Hi, I need to describe what I need in proper terms that can be used as
a specification for a math professional to find or design the right
model for me.
Then I actually need the model itself.
The budget is very limited, but I am very interested in doing it the best way.
Here is what I need in plain english. Let us say I need to buy a
computer or an appartment or to hire an assistant etc. I need to enter
many objects (of the same type) available on the market, specify my
preferences, quantify and prioritize them them and calculate what is
the best choice for me.
For example criteria for a computer would be size of RAM, size of HDD,
speed of CPU, price etc. For an appartment will be distance from a
perfect location, price, number of bedrooms, condition, noise, etc.
For an assistant I'll need to enter quantified knowledge in many
areas, friendliness, compatibility with me, easiness in communication
with me, with others, english skills, wage/salary expectations etc.
Then I need to rate them all based on my criteria and on the
importance that I give to each of those criteria.
The final result - I need to rate them all and find the best choice.
Please let me know if you have anything in mind or can recommend
something or can provide a complete solution, or may be if you can
recommend someone. |
Request for Question Clarification by
leapinglizard-ga
on
07 Jun 2005 14:29 PDT
There are sophisticated mathematical methods for optimizing numerical
constraint-satisfaction problems, but it seems to me that your
constraints are largely subjective. Although you might be able to
attach numbers to some of the product criteria, the way in which you
value those numbers is itself subjective.
Thus, I would say that the proper approach in your case is to develop
a weighted rating scale for each product type. You would then choose
the product with the highest arithmetic average over all ratings. This
the model that Car and Driver uses to decide the winners of its
automobile comparison tests, for example, and the method used in many
Slate.com stories to find the best popcorn, the best pen, and so on.
If I were to point you to some of these stories and to develop one or
two examples of my own -- I could work out weighted rating scales for
a computer purchase or an apartment rental, say -- would you consider
your question answered?
leapinglizard
|
Clarification of Question by
gethelp-ga
on
07 Jun 2005 15:39 PDT
You are right, it is not just subjective, it is nearly 100%
subjective. Even wirh a computer, for me personally the size of RAM
may have much more value than of the hard drive, but for a stororage
computer it could be the opposite. If I could give a proper weight to
each value of each criteria, I could do the rest by myself. My main
problem is how to convert a relational human perception into a weight
of a criteria. And again, it is absolutely subjective. I will myself
pick criterias, then I will determine (just arbitrary assign) a value
to each of the criteria, for example on a scale 1 to 10 this
parameter's value (for me personally) is 7. etc. Of I can give an
exact number if given a range (like for amount of RAM if I say that I
am looking for a computer with RAM between 256Mb and 1Gb (that would
be the range) and the one that is in question now has 512Mb of ram -
it is clear that it can be converted to a scale from 1 to 10 for the
value of this parametyr.
The real trick is how to incorporate here priorities/weight of the
parameters/criteria themselves based on relational human thinking.
Here is an example. Let us say we are talking about hiring an
assistance. I can say that having good English is more important to me
than having computer skills. Understanding what I am saying is more
important than computer skills too but less important that English
scills. Having computer skills is 10 times more important than being
attractive. Experience is twice as important than compensation
expectations. Etc. So first I need to have a simple, "human" way to
formalize the scales (parameters/criterias) themselves. Then when the
scales are sorted out I can give each candidate a mark in each scale.
And the last part, I guess the most straight forward is to calculate
rating for each candidate based on that candidate's position on each
scale also taking in consideration the difference in weight of each
scale.
I need a mathematical formula and an algorithm/methodology how to give
waight to the scales. I will come up with a different set of scales
each time (for computer one set, for an assistance another, for an
appartment yet another). The system should force the user to answer
some questions or to make some choices or do whatever it takes (but
the simpler for the user the better) to come up with weight of each
scale. The rest I guess is trivial.
Now I cannot answet your question because I do not have enough info to
base my answer on. May be you can answer how far away what you
suggested from what I need. Please feel free to ask if I am not very
clear in my comments.
|
Request for Question Clarification by
leapinglizard-ga
on
07 Jun 2005 16:44 PDT
I believe our thinking is fairly close. The way I would model
attribute preferences is to attach a numerical weight to each
attribute depending on how important it is. The relative magnitude of
the weights should reflect the relative importance I attach to the
corresponding attributes. Then, after rating a candidate for each
attribute on numerically identical rating scale, I take the weighted
arithmetic mean of the ratings to determine my overall favorite.
To take your example, suppose I'm evaluating secretarial candidates
based on English fluency, computer skills, comprehension ability,
attractiveness, salary expectation, and employment experience. If the
least important of these is attractiveness, I'll give it a weight of
1. Since computer skills are 10 times more important, they get a
weight of 10, and so forth. I end up with the following weights. Note
that comprehension ability is more important than computer skills, but
English fluency is more important yet. Experience is roughly halfway
between attractiveness and computer skills in importance, and salary
expectation is twice as important as experience. These relationships
are based on the comments you made above.
attractiveness 1.0
computer skills 10.0
English fluency 15.0
comprehension ability 12.5
employment experience 5.5
salary expectation 11.0
Now I work out some way to rate each attribute on a scale of 1 to 10.
