# br If Xvalue Minvalue br Through the linear variation

If Xvalue < Minvalue

Through the linear variation equation, the normalized evidence degree in an interest interval (or discourse universe) can be obtained.

3.3. Acquisition of paraconsistent patterns for each histopathological group and arrangement

At this stage of data preparation, the histopathological group under study (NO and [BCC + SCC] and AK) goes through the algorithm ex-tractor of eﬀects of contradiction (Section 1.5), whose details for other applications can be seen in [5].

In this process, the degree of real evidence that characterizes the paraconsistent pattern value (PPμE) for each measure of the Raman wavelength is obtained. In this data treatment, in addition to the actual degree of real evidence, the maximum and minimum values of each measurement of the Raman wavelength are also stored in the database table. This way, the necessary measures are established by the SPA-PAL2v for comparisons, which will improve the future study of the samples and their recognition to promote a diagnosis and thus char-acterize the paraconsistent pattern values for NO (PPμENO), BCC + SCC (PPμE(BCC + SCC)), and AK (PPμEAK).

3.4. Algorithms to randomly select and extract the sample evidence degree

Through this algorithm, a sample is randomly selected from the Raman database.

The extractor degree of evidence algorithm [5] is applied to the selected sample (Avalue).

The normalization process of this step is based on the Maxvalue and Minvalue established in the study of the pattern of each type (PPμE) to create the interest interval through the following equation:

1
If Avalue > Maxvalue

Avalue − Minvalue
If Avalue ∈ [Min value , Maxvalue]

μA =
Max value − Minvalue

If Avalue < Minvalue

The algorithm works by randomly selecting and generating a sample and compares it Coelenterazine with the range of interest in the studied histopatho-logical group. By applying the above equation, the sample’s evidence degree values for the NO group (μA_NO), the BCC + SCC group (μA_BCC + SCC), and the AK group (μA_AK) are obtained.

3.5. Algorithm to detect the number of occurrences of similarities

To initiate this algorithm, the SPA-PAL2v initially groups the ma-trices μA with the histopathological group pattern (PPμE) and then makes line-by-line comparisons with μA to detect similarities.
The verification is performed considering two conditions: first, if the sample is within the maximum and minimum Raman intensity limits, therefore it is within the interest interval defined in the previous
Vibrational Spectroscopy 103 (2019) 102929

algorithm; second, if the sample’s evidence degree of the Raman in-tensity (μA) is greater than 0.5 (established cutoﬀ value), O(i,j) = 1; else, O(i,j) = 0; this condition is described through the following logical sentence:

else

end

This conditional is within a repeating structure, traversing all the lines and columns of the μA matrix of each representative of the his-topathological group under analysis. Thus, a positive occurrence (O (i,

j) = 1) indicates that the sample line belongs to the histopathological group under study.

3.6. Algorithm to extract the evidence degree of frequency

The extractor of evidence degree of frequency algorithm uses the fundamentals of the concepts of PAL2v and statistics to extract the degree of frequency (μFr). This algorithm is based directly on the oc-currence matrices (O (i, j)) created by the number of occurrences de-tection algorithm described above. The procedures are briefly described as follows:

a) Return the sum of each column of the matrix O (i, j).

b) Calculate the total sum of occurrences.

c) Determine the frequency calculation for each type of histopatholo-gical study group.

d) Identify the calculation of the frequency that represents the highest value.

e) Compare each calculated frequency with the highest value found.

In the final execution of the algorithm, the SPA-PAL2v presents the highest value of μFr related to the degree of relevance of the sample under analysis. The higher value of μFr indicates the diagnosis; thus, the SPA-PAL2v supports skin cancer diagnosis. The information provided is the type of sample, the value of the occurrence, and the degree of fre-quency evidence, as well as the scatter plot of similarity occurrence points. This information forms the basis for a more detailed analysis by the health professional.

4. Results

In the following sections, the results of the Raman patterns are first presented, and then the results related to the validation and diagnostic tests are presented.

4.1. Paraconsistent patterns of histopathological groups created from the Raman database