### An Application of Fuzzy Pearson Correlation Methods in Animal Sciences

Derviş Topuz, İsmail Keskin

#### Abstract

How to evaluate an appropriate correlation to find the fuzzy relationship between variables is an important topic in the lactation milk yield and reproduction characteristics measurement. Especially when the data illustrate uncertain, inconsistent and incomplete type, fuzzy statistical technique has some theoric features that help resolving unclear thinking in human logic and the source of uncertainties in the natural structure of the data. Traditionally, we use Pearson’s Correlation Coefficient to measure the correlation between data with real value. However, when the data are composed of fuzzy numbers, it is not feasible to use such a traditional approach to determine the fuzzy correlation coefficient. This study proposes the calculation of fuzzy correlation with triangular of fuzzy data. Using Matlab application, fuzzy Pearson correlation coefficients and their membership degrees which belong to Holstein Friesian cows for the relationship between lactation milk yield, the age of the animal at lactation, number of days milked, service period and first calving age were calculated (-0.0056; 0.95), (0.1419; 0.98), (-0.272;1.0) and (-0.2543; 0.90) respectively. The membership degrees of the calculated fuzzy Pearson coefficient values are more reliable and a consistent coefficient since it determines the size of the relationship between the sets, which belong to variables.

As a result of the study, the fuzzy Pearson correlation coefficient analysis may be preferred to calculate the degree of uncertainty and membership degrees between variables that should be used in studies to increase lactation milk yield.

#### Keywords

Holstein Friesian cows; Lactation Milk Yield; Reproductive Properties; Fuzzy logic; Fuzzy Pearson correlation coefficient

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DOI: https://doi.org/10.15316/SJAFS.2021.256

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