Indiscernibility classes

Thus, the subsets of X(A) correspond to equivalence classes, which in RST are called indiscernibility classes or elementary sets. Regardless of the nomenclature used, all of the elements within a given indiscernibility class are equivalent to or are indiscernible from each other with respect to the subset of condition or decision attributes being considered. The set of indiscernibility classes induced by a given subset of condition or decision attributes constitute the respective C- and D-spaces, of the problem. One of the powers of RST is that it provides mathematical procedures for eliminating... 

FIGURE 3.1 The Universe of Discourse X is partitioned into 10 indiscernibility classes by the set of attributes A,. See Section 3.2.1 of the text for further discussion, three of which lie within the set 5 being approximated. 

There are several measures that are related to the accuracy of the classification of a given subset S with respect to the partition induced by a subset of attributes [6,11,34]. The most universally applied measure is the accuracy by which S can be approximated by the set of indiscernibility classes induced by the subset of attributes A, ... 

TABLE 3.2 The DT Derived from the Data Given in Table 3.1 with the Five Indiscernibility Classes X°, X°, X°, X°,andXf Induced by the Set of Condition Attributes... 

Note that the column of the table corresponding to the decision attribute p is grayed out since its values are not consid ed in the determination of the indiscernibility classes induced by the conditional attributes (see text and Eq. 3.2.19 for further details). Up regulated genes are indicated by an upward arrow ( ), down regulated genes by a downward arrow ( I ), and normally expressed genes by a filled square ( ). Phospholipidosis p is indicated by a plus (+) if it occurs and an open circle (O) if it does not occur. 

The value of each of the three gene expression levels is identical for all elements within a given indiscernibility class. For example, consider the indiscernibility class Xf, which is made up of molecules 1 and 6. Table 3.2 shows that gene- is up regulated (expression-level = ), while gene-2 and gene-3 are normally expressed (expression-level = ) for both molecules. Interestingly, the two molecules behave differently... 

As shown in Table 3.3, the decision attribute partilions the set of compounds into two indiscernibility classes, called D-indiscemibility classes,... 

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