On-Line Monitoring of Milk Electrical Conductivity by Fuzzy Logic Technology to Characterise Health Status in Dairy Goats

Figures & data

Figure 1. Example of milk yield as a possible linguistic variable with its three terms membership functions: low, moderate, and high. The degrees of membership for each fuzzy set of a specific milk yield (i.e. the intercepts with the horizontal grey line corresponding to the milk yield of 1.95 kg) are also highlighted.

Table 1. Membership functions for the traits considered in the study.

Trait	Function	Shape	Point of characterisation
Maximum EC	Low	Trapezoidal	(4;1) (9;1) (12;0)
Middle	Triangular	(9;0) (12;1) (15;0)
High	Trapezoidal	(12;0) (15;1) (20;1)
Deviation in EC	Low	Trapezoidal	(0;1) (0.04;1) (0.07;0)
Middle	Triangular	(0.04;0) (0.07;1) (0.1;0)
High	Triangular	(0.07;0) (0.1;1) (0.13;0)
Very high	Trapezoidal	(0.1;0) (0.13;1) (1;1)
Deviation in MY	Very low	Trapezoidal	(0;1) (0.09;1) (0.13;0)
Low	Triangular	(0.09;1) (0.13;0) (0.17;0)
Middle	Triangular	(0.13;0) (0.17;1) (0.21;0)
High	Triangular	(0.17;0) (0.21;1) (0.25;0)
Very high	Trapezoidal	(0.21;0) (0.25;1) (1;1)

EC, electrical conductivity; M Y, milk yield.

Table 2. Rules of the fuzzy inference step about the traits considered in the study. As shown when deviation in milk yield changes from middle to high or very high, values in the table increase in order to highlight an higher probability of disease. On the contrary, values decrease when the deviation in milk yield becomes low or very low. Similar trends can be observed considering the other traits reported in the table.

Fuzzy inference rules	Deviation in MY
	Very low Maximum EC			Low Maximum EC			Middle Maximum EC			High Maximum EC			Very high Maximum EC
	Low	Middle	High	Low	Middle	High	Low	Middle	High	Low	Middle	High	Low	Middle	High
Deviation in EC
Low	None	None	None	None	None	None	None	None	None	None	None	Low	None	Low	High
Middle	None	None	None	None	None	None	None	None	Low	None	Low	High	Low	High	Very high
High	None	None	None	None	None	Low	None	Low	High	Low	High	Very high	High	Very high	Very high
Very high	None	None	Low	None	Low	Middle	Low	Middle	Very high	Middle	Very high	Very high	Very high	Very high	Very high

EC, electrical conductivity; MY, milk yield.

Table 3. Distribution of mammary glands by health status in different samples groups.

HS	Total		C2		C3
	n	%	n	%	n	%
Healthy	1158	41.3	-	-	-	-
Not healthy (from goats unilaterally)	304	10.8	275	9.8	29	1.1
Not healthy (from goats bilaterally)	1342	47.9	1299	46.3	43	1.5
Total	2804	100	1574	56.1	72	2.6

HS, health status; C2, milk samples with bacteriological analyses positive for intramammary infection; C3, milk samples with somatic cell count>1,000,000 cells/mL.

Table 4. Distribution of pathogenic microorganisms found in infected mammary glands.

Isolated bacterial strains	n	%
Staphylococcus aureus	10	0.6
CNS	1418	90.1
Escherichia coli	17	1.1
Streptococcus spp.	88	5.6
Lactose-negative bacteria	22	1.4
Pseudomonas	19	1.2
Total	1574	100

CNS, coagulase-negative Staphylococcus.

Table 5. Overall means and standard errors of somatic cell count of milk samples according to goats’ health status and lactation stages.

DIM	SCC, log
	Total goats	Healthy goats	Non-healthy goats
0 to 180	5.42±0.01	5.33^A±0.02	5.45^B±0.02
0 to 60	5.26^a±0.02	5.22±0.03	5.29±0.03
61 to 120	5.40^b±0.02	5.33±0.03	5.46±0.03
121 to 180	5.51^c±0.03	5.42±0.06	5.59±0.02

DIM, days in milking; SCC, somatic cell count.

^ABMeans in the same row with different uppercase letters differ significantly (P<0.05)

^a-cmeans in the same column with different lowercase letters differ significantly (P<0.001).

Table 6. Overall means and standard errors of electrical conductivity of milk samples according to goats’ health status and lactation stages.

DIM	EC, mS/cm
	Total goats	Healthy goats	Non-healthy goats
0 to 180	13.25±0.05	13.10^A±0.08	13.31^B±0.06
0 to 60	11.14^a±0.07	11.11±0.10	11.17±0.11
61 to 120	14.08^b±0.08	13.82±0.12	14.34±0.11
121 to 180	14.40^c±0.10	14.34±0.20	14.43±0.07

DIM, days in milking; EC, electrical conductivity.

^ABMeans in the same row with different uppercase letters differ significantly (P<0.05)

^a-cmeans in the same column with different lowercase letters differ significantly (P<0.001).

Table 7. Overall means and standard errors of milk yield according to goats’ health status and lactation stages.

DIM	MY, kg/milking
	Total goats	Healthy goats	Non-healthy goats
0 to 180	1.09±0.01	1.09±0.02	1.08±0.01
0 to 60	1.07±0.02	1.08±0.02	1.06±0.03
61 to 120	1.07±0.02	1.09±0.03	1.06±0.03
121 to 180	1.12±0.03	1.10±0.05	1.13±0.02

DIM, days in milking; MY, milk yield.

Table 8. Accuracy reached by the fuzzy logic model in terms of sensitivity and specificity at different cut-off levels.

Cut-off levels	Sensitivity, %	Specificity, %
0.90	62	86
0.80	73	79
0.70	81	69
0.60	85	66
0.50	89	64
0.40	93	58
0.30	95	52
0.20	98	41
0.10	100	23