For the sake of our discussions we will consider independently

For the sake of our discussions, we will consider independently the following three cases:
5.1. Comparison of rule induction approaches in strongly consistent multi-scale decision table
Definition 11 [23] and [24].
          Let S=(U,C∪ d )=(U, ajk:k=1,…,I,j=1,…,m ∪ d ) be a consistent multi-scale decision table. The k  th level of scale is said to be optimal if SkSk is consistent and Sk+1Sk+1 (if there exists k+1k+1) is inconsistent.
Observe that ARP 100 the notion of optical level of scale in [23] and [24] is defined with respect to all objects in the universe, or in other words, all objects in the universe have a common optical scale, consequentially, all decision rules will be derived at coronary arteries level of scale. Comparatively, in our approach, the optical level of scale is defined in a pointwise way, that is, different objects in the universe may have distinct optical levels of scale and the set of decision rules will not be obtained in a single level of scale. We can thus safely say that the optical level of scale is given from a global viewpoint while our approach is presented from a local viewpoint.