# Ranking the objects

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If we have two objects Obj1 and Obj2  along with we have two Methods for weight calculation of theses objects i.e. Method1 and Method2

If Obj1 have weight X1=0.7 from Method1 and weight Y1=0.5 from Method2

similarly, Obj2 have weight X2=0.5 from Method 1 and weight Y2=0.7 from method2

My objective is to Rank the obj1 and Obj2 according to there weight values determined from Method1 and Method2.

Can anyone help me to tell the defined mathematical formula to get the,

Rank of Obj1 = ?

Rank of Obj2= ? ##### Share on other sites

I guess you are searching for some sort of statistical weighting process here ???

If this is the case you have posted in the wrong section - on this webforum statistics belongs in the applied maths section.

Anyway back to your question, you have not enough information to compare since you have two objects (obj1 and obj2) and two measurements (meas1 and meas2)  of two properties (X and Y )  to consider.

So for instance you have for object 1 only property x1 but not property x2  so you cnnot directly compare (or weight) them.

Perhaps I have totally misunderstood your intention so please tell us more.

Edited by studiot
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Sir  here i am giving you little details:

Ranking the criteria "A" and "B" based on result generated by Method1 and Method2 :

CRITERIA                     METHOD1                           METHOD2

A                                   0.7                                           0.5

B                                    0.5                                           0.7

here i want to know is there any concept that we can add here in this situation to get the final rank if both the Methods have equal importance.

Note:  i can not add the result of both methods to get the final result.

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1 hour ago, Amit Mishra said:

Sir  here i am giving you little details:

Ranking the criteria "A" and "B" based on result generated by Method1 and Method2 :

CRITERIA                     METHOD1                           METHOD2

A                                   0.7                                           0.5

B                                    0.5                                           0.7

here i want to know is there any concept that we can add here in this situation to get the final rank if both the Methods have equal importance.

Note:  i can not add the result of both methods to get the final result.

To my way of thinking, this question is still seriously lacking in detail.
I do not think you have added anything to your opening post.

Perhaps we can clarify what you want by considering some examples, rather than symbolic processes.

Ranking has a number of possible variations.

1. Two students, A and B take an exam which is marked by teachers, C and D and it is desired to combine the marks for each student to get their overall exam result.
Teacher C give A - 5/10 and B - 7/10, whereas teacher D gives at 7/10 and B at 5/10.

2. Two states (North and South) are ranked 5th and 7th by annual individual earnings, but ranked 7th and 5th by individual car ownership.
Again their overall standing is required.

In the first example the exam is a common feature to both students and teachers.

In the second example the two 'methods' in your terminology are different.
There is a formula, known as 'rank correlation', which allows the user to expore the possibility that earnings and car ownership are related.

But there is not enough data in your example to make any other statement than the rankings in either case should be taken as equal.

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• 3 weeks later...

Hi,

I have a lot of experience in coding, and this is a common problem, ranking objects (usually you need ranking to store them in a tree that you can request fast, using a "index", the index need ranking).. if what you need is just a way to rank objects.
A usual way is simply to sort them using each of their properties sequentially : compare them using the first method, and if they are equal, then use the second method.. it's what we all do with word with more than 1 letters (we compare the first letter, then if it fails, we compare the second letter etc..)

but if the methods must have the same importance, there is no method that wouldn't give equality, because your values are symmetrical.

Edited by Edgard Neuman
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• 5 months later...

You have two different ranking methods with rank A and B in different orders.  To be able to determine an order for A and B you will have to decide on how to weight the two methods.  That will depend on which you think is more "accurate".  For example if you think method 1 is twice as accurate as method 2, you would give 1 a weight of 2/3 and 2 a weight of 1/3 (because 2/3 is twice 1/3 and they add to 1).  So you would rank A as (2/3)(.7)+ (1/3)(.5)= 19/3 and would rank B as (1/3)(.5)+ (1/3)(.7)= 12/3.  A is ranked higher than B.  But if you thought 2 was 50% more accurate than 1 you would give 1 a weight .4 and 2 a weight of .6 (.6= (1.5)(.4) and .4+ .6= 1).  So now you would rank A as .4(.7)+ .6(.5)= .28+ .30= .58 and B as .4(.5)+ .6(.7)= .20+ .42= .62.  Now B is ranked higher than A.  Of course, if you believe they are equally accurate, you would weight both 1 and 2 as 0.5.  Now A is given the combined ranking of 0.5(0.7)+ 0.5(0.5)= .35+ .25= 0.6 and B is given the combined rating of 0.5(0.5)+ 0.5(0.7)= .25+ .35= 0.6 and both are equal in rating.

(Note that if methods 1 and 2 gave the same ranking for A and B, no matter what the actual values are, the combined ratings, using any weights, would give the same ranking.)

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