Question about geometric mean

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Question about geometric mean

Mehdi Dadkhah
Hi,

I hope you are doing well.

I am using Interpretive structural modeling (ISM) and need to build a
“reachability matrix” to use it as the input for “ISM” package. In ISM
method, the opinion of some experts should be collected. For example,
attached image includes matrices which show opinions of four experts about
relationship of A1, A2, and A3 together. To integrate these matrices
together, I should use The geometric mean of experts’ opinions. In the
Yeh’s paper wrote that:

*“The geometric mean of experts’ opinions on the relationship between a
pair of criteria (sub-criteria) was **calculated. Set the threshold value
0.50 which represents that more than 50% of the experts determine the
interrelationship. If the value of the element is less than 0.50, the value
is counted as 0”.*

Ref: http://dx.doi.org/10.3846/20294913.2015.1071293



My question is: How should I calculate geometric mean of experts’ opinions
in example attached matrices? In other words, I do not know how should I
calculate geometric mean. I read some papers, but could not clearly
understand.

Many thanks!

With best regards,



--
*Mehdi Dadkhah*
PhD candidate & Research assistant
Department of Management, Faculty of Economics and Administrative Sciences,
Ferdowsi University of Mashhad, Mashhad, Iran
*Email Addresses:*
[hidden email]
[hidden email]

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Re: Question about geometric mean

Rich Shepard
On Fri, 18 Oct 2019, Mehdi Dadkhah wrote:

> I am using Interpretive structural modeling (ISM) ...

> My question is: How should I calculate geometric mean of experts’ opinions
> ...

I'm not a statistician, nor do I know anything about ISM. With that
disclosure I offer a couple of thoughts.

First, the calculation of a geometric mean involves multiplying the 'n' data
points and taking the 'nth' root of the product.

Second, expert (and others') opinions are along a continuum of a set,
perhaps ranging from 'Completely False' to 'Completely True'. I addressed
the need to quantify this subjectivity in environmental impact assessments
by using fuzzy sets and fuzzy logic in applying Thomas Saaty's 'Analytical
Hierarchy Process.'

Perhaps these thoughts are usfull for you.

Regards,

Rich

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