Jaccard coefficient similarity measure for asymmetric binary variables

How to calculate the similarity of an asymmetric binary variable using Jaccard coefficient?

There are many methods to calculate the similarity of data. Jaccard coefficient is one of them.

Jaccard coefficient is used to calculate the similarity among asymmetric binary attributes. 

Contingency table for binary data:

Object 2
Object 1   1 / True / Positive 0 / False / Negative Sum
1 / True / Positive A B A + B
0 / False / Negative C D C + D
Sum A + C B + D  

In table 1 we can consider the following facts.

A represents that object 1 is True and object 2 is also True.

B represents that object 1 is True and object 2 is  False.

C represents that object 1 is False and object 2 is  True.

D represents that object 1 is False and object 2 is also False.

Name Fever Cough Test 1 Test 2 Test 3 Test 4
Asad Negative Yes  Negative  Positive  Negative  Negative
Bilal Negative  Yes  Negative Positive  Positive  Negative
Tahir Positive Yes  Negative  Negative  Negative  Negative

In table 2, Asad, Bilal and Tahir are objects. Negative values represents False and Positive represents Negative.

Consider 1 for positive/True  and 0 for negative/False.

jaccard similarity in statistics

Similarly, we can calculate the similarity of one object with each other object.