I know one may suggest these are simple integrations that can be solved using the well known integration principles however my question is there what is x and y in the two matrices, A = (...) and B = (...)? These two matrices only contain fixed numerical (constant) values. For integration we need variables.
Theme is Three Dimensional Absolute Degree of Grey Incidence Model
If $A^0$ and $B^0$ are matrices with the elements not dependent on $x$ and $y$ then matrices $s_a$ and $s_b$ are:
$s_a=S(D_a) A^0$,
$s_b=S(D_b) B^0$,
where $S(D_a)$ and $S(D_b)$ are areas of $D_a$ and $D_b$ respectively
($S_a=\int_{D_a} dx dy$, $S_b=\int_{D_b} dx dy$).
I hope that this will help you in resolving your question.
In addition to my first note you can consult also the following site
http://mathinsight.org/greens_theorem_find_area
It is quite useful when the domains $D_a$ and $D_b$ are of not trivial shape.
PS. In my first note I have used consistently the TeX notation; I hope that this is fine with you (if not I will sent you a PDF version).
@Janusz Pudykiewicz,
I'm a beginer in the field so not familiar with TeX notation. Plz share PDF. Thanks.
@Saad Ahmed Javed,
Attached please find a pdf file with my answer. As You can see the problem is in calculation of the areas. I hope that this will resolve your problem.
With my best regards,
Janusz
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