weight".
We prefer passive or over-active cat to the one never awake, so "Hours a day sleeping” essentially more important than "Playfulness".
Now we need to express our preferences for each parameter. Fuzzy Sets Theory gives us a convenient instrument to do just that. It's called desirability function.
For example, suppose we consider cat’s fur to be perfect when its length is 1 centimeter and we are not ready to deal with heaps of lint a cat with two-centimeter length fur will produce. We would build something like that:
We love playful cats, so “twister with a tail” is our dream. The desirability function will look like this:
A cat sleeping more than 16 hours sounds quite boring, and keeping in mind our fondness for playful cats it is unwise to wish for a cat sleeping less than 10 hours a day.
We think a healthy cat shouldn’t weight less than 4 kilograms, and it may be not so good idea to have very active cat weighting more than 6 kilograms. Something more than 10 kg is going to be plainly dangerous.
Now we are ready to go shopping! Using our technique of aggregating multiple criteria into single criterion (of cat quality, in our case), we can choose a cat at no time. Here are some of the cats we might encounter:
Meet Anfisa. She's fuzzy (1.9 cm), not especially responsive (Playfulness 1), almost never seen awake (Hours a day sleeping - 23) and she is big (Weight 9 kg). Our global criterion for her is 0.2.
Meet the Beast. He has short fur (0.5 cm), restless (Playfulness 10), doesn't really sleep (Hours a day sleeping - 23) and light as a feather (Weight 3.5 kg). He's close to what we want, global criterion for him is 1.22.
This is Berta. She has virtually no fur (0.1 cm), no sleep disorders (Hours a day sleeping - 10) and is good tempered (Playfulness 7). Nice, but skinny (Weight 4 kg). Global criterion is 0.6.
It's an ideal cat. He's just ideal. He is a super cat. We will buy him. Fuzziness 1 cm, Playfulness 7, Hours a day sleeping 10, Weight 5 kg. Global criterion is 2.
Last, but not the least - Tiger. Furry (1.9), loves fitness (Playfulness 8), though doesn't sleep enough (8 hours a day). Considering the fact that he weights 9 kg, he will have no trouble getting you out of bed on Saturday morning. Global criterion is 0.5.
Please reach out if you want to find out more about the way Global criterion is calculated.
Have a nice cat!
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