Introduction. Maintaining cattle population on the farms and private households is an important objective set forward before the Russian agro-industrial complex. Pasture treatment, stall disinfections and other measures are carried out to combat infections, however noncontagious diseases may not manifest any signs until they reach a severe stage. One of such pathologies is rumen acidosis in cows, a widespread disease that causes significant damage to agricultural sector. Rumen acidosis is quite difficult to diagnose at once, even for an experienced veterinarian. The problem of early diagnosis of acidosis has been investigated in a number of studies [1–4], which offered recommendations on improving this process.

Acidosis is characterized by increased acidity (pH) of rumen contents, which occurs due to metabolic disorders caused by low amount or absence of solid feed in the animal diet. Accurate and early diagnosis is essential for successful treatment of any disease. Rumen acidosis in cows at its early stages can have the similar picture of the disease as atony and hypotonia of the forestomachs, and during prophylaxis or treatment, it can sometimes be mistaken for alkalosis. In case of belated diagnosis of acidosis or diagnosis at the severe-stage, the following consequences as shown in Figure 1 can occur.

The large scale of the disease and the risk of late or incorrect diagnosis (due to the similarity of symptoms with other pathologies) make the problem of improving the rumen acidosis diagnostic process highly relevant. Since the uncertainty of the parameters plays a significant role in this problem, its solution using advance methods of addressing and formalizing uncertainties, i.e., intelligent system methods, appears to be the most efficient approach. Today, practices of using such systems in veterinary medicine are already known. For example, work [2] presents the mathematical foundations of fuzzy set theory, and, using the Sugeno method, provides solution of the problem in Python. For mass diagnostics and for educational purposes, the authors recommend to use the tests in the “Eidos-X++” intelligent system without programming. Works [3][4] describe the cases of artificial intelligence finding a number of errors made by veterinarians. However, the lack of advanced methods for assessing the development of pathology based on mathematical apparatus prevents the efficient use of modern intelligent systems in Russia.

Taking into account the above, the aim of our study (consisting of two parts) is to create an intelligent system for diagnosing rumen acidosis in cows based on fuzzy logics. In the first part, we plan to formalize the tasks for diagnosing acidosis. For this purpose, it is required to:

1) Justify the set of necessary diagnostic parameters;

2) Complete a substantive formulation and formalization of the problem of fuzzy inference for assessing rumen acidosis pathology;

3) Develop the structure of the hierarchical-type intelligent system;

4) Formalize intermediate variables within the fuzzy model of the intelligent diagnostic system.

Materials and methods. The study was conducted at the Ural State Agrarian University (Ekaterinburg) and the Northern Trans-Urals State Agricultural University (Tyumen) from 2022 to 2025. The list of diagnostic parameters required for formalization of the tasks included: pH values of rumen contents, milk fat content, pulse rate, and respiratory rate (based on the data obtained from the specialized reference books and scientific publications). The study excluded cows: 1) with a history of contagious diseases due to possible complications and weakened immune system; 2) preparing for calving (approximately 30-40 days in advance); 3) recently calved (approximately 30 days since) due to hormone profile adjustment and natural restoration of pH balance.

This minimal list of diagnostic parameters is sufficient for an accurate diagnosis of rumen acidosis provided the correlation with other diseases is absent. Especially difficult can be the combinations of several parameters exceeding reference values, imparting uncertainty to the problem parameters. To correctly solve the problem in the given settings, a method for formalizing uncertainties—fuzzy set theory—was used. A hierarchical structure of the intelligent system makes it strictly logical and transparent for analysis. Scilab open-source software (Scilab Consortium, France) with embedded text editor Scinotes were used to develop the intelligent system software.

Results

1. Justification of the set of diagnostic parameters. A veterinarian can make a preliminary diagnosis of rumen acidosis by observing the cow’s behaviour and finding out her feeding ration. Rumen acidosis is characterized by:

– pH of rumen contents below 6 (normal 6–6.9);

– pH of blood below the normal value of 7.35;

– lactic acid levels 3–4 times higher than normal (9–13 mg/dL);

– pulse rate rise to 120–140 bpm (normal 80-100 bpm); pulse rate increases with increasing acidity;

– respiratory rate increase to 50–60 breaths per minute and reaches a maximum of 70 bpm (normal 18–28 bpm);

– cow consumption of less than 15–20 kg of roughage and root vegetables, on average;

– milk protein and fat content drop below 4%;

– weight loss (the average adult cow weighs 300–450 kg);

– salivation above 90–180 liters, which indicates pH imbalance in rumen contents;

– pH of urine below the normal range of 7.6–8.5±0.2;

– decrease in the number of chewing movements to 30–40 (the average number of chewing movements after regurgitation in a lactating cow is 55, with a maximum of 60).

The pH of rumen contents plays a vital role in cow’s life. In the publication [5] it was revealed that systematic rumen lavage in lactating cows and addition of a microbial premix, sodium bicarbonate and minerals to the basic diet increased average daily milk yield by 31.3%. The publication [6] established a positive statistically significant correlation between temperature of rumen contents and rectal temperature, suggesting that measuring rectal temperature could help to prevent the development of subacute ruminal acidosis in cows.

