Hi Reza,

You should understand like this:

You have similarity on an attribute a: R_a(x,y).

       The example you mentioned for the second paper is calculated by distance based methods:

        Distance d_a(x,y) = (a(x) - a(y))^2. It is normalized, thus, d_a \in [0,1]

        Relation R_a(x,y) = 1- d_a(x,y)

Then, combining similarities on all attributes by t-norm "T", you will have the similarity on all attribute: R(x,y) = T(R_a(x,y))

Their idea in the first paper:

- Put a parameter into equation R_a(x,y) = 1- d_a(x,y) then you have R_a(x,y) = 1 - sigma*d_a(x,y).

- Change sigma to see how POSITIVE regions change. They compute R_a(x,y) = max(0,1-sigma*d_a(x,y)) to ensure that R_a(x,y) will never less than 0 while sigma changes.

- Calculate max.sigma (satisfy some criteria) for each instance.

- QUALITY(x) = max.sigma

Their idea in the second paper:

- Not use sigma (or sigma = 1)

- QUALITY(x) = average of Lower and Upper approximation

Last, choose or eliminate instance x by comparing QUALITY(x) with thresholds.

By the way, you should ask the authors for the best understanding.

Regards,