An Application of Fuzzy Pearson Correlation Methods in Animal Sciences

Derviş Topuz, İsmail Keskin


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.


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

Full Text:



Arnold SF (1990). Mathematical Statistics. New Jersey. Prentice-Hall.

Abdalla HA (2012). Possibilistic logistic regression: In fuzzy environment. Lap Lambert Academic Pub-lishing. Saarbrücken- Germany

Atanassov K (2012). On intuitionistic fuzzy sets theory. Studies İn Fuzziness and Soft Computing, Berlin- Germany.

Bede B (2013). Mathematics of fuzzy sets and fuzzy logic. Springer, Heidelberg New York Dordrecht London.

Buckley JJ (2006). Fuzzy probability and statistics. Studies İn Fuzziness and Soft Computing, Publ., No: 2, Springer, Berlin- Germany.

Chiang DA, Lin NP (1999). Corelation of fuzzy sets. Fuzzy Sets and Systems 102(2): 221-226.

Chiang DA, Lin NP (2000). Partial corelation of fuzzy sets. Fuzzy Sets and Systems 110(2): 209-215.

Chiang J.H, Yue S, Yin Z (2004). A new fuzzy cover approach to clustering. IEEE Transactions on Fuzzy Systems 12(2):199- 208.

Ding -An Chiang and Nancy P. Lin (1999). Correlation of fuzzy sets. Fuzzy Sets and Systems 102(2):221-226.

Xie MC, Wu B (2012). The relationship between high schools students time management and academic performance: an application of fuzzy correla-tion. Educational Policy Forum 15(1): 157–176.

Nguyen HT, Wakler EA (2000). First course in fuzzy logic. 2nd edition. Chapman & Hall/CRC. Boca Raton, FL, 1 January, NewYork, pp.359.

Lin NP, Chen JC, Chueh HE, Hao WH, Chang CI (2007). A fuzzy statistics based method for mining fuzzy correlation rules. WSEAS Transactions on Mathematic 11(6): 852-858.

Paksoy T, Yapıcı Pehlivan N, Özceylan E (2013). Bu-lanik küme teorisi. Nobel Akademik Yayıncılık, An-kara-Turkey. (in Turkish)

Ross TJ (2004). Fuzzy logic with engineering applica-tions, John Willey and Sons Inc, Fuzyy Sets, Wiley- New York.

Trillas E, Eciolaza L (2015). Fuzzy logic studies in fuzz-iness and soft computing. Springer. ISBN 978-3-319-14203-6.

Sakawa M (1993). Fuzzy sets and ınteractive multi-objective optimization. Plenum Pres, New York, 305 p.

Şentürk S, Aşan Z (2007). Correlation coefficient in fuzzy logic; an application in meterological events. Eskisehir Osmangazi University Journal Of Engi-neering And Architecture 20 (1):149-158.

Tanaka H (1997). Fuzzy data analysis by possibilistic linear models. Fuzzy Sets and Systems 24(3): 363-375.

Tanaka H, Guo P (1999). Possibilistic data analysis for operations research. Physica-Verlag Heidelberg, New York.

Tansu A (2012). Fuzzy linear regression: fuzzy regres-sion. Lambert Academic Publishing, Springer, Ber-lin- Germany.

Yang CC (2016). Correlation coefficient evaluation for the fuzzy interval data. Journal of Business Re-search 69(6): 2138–2144.

Yu C (1993). Corelation of fuzzy numbers. Fuzzy sets and Systems 55(3): 303-307.

Yongshen N, Cheung JY (2003). Correlation coefficient estimate for fuzzy data. In Intelligent Systems De-sign And Applications, Publ. No: 23, Berlin- Ger-many.

Yongshen N (2005). Fuzzy correlation and regression analysis. university of oklahoma graduate college; UMI number: 3163014.

Zimmermann HJ (1996). Fuzzy set theory and its ap-plications, springer science+business media. 3rd Edition, Kluwer-Nijhoff, Boston, New York, pp. 203-240.

Zadeh LA (1965). Fuzzy sets. Information and Control 8(3): 338-353.

Zadeh LA (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1(1): 3–28.



  • There are currently no refbacks.

Creative Commons Lisansı
Bu eser Creative Commons Alıntı-GayriTicari-Türetilemez 4.0 Uluslararası Lisansı ile lisanslanmıştır.