Bipolar Dissimilarity and Similarity Correlations of Numbers
2. Materials and Methods
2.1. Correlation Functions (Association Measures)
2.2. Similarity and Dissimilarity Functions (Fuzzy Relations)
2.3. Constructing Correlation Functions from Similarity and Dissimilarity Functions
- Correlation between x and y is positive if the similarity between x and y is greater than the dissimilarity between them. In the opposite case, the correlation between x and y is negative.
- Correlation between x and y is positive if they are “similar” and negative if they are “different”.
3.1. Constructing Pearson’s Linear Correlation Coefficient Using Bipolar Dissimilarity Function
3.2. Non-Bipolar Similarity, Dissimilarity, and Correlation Functions for Real Numbers
3.3. Bipolar Similarity, Dissimilarity, and Correlation Functions for Real Numbers
4. Bipolar Dissimilarity and Similarity Correlation in Risk Assessment
- Measured values (see Figure 6) are stored in a database.
- Histogram is created based on the stored data as illustrated in Figure 7.
- Fuzzy set is fitted to the histogram, (see in ). This set represents the normal reactions of the patient under the same conditions. Medical recommendations for the specific patient should be available in the database as well, or the age- and sex-specific values from the literature can be used instead. Figure 8. shows the fuzzy sets generated based on the measurements and medical recommendations for the above case study.
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Conflicts of Interest
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Batyrshin, I.Z.; Tóth-Laufer, E. Bipolar Dissimilarity and Similarity Correlations of Numbers. Mathematics 2022, 10, 797. https://doi.org/10.3390/math10050797
Batyrshin IZ, Tóth-Laufer E. Bipolar Dissimilarity and Similarity Correlations of Numbers. Mathematics. 2022; 10(5):797. https://doi.org/10.3390/math10050797Chicago/Turabian Style
Batyrshin, Ildar Z., and Edit Tóth-Laufer. 2022. "Bipolar Dissimilarity and Similarity Correlations of Numbers" Mathematics 10, no. 5: 797. https://doi.org/10.3390/math10050797