**6.1 Total numbers**

For a finite set S, the summation of numbers obtained from elements of S is called the total number of S. For example, if each element is assigned to 1 as the existence of the element, then the total number is the same as the cardinality of S. The quantifying concept ⫷cardinality⫸ is regarded as a function that has an objective graph � as input data and that outputs the cardinality of [[�]].

For a concept S, attributes *A1*,…, *An* of S, and the real-valued function f on the set of values of instances of S with respect to *A1*,…, *An*, the summation Σ <sup>s</sup>∈<sup>S</sup> *f*(*s.A1*,..., *s.An*) is called the total attribute number of S with respect to *A1*,…, *An* and *f*, where *s.Ai* denotes the value of an instance s with respect to *Ai*, is an attribute quantifier function.

The quantifying concept ⫷total attribute number⫸ is regarded as a function that has the following data as input data:


⫷total attribute number⫸ outputs the total attribute number of [[�]] with respect to *A1*,..., *An* and *f*.

Representation System for Quality Indicators by Ontology 207

Fig. 8. Quality indicator "Stomach cancer 5-year survival rate".

Fig. 9. Objective graph describing Hospital stays for stomach cancers.

stomach cancers", as follows.

6.3).

To be more precise, Figure 9 denotes the set of hospital stays that have admissions with purposes treatments of stomach cancers and operations for stomach cancers by laparotomies. By using the objective graph above, the quantifying concept ⫷average⫸ (cf. Section 6.3) and a function that assigns to two dates the number of days between the two dates, one can obtain the quality indicator "the average length of the hospital stays for

Fig. 10. Quality indicator "The average length of the hospital stays for stomach cancers"

In Figure 10, the objective graph in Figure 9 is the first input data of ⫷average⫸, two attributes ⟨starting time point⟩ and ⟨terminating time point⟩ of the concept [hospital stay] are assigned as second input data of ⫷average⫸, and the function that assigns to two dates the number of days between the two dates is the third input data of ⫷average⫸ (see Section