The authors of publication [7] found that acidosis was coupled with a significant increase of sodium ion concentration in erythrocytes and decrease of their concentration in blood plasma, alongside, they observed the potassium ion level decrease in erythrocytes and increase in plasma. That proved the negative effect of acidosis on energy metabolism, impairing ATP synthesis. It was also suggested [8] that an optimal way for accurate measurement of the pH of rumen contents was obtaining a sample by rumenocentesis, since the concentration of hydrogen ions in samples obtained by gastric probing could be to some extent effected by saliva, which leads to changes in pH balance towards alkalinity within 0.14 units (2.3%).

The authors of publication [9] found that in cows with rumen acidosis, clinical and morphological parameters were generally stable, with the exception of respiratory movements, which were up to 7% higher than normal during the disease. A study of the digestive physiology of cows [10] revealed that a decrease in urine pH could be a diagnostic parameter indicating the signs of chronic rumen acidosis, which, in turn, was confirmed by the results of milk production in experimental animals.

Today, there are examples of successful application of remote monitoring systems in veterinary medicine [11–12], including remote monitoring of the pH of rumen contents [13]. This study found that pH of rumen contents and temperature in cows fluctuated during the day, suggesting that pH fluctuations of rumen contents were related to feed intake, whereas the body temperature fluctuations reflected the amount of water consumed by an animals.

In the foreign sources the problem of rumen acidosis in cows was also studied taking into account the inherent conditions of its development [14–15] and possible consequences [16–18]. For more accurate diagnosis of rumen acidosis, in the veterinary medicine abroad, there were used the same methods as in the domestic veterinary medicine: rumenocentesis and gastric probing [19] or identification of biomarkers [20]. Worth mentioning is the research of the authors who paid attention on the manifold elevation of lactic acid produced from starch [21–22], which in turn contributed to the development of rumen acidosis.

In the context of present study, it’s worth noting some uncertainties in the interpretation of values in different sources. For example, the normal pH of rumen contents in cows is 6, however, some veterinary experts ascertain 7 as the limit, and anything above that is considered alkalosis, when the alkalinity is exceeded. Other experts in this field believe that although the pH below 6 indicates elevated rumen acidity, it is premature to immediately diagnose the animal with rumen acidosis if, for example, pH equals to 5.5 for a short period of time. By assessing all acid-base balance values in rumen of cows of all breeds, the normal pH can be concluded to be within the range of 6–7, and anything below or above should be considered abnormal. A value below the normal range indicates acidosis, whereas a value above the normal range indicates alkalosis.

With a proper diet, a young, healthy cow produces high-fat milk, upon cow aging, the fat content of milk gradually decreases. At the first signs of rumen acidosis in cows, milk fat content drops abruptly to 3–4%, and sometimes even below 2.5%; i.e. 2.0% could be considered the minimum. This is due to the high content of lactic acid, which reduces the fat content in milk.

In addition to these parameters, veterinarians sometimes take into account the blood pH as a control parameter. This is only necessary if the rumen pH is normal but milk fat content is significantly reduced. The levels of the pH of rumen contents and blood pH are interrelated, as rumen contents can be released into the animal’s bloodstream. Values of blood pH in the range of 7.1–7.3 indicate the sign of rumen acidosis. However, these values are too close to those of healthy animals, therefore this parameter is not the primary or sufficient one for diagnostics. Therefore, fat content in milk, which is typically measured at least twice a day during milking, should be considered a priority parameter instead.

Other important parameters for identifying signs of rumen acidosis in cows include physiological indicators such as respiratory rate and pulse rate. The normal pulse rate in a normal state, i.e. without active movement of an animal, is between 80 to 100 beats per minute, whereas in acidosis it can increase to 120 beats per minute, and reach 130–140 beats per minute. Respiration rate will also increase as animal’s condition worsens. Without physical exertion, a cow can normally make 15 to 30 breathes; with complications caused by acidosis, this parameter can reach 50–60 or more (up to 70) breathes per minute.

Thus, four parameters can be identified that clearly correlate with rumen acidosis: pH of rumen contents, fat content in milk, pulse rate and respiratory rate. The remaining parameters are highly probable to be the complications caused by other diseases. Therefore, to develop an intelligent diagnostic system, these four parameters will be used as input variables for the fuzzy system.

2. Completing the substantive formulation and formalization of the problem of fuzzy inference for assessing rumen acidosis pathology.

Substantive formulation of the problem. In fuzzy modeling, the purpose of problem formulation is to represent the empirical data about an object in the form of definite heuristic rules: the task of determining object’s condition (in this case, rumen acidosis in a cow) is verbally described based on diagnostic parameters. In the frame of substantive formulation of the problem, the most specific features of the veterinary diagnosis are defined.

Information about the signs of rumen acidosis in cows, the effect of various factors on the course of the disease and correlation of the disease with diagnostic parameters is provided in sufficient detail in veterinary reference books1,2,3,4,5,6,7 и and scientific articles [7–10]. However, as we’ve already mentioned, there’s some uncertainty in the interpretation of some values. Fuzzy modeling enables integration of scattered experimental and expert data and obtaining a more comprehensive picture of animal’s condition according to the combination of parameters, which serve the basis for an accurate diagnosis.

