**4. Discussion**

**Target coverage equation** 001. Normal (prostate) 0.03 (11) 002. Suspect (prostate) 2.89 (11) 003. Positive (prostate) 34.68 (11) 004. Normal (Bartholins gland) 0.01 (11) 005. Suspect (Bartholins gland) 13.49 (11) 006. Positive (Bartholins gland) 34.68 (11) Total coverage 85.79 (12)

The correlation between the features is shown in Table 4. Only a full correlation is found be‐ tween the two features indicating the presence of metaplasia. This feature is included twice since different weighting factors appeared to be needed for the different animal types. An‐ other reasonable high correlation factor was found between the duct ratio and the combined presence of metaplasia and elevated duct ratio. The presented level of correlation coeffi‐

**Table 4.** Matrix with Pearson's correlations between the features of the kernel model for diagnosis of illegal hormone use in veal calves. The colour of every cell (running from red to green) represents the value of the correlation coeffi‐

The match table (Table 5) shows the relative resemblance between the targets based on equation (7). Except for the diagonal, the green colour, based on the calculations using equa‐ tion (9), indicates that every target can be diagnosed uniquely compared to any other target.

**Table 5.** Matrix with the matches between the targets of the model for diagnosis of illegal hormone use in veal calves. The figure in every cell is calculated according to equation (7), the colour of every cell is based on equation (9).

**Table 3.** Coverage of the variability space by the individual targets and the total dataset.

cients is in line with the calculated average redundancy: 0.405 (equation (8)).

Hence, the separation capability is 100% (equation (10)).

cient.

62 Decision Support Systems

The process of identifying the level of treatment with growth hormones of veal calves is a rather specific situation for diagnosing in the broader framework of application of DSS in medicine [8-10]. Only one feature matters, all other features will only modify the probability that a diagnosis belongs to the correct class. Besides that, a constraint dependency rule exist‐ sbetween feature 13 (number of deviating features; Table 1) and the totalof features from group III plus either from group I or group II which show a state other than normal. The importance of the main features is visible in Table 2 and Figure 4. The two main features (male: presence of metaplasia, female: combined presence of metaplasia and an elevated duct ratio) both got a weighting factor of 9 in order to outnumber the features in group III for reaching a correct diagnosis (number of features in group III plus 1). Since the presence of metaplasia in the diagnosis of a female calf does not form the exclusive indicator for treat‐ ment in contrast to the position of that feature in the diagnosis of the male calf, it got a weighting factor of only 1. The weight factors in the current model are fixed instead of being input sensitive [11].

There is no generic method for validation of data models in expert systems [7]. In the cur‐ rent study a top down modelling approach was chosen: logic tables lead to a decision tree, which was the basis for the full matrix of the free access key. This approach does not pro‐ vide a tool for handling constraint dependency rules [7], which was solved here by optimis‐ ing the weighting factors. Rass et al. [12] listed a number of requirements for valid expert systems. Of these, the requirements for minimising the redundancy and for avoiding unin‐ tended synonyms are now supported bymeasures to calculate the extent of these parame‐ ters: redundancy (equation (8)) and separation capability (equation (10)), respectively.

The position of the features of group III (Table 1: indicating the individual deviating charac‐ teristics) in an extended diagnosis (Figures 4b, 4d, 5d) can be discussed in terms of fuzzy logic principles. In several experiments with fuzzy logic comparable results have been found [9, 13]. Here, probability or uncertainty is the basic aspect causing patterns in the model outcomes that can be explained as membership functions [13]. As an example, the presence of metaplasia in a prostate is a definite diagnosis for treatment with growth hor‐ mones (n = 1 in Figure 5c in concordance with the tree in Figure 4), but it is highly unlikely that with such a diagnosis none of the other features of group III (Table 1) would show a state deviating from normal. The probability that an animal with the sole presence of meta‐ plasia belongs to membership class "positive" is only slightly higher than its membership to the class "suspect" (n=1 in Figure 5d). The kernel model without using the individual fea‐ tures of group III (strategy A) seems sufficient to reach a diagnosis. All the features underly‐ ing the depending feature 13 (group IV) are nevertheless included in the model in order to improve the performance of the user by supporting his or her examinations, and to provide the possibility of an iterative process of optimising the diagnosis [14].

