key: cord-0707732-9xc84q3x
authors: Şimşek, Hakan; Yangın, Elifnaz
title: An alternative approach to determination of Covid-19 personal risk index by using fuzzy logic
date: 2022-01-27
journal: Health Technol (Berl)
DOI: 10.1007/s12553-021-00624-9
sha: c49de6ba525d4fd0a9ba64d988efa034ae24ad28
doc_id: 707732
cord_uid: 9xc84q3x

COVID-19 disease is an outbreak that seriously affected the whole world, occurred in December 2019, and thus was declared a global epidemic by WHO (World Health Organization). To reduce the impact of the epidemic on humans, it is important to detect the symptoms of the disease in a timely and accurate manner. Recently, several new variants of COVID-19 have been identified in the United Kingdom (UK), South Africa, Brazil and India, and preliminary findings have been suggested that these mutations increase the transmissibility of the virus. Therefore, the aim of this study is to construct a support system based on fuzzy logic for experts to help detect of COVID-19 infection risk in a timely and accurate manner and to get a numerical output on symptoms of the virus from every person. The decision support system consists of three different sub and one main Mamdani type fuzzy inference systems (FIS). Subsystems are Common- Serious symptoms (First), Rare Symptoms (Second) and Personal Information (Third). The first FIS has five inputs, fever-time, cough-time, fatigue-time, shortness of breath and chest pain/dysfunction; the second FIS has four inputs, Loss of Taste/Smell, Body Aches, Conjuctivitis, and Nausea/Vomiting/Diarrhea; and the third FIS has three inputs, Age, Smoke, and Comorbidities. Then, we obtain personal risk index of individual by combining the outputs of these subsystems in a final FIS. The results can be used by health professionals and epidemiologists to make inferences about public health. Numerical output can also be useful for self-control of an individual.

The severity of COVID-19 symptoms can range from very mild to severe. Some people may have only a few symptoms, and some people may have no symptoms at all, called asymptomatic. Some people may experience worsened symptoms, such as worsened shortness of breath and pneumonia. Because some of the symptoms of flu and COVID-19 are similar, it may be hard to tell the difference between them based on verbal, ambiguous and intuitive responses. On the other hand, older people are at higher risk of serious illness from COVID-19, and the risk increases with age. People with existing medical conditions may have a higher risk of serious illness. In [13] , the symptoms of 46,248 COVID-19 infected patients were examined. Chronic diseases accompanying infected patients were frequently associated with 17% hypertension, 8% diabetes, 5% cardiovascular diseases and 2% respiratory diseases. In [14] , it was found that of 76.993 patients infected with COVID-19, 16.37% had hypertension, 12.11% had cardiovascular disease, 7.63% had a history of smoking, and 7.87% had a history of diabetes. Asymptomatic or mildly symptomatic individuals are not aware of their contagion, causing them not to seek healthcare professional support and an increase in the number of infected people. At the same time, rapid detection, isolation, and contact tracing of community COVID-19 cases are essential measures to limit the community spread of COVID-19, [15] .

In the medical field, many of the concepts are fuzzy, making them difficult to model and objectify. Moreover, medical diagnosis is a complex process since the associated symptoms can be complex and the vague, and indirect-unknown relationships of the symptoms with the final output is very difficult to recognize and work with, [16] . Today, medical diagnosis processes are carried out with the help of computer-related technologies based on human reasoning, which is increasing day by day. These systems are mostly based on the principles of artificial intelligence and are designed not only to make a diagnosis based on symptoms but also to prescribe treatments based on it. Fuzzy modelling is deemed to be an appropriate technique for modelling the uncertainty in the medical domain, [17] . Thus, fuzzy approach is the most suitable technique for modelling and supporting the medical diagnostic decision. On the other hand, the outputs of this approach will help both to gain awareness and to be able to separate information by synthesizing and to choose the best / right among the options. Consequently, alternative studies on smart systems that provide rapid results regarding COVID-19 symptoms are very important to help detect in time whether a person has been infected or not with the virus.