Formalization of the problem of fuzzy inference for assessing rumen acidosis pathology. Introducing fuzziness into solution of a problem (fuzzification) implies formalization of the input and output parameters in the form of linguistic variables8. It is worth reminding, the following parameters were specified as input variables: pH of rumen contents, fat content in milk, respiratory rate and pulse rate. The output parameter is the degree of animal pathology (disease severity).

To assess the pH of rumen contents in veterinary medicine, the terms “Acidity” and “Alkalinity” are used. In fuzzy set theory, the similar notations have been used: “Highest acidity” – up to pH 4; “Moderate acidity” – from pH 4 to pH 6; “Neutral value” from pH 6 to pH 7; “Moderate alkalinity” from pH 7 to pH 9; “Highest alkalinity” over pH 9 to pH 9.5.

For the second variable, “Fat content in milk, F”, in fuzzy modeling terminology, the following values have been assigned: “Minimum” from 2.5 to 3%; “Low” from 3 to 4%; “Average” from 4 to 6%; “High” from 6 to 7%; “Maximum” from 7%.

The third variable, “Pulse rate, PR”, have been assigned the following values: “Minimum” up to 60 beats/min; “Low” from 60 to 80 beats/min; “Medium” from 80 to 100 beats/min; “High” from 100 to 120 beats/min; “Maximum” from 120 to 130 beats/min.

The fourth variable “Respiratory rate, RR” have been assigned the following values: “Minimum” from 5 to 10 movements/min; “Low” from 10 to 15 movements/min (signs of alkalosis); “Average” from 15 to 30 movements/min (normal); “High” from 30 to 50 movements/min; “Maximum” from 50 to 70 movements/min.

The "Degree of Acidosis Pathology, DAP" parameter has been introduced for the output variable. For convenience, this parameter has been defined on a scale from 0 to 5 and in the non dimensional form. The variable takes the following values: “Minimum” up to 1; “Low” from 1 to 2; “Moderate” from 2 to 3; “High” from 3 to 4; “Maximum” from 4 to 5. The severity of pathology is gradated as follows:

1 – Permanent (the animal is healthy);

2 – Subacid (forestomach hypotension or the first pronounced signs of rumen acidosis);

3 – Chronic (clearly pronounced signs of acidosis with moderate manifestations);

4 – Subacute (severe manifestations of acidosis signs);

5 – Acute (critically severe acidosis).

In the terminology of fuzzy set theory, the linguistic variables have been assigned the term sets with the following values and notations:

“Rumen pH index, pH” {HighestAc, ModAc, Neutral, ModAlk, HighestAlk};

“Fat content in milk, F” {Min, L, Av, H, Мах};

“Pulse Rate, PR” {Min, L, Av, H, Мах};

“Respiratory Rate, RR” {Min, L, Av, H, Мах};

“Degree of Acidosis Pathology, DAP” {Min, L, Av, H, Мах}.

Fig. 3 (a–d) shows the membership functions of the input variables in the form of triangular fuzzy numbers and trapezoidal intervals, and Fig. 3e shows the fuzzy function of the output linguistic variable “Degree of Acidosis Pathology, DAP”. We adopt triangular or trapezoidal fuzzy numbers for the values of term sets of linguistic variables, and z-shaped and s-shaped functions at the boundaries of the definition domain (Fig. 3).

3. Developing the structure of the hierarchical-type intelligent system. We shall define the system structure as a hierarchical fuzzy system9. First, fuzzy inference (FI) from two parameters is performed: the pH of rumen contents and the fat content in milk values. The resulting function of this fuzzy inference from the first two variables is designated as the factor “pH–Fat content, Y12”.

Then, the input variables “Respiratory rate, RR” and “Pulse rate, PR” are fed to the fuzzy inference engine (FIE). The resulting function of this fuzzy inference is designated as the factor “Respiration–Pulse, Y34”.

By fuzzy inference from the values of variables’ factors Y12 and Y34, the value of the “Degree of acidosis pathology, DAP” is calculated. This model structure is shown graphically in Figure 4.

4. Formalization of intermediate variables in the fuzzy model of the intelligent system. Since the model structure contains intermediate variables, they also need to be fuzzified. For convenience, the linguistic variables have been defined in the range from 0 to 5 and divided into five intervals for five fuzzy membership functions. The variables are shown graphically in Figure 5.

The completed formalization of all necessary tasks allows us to develop the corresponding intelligent system model and implement it in software code.

Discussion and Conclusion. In the context of high-tech veterinary care development, implementation of the intelligent systems is currently considered to be a priority direction. In the first part of the study, we have justified the list of parameters required for diagnosing rumen acidosis in cows, proposed the structure of an intelligent system, and formalized the models of all the variables to solve the problem using fuzzy set theory and its practical applications—fuzzy logics and fuzzy modeling. In the second part of the study, we plan to create an intelligent system for diagnosing rumen acidosis pathology in cows by means of computer technologies, based on the formalized data described here.

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