Existing results of optimising a datamodel for reaching a diagnosis reveal that lower num‐ bers of features appeared to be optimal [10]. In those cases that a model consists of only a few features, expressing them in terms of space dimensions (e.g. a two-dimensional space in Figure 2), a major part of the variation space might be covered. Increasing numbers of fea‐ tures (i.e. dimensions) result in an exponentially growing number of theoretically existing feature combinations that are not linked to a target. In the present study a total of approx. 14 % of the variability space was not covered by any target (Table 3). In order to evaluate this non-assigned part of the variability space, let us assume a variable number of features *n* each consisting of three feature states, a number of targets that can be accommodatedby in‐ creasing with a factor of 2 with every additional feature, and one and only one state per fea‐ ture identifying a target *p*:

$$\left(F\_{i,k}\Rightarrow T\_{\;p}\right)\land\left(F\_{i,\neg k}\Rightarrow T\_{\;p}\right)\tag{13}$$

**5. Conclusion**

**Author details**

**References**

L.W.D. van Raamsdonk1\*, S. van der Vange1

*niUniversità di Trieste*, 213-216.

*ciety. Leipzig*, July 1-5.

Rijeka, Croatia.

54, 238-246.

\*Address all correspondence to: Leo.vanraamsdonk@wur.nl

1 RIKILT, Wageningen UR, Wageningen, the Netherlands

2 Alterra, Wageningen UR, Wageningen, the Netherlands

The presented parameters for redundancy, uniqueness, separation capability and coverage of variability space provide useful tools for the validation of a datamodel. The Developer as part of the Determinator system implements these parameters in an ordered manner, as exempli‐ fied in Table 5. The development and performance of the datamodel for reaching a diagno‐ sis of the treatment of veal calves with hormones in the framework of Determinator reveals that a specific model can be developed and applied successfully in a generic framework.

Reliability and Evaluation of Identification Models Exemplified by a Histological Diagnosis Model

, M. Uiterwijk2

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[2] Uiterwijk, M., van Raamsdonk, L. W. D., & Janssen, S. J. C. (2012). Determinator- a generic DSS for hazard identification of species or other physical subjects. *In: R. Sep‐ pelt, A.A. Voinov, S. Lange, D. Bankamp (eds.), Managing resources of a limited planet, sixth international congress of the International Environmental Modelling and Software So‐*

[3] Hagedorn, G., Rambold, G., & Martellos, S. (2010). Types of identification keys. *In: P.L. Nimis and R. VignesLebbe, Proceedings of Bioidentify.eu: "Tools for identifying biodi‐*

[4] Yost, R., Attanandana, T., Pierce Colfer, C. J., & Itoga, S. (2011). Decision Support Systems in agriculture: some successes and a bright future. *In: C.S. Jao (ed.), Efficient decision support systems: practice and challenges from current to future*, 291-330, Intech,

[5] Groot, M. J., Ossenkoppele, J. S., Bakker, R., Pfaffl, M. W., Meyer, H. H., & Nielen, M. W. (2007). Reference histology of veal calf genital and endocrine tissues- an update for screening on hormonal growth promoters. *J. Vet. Med. A Physiol Pathol Clin. Med.*,

*versity: progress and problems", Edizioni Università di Trieste*, 59-64.

and M. J. Groot1

http://dx.doi.org/10.5772/51362

65

Whereas equations (1) and (2) apply.

The resulting multidimensional spaces for a number of features ranging from 2 to 8, the number of targets accommodated and the resulting coverage are shown in Table 6. If more than one state of a feature can identify a target a larger coverage can be expected. This is the case in the here presented datamodel for the diagnosis of hormone treatment, since the probability to correctly classify all situations of hormone treatment was maximised. This is illustrated in Table 3. The high coverage of approx. 85.8% of the current model can be ex‐ plained by the situation that the model was optimised to find all occasions of illegal use of hormones, i.e. the coverage of the classes "positive" was maximised.


**Table 6.** Relationship between the number of dimensions of a variability space (n), the possible number of combinations of feature states, and the coverage of the associated number of targets under the assumption of only one state per feature identifying a target (equation (13)).

The development of a specific model for reaching a histological diagnosis in a general plat‐ form provides several constraints, such as the lack of automatically calculating the number of deviating features (feature 13) from the number of individually selected features of group III. The advantage of the current procedure is the strict framework which forces to analyse the information structure in detail, and generic tools are available for testing and evaluation.