You can also use percentages or a 1 to 5 scale, as you wish, since
what truly matters is the final ranking. To rate attractiveness, I
suppose that the ugliest possible candidate is a 1 and the most
beautiful in the world is a 10. For employment experience, I'll say
that a novice gets a 1 while a lifelong secretary, with 50 or more
years under her belt, gets a 10. I can similarly scale the salary
expectation to a 1-to-10 range, while English fluency is more of a
subjective impression, and so on.
Finally, to compute the weighted average for a given candidate, I
multiply each of her attribute ratings by the attribute weight, take
the sum of all these, and divide the total by 55, which is the sum of
all the attribute weights. This gives me the weighted arithmetic mean
of the attribute ratings. The candidate with the highest mean score
wins.
It's a fairly simple scheme, but I think it's reasonable. Has this
been helpful to you at all?
leapinglizard
|
It seems to me that what gethelp-ga is after is more a way of actually
determining on an interactive basis what weights to assign to various
elements. (The ranking part is reasonably straightforward.) This makes
the process much more reusable.
Here's one approach I've seen used (by a bank). The various elements
are divided into groups of a few related elements. (In the bank's
approach there was also filtering based on which elements the user
said they wanted; you may or may not want to include this aspect.) If
there were two elements requested in the same group a slider was put
up to choose between them (1-5). If there were three they put up a
slider from each of the three possible pairs; presumably they did some
sort of fit to get a compromise set of weights. Obviously you don't
want to put up six sliders where there are four elements in the group
- too much effort for the user. Indeed, I found the bank's one
confusing enough because some of the elements I was being asked to
compare seemed to mean the same thing. So probably three-way
comparisons are the most that is practical with this approach.
Note that you can operate on a hierarchical level, getting the user at
each level to indicate the relative weights of various groups.
Probably a better way of organising it if you have larger numbers of
elements is to use a panel of sliders (much like the Windows volume
control panel). You can have half a dozen or so elements being
directly compared this way. You could again use a hierarchical
approach if you have many elements. For instance, for a computer you
could have main areas of (say) Performance, Storage, Expandability and
Price. Performance could be divided into CPU speed, HDD speed, amount
of RAM, etc. Storage could be divided into HDD size, CD/DVD readers,
CD/DVD burners. Expandability could cover things like USB ports,
expansion slots, spare memory slots, CPU upgradability, etc.
If you provide sensible defaults for the relevant areas within each
group, the user only has to rate the main headings against each other.
But they can also go into the details for each group to fine-tune the
results, if they want to. |
Thank you, this is much closer to what I asked. Eventually I will need
to be able to calculate a final result based on those choices, but I
assume the math behind it will be simple. This is a great approach for
large sets. What if I have only let us say 4 parameters for a computer
- RAM, HDD, CPU Speed, Price.
I was thinking of a bubble algorithm where a user is asked to compare
each parameter with every other, asking them not only which one in
each pair is more important, but also how much more important. Then
when I have all those quantified relations between parameters (scales)
what do I do with them?
This is ideal because humans can compare 2 objects much easier than 3
or more of them at once plus it is not natural for most of average
people to make a relatively correct numeric chart as leapinglizard
suggested.
Also my approach (bubble comparing each pair of the set) looks like
compete, but the more parameters(scales) are involved the more tedious
the process will be for the user.
Do you see any compromise between my complete and easy but very long
bubble approach and may be something else that is as complete and easy
but not so time consuming as bubble?
Also if you agree than a bubble comparison is good enough, I do not
know how to convert my bubble results into a weight chart as
leapinglizard showed above.
One more thing that confuses me. Let us say we are talking about CPU.
A CPU may be Intel or AMD. I may have a preference of one over
another. Then I am not absolutely sure that for a binary answer
(yes/no) one should be at one end of the scale, another one will be at
another end of the scale. Even if the weight of the scale is not big
enough, won't my slight preference in CPU (If I do not have strong
opinion about which one to choose, but I have a mild wish) affect the
result too much? And after all, how do I compare speed then? Let us
say there are computers with Intel CPU with different speeds and
others with AMD CPUs with their speeds too, but I cannot compare the
speed of AMD with the speed of Intel, the comparison of just that
number would not be correct. I can split all contestant computers in 2
groups, one with Intel, another group with AMD. Then compare 2 groups,
find the winner in both, and then what to do with 2 winners? It comes
down again to comparing apples to oranges. Not to mention that I would
not want to complicate te process by splitting a set of objects to
compare into groups. I just need to come up with how to rate such
different things. |
