br universe br Display the measured value of greatness
2 Display the measured value of greatness (X value) in its unit of measurement.
3 Determine the favorable evidence degree μ by applying a selected mathematical function considering the conditions:
1IfXvalue > Maxvalue
μ = selected mathematical function IfXvalue ∈ [Min value , Maxvalue ] IfXvalue < Minvalue
Fig. 2. Representation of typical geometric interpretations and the signals flux for PAL2v application.
4 Determine the unfavorable evidence degree λ with the complement of the favorable evidence degree: λ = 1 − μ
The second algorithm is named paraconsistent analysis Digitonin (PAN). The PAN receives two inputs of information signals represented by evidence degrees (μ, λ) and using Eqs. (1), (2) and (4) presents as a final result a single value of the resulting evidence degree (μER). The PAN is described below in its simplified form :
1 Present two values of favorable evidence degrees, μ1 and μ2 (ob-tained by the extractor of degree of evidence).
2 Calculate the unfavorable evidence degree using the complement of μ2: λ1 = 1 − μ2
4 Calculate the degree of contradiction using Eq. (2):
5 Determine the distance: d =
If not, calculate the real certainty degree considering the fol-
9 Calculate the resultant real evidence degree using Eq. (4).
10 Present the results in the output:
The third is the algorithm extractor of contradiction eﬀects (ParaExtrctr). The ParaExtrctr receives a set of signals and, regardless of any other external information, has the function of performing a paraconsistent analysis of their values by subtracting the eﬀects caused by the contradiction . With this algorithm, the signals of the input set are presented in the output as a single resulting degree of evidence, which is the representative value of the group. The ParaExtrctr [5,26,27] is described below:
1 Present n values of evidence degrees that comprise the set of signals in this study.
2 Select the largest value among the evidence degrees of the set of signals.
a Consider the largest value among the evidence degrees of the set of signals as the favorable evidence degree: μmaxA = μsel
b Select the smallest value among the evidence degrees of the set of signals.
a Transform the smallest value among the evidence degrees of the set of signals in the unfavorable evidence degree: 1–μminA = λsel b Perform the paraconsistent analysis among the selected values: μR1 = μsel ◊ λsel */, where ◊ is a paraconsistent action of the PAN Vibrational Spectroscopy 103 (2019) 102929
5 Increase the obtained value μR1 in the set of signals, excluding the previously selected two values, μmaxA and μminA. Gμest = (μA, μB, μC, …, μn, μR1)−(μmaxA, μminA) 6 Return to item 2 until the set of signals has only one element re-sulting from the analyses.
2. Material and methods
In this work, a set of paraconsistent algorithms (SPA-PAL2v) was used to analyze Raman spectroscopy data for application in skin cancer diagnosis; thus, an arrangement of interlinked algorithms was extracted from the fundamentals of PAL2v. Due to the disposition of the values in the Raman database, the SPA-PAL2v was implemented as a computa-tional matrix in the MATLAB simulator (software version R2008a, The Mathworks Inc., MA, USA).
2.1. Raman spectra database: data acquisition
In this work, a database composed of values obtained by Raman spectroscopy analysis of skin tissue samples was used . This re-search has been approved by the Human Research Ethics Committee at Camilo Castelo Branco University (protocol no. 2815-3035/09). The procedure was as follows: Soon after the surgery, samples were im-mediately analyzed ex vivo to collect Raman spectrum and then fixed with 10% formaldehyde and subjected to a histopathological evalua-tion. All data were obtained using a dispersive Raman spectrometer (Dimension P-1 model, Lambda Solutions, Inc., MA, USA, 830 nm, 350 mW) with a spectral resolution of 2 cm−1 in the 400 to 1800 cm−1 wavelength range. The Raman system was composed of a Raman probe with a removable aluminum tip, which maintained the 10 mm focal length between the end of the probe and the tissue fragment, and the probe was disinfected. The laser power was adjusted to 250 mW at the probe output to avoid sample damage. The exposure time for spectra collection was adjusted to 20 s [14,19].
A preprocessing routine was applied oﬄine in the spectra, whereby the signals were subjected to background fluorescence removal by ad-justing and subtracting a polynomial of order [14,19]. The cosmic ray peaks were manually removed, and the spectra were normalized by the area under the curve (1-norm) . In the database, the Raman spectra obtained were correctly stored with the abscissa axis information (Raman shifts in the range of 400–1800 cm−1) and ordinates informa-tion (normalized intensities of Raman peaks in the specified range).