Some of the researches based on the relationship between the fuzzy approach and medical field can be seen as follows. In [18] , design and development of a fuzzy rule-based expert system to identify the current stage of chronic kidney disease is proposed. The development of a medical diagnostic system using fuzzy logic is covered in [19] in order to enhance the accuracy and precision of medical diagnosis. In [20] , a new Hybrid Diagnose Strategy (HDS) that consists of two classifiers; fuzzy inference engine and Deep Neural Network (DNN) is introduced for COVID-19. In the study [21] , an intelligent fuzzy inference system for the primary diagnosis of COVID-19 is proposed, which infers the likelihood level of COVID-19 infection based on the symptoms. an Adaptive Neuro-Fuzzy Inference System (ANFIS) is proposed in [22] as a key rule for automatic COVID-19 detection from chest X-ray images based on the characteristics derived by texture analysis. In another similar study [23] , a fuzzy rule-based inference system is presented to support medical diagnoses, to minimize health costs and to maximize health resources based on real data selected by medical groups in the health market. In [24] , an intelligent medical diagnostic system to diagnose renal cancer is developed by using fuzzy and neuro-fuzzy techniques. A fuzzy model for a bone disease to have the right diagnosis answer is proposed in [25] . Based on the references of 173 articles from 124 journals, the development trend and application potential of fuzzy expert system in the medical field over the past two decades are reviewed in [26] . In [27] , fuzzy inference systems to improve the quality of the day-by-day clinical care of type-2 diabetic patients of Anti-Diabetes Centre (CAD) of the Local Health Authority ASL Naples 1 are presented. Govindan et al. [28] developed a decision support system based on physicians' knowledge and fuzzy inference system (FIS) in order to help with the demand management in the healthcare supply chain and to break down the COVID-19 propagation. Mangla et al. [29] cover three important types of factors, risk factors, clinical factors, and miscellaneous factors, that influence the mortality rate of COVID-19 under the Mamdani-based fuzzy expert system. In [30] , a fuzzy expert system, a clinical decision support system, is developed for diagnosis and prediction of chronic kidney disease.

There are many studies and researches on various issues related to COVID-19 in fuzzy environment. Al-Qaness et al. [31] presents a forecasting model to estimate the number of confirmed cases of COVID-19 in the upcoming ten days based on the previously confirmed cases recorded in China by using ANFIS. By using fuzzy logic, Boucenna et al. [32] dealt with the analysis of the spread of COVİD-19 and the people likely to be affected. Chowdhury et al. [33] worked on the assessment of the effective role of various environmental conditions in the spread of COVID-19 with the help of the fuzzy inference system. Fu and Liang [34] analyzed household medical products using fuzzy logic for the COVID-19 anti-epidemic normalization. Gemmar [35] compared alternative and advanced model approaches with models proposed in literature in order to estimate the state of health and to predict patient mortality risk. Painuli et al. [36] tried to propose a fuzzy rule based system to give predictions related to whether one is suffering from COVID-19 or not. Shaban et al. [37] introduced a new Hybrid Diagnose Strategy (HDS) relying on fuzzy logic and deep neural network to detect COVID-19 patients. Chowdhury et al. [38] used the Adaptive Neuro-Fuzzy Inference System (ANFIS) and the long short-term memory (LSTM) to predict the newly infected cases of COVID-19 in Bangladesh. Castillo and Melin [39] offer a hybrid intelligent approach for forecasting COVID-19 time series combining fractal theory and fuzzy logic. Ardabili et al. [40] described a comparative analysis of MLP and ANFIS models to predict the COVID-19 outbreak. Sharma et al. [41] proposed a mediative fuzzy correlation mathematical technique providing a relation between the increments of COVID-19 positive patients in terms of the incremental transition with respect to time.

The aim of this article is to construct more practical and useable Mamdani-type fuzzy inference intelligent technique for experts to help detect of COVID-19 infection risk and to get a numerical output on symptoms of the virus from every person coming testing for COVID-19. The paper is organized as follows. In Section 2, the structure of fuzzy logic inference system is explained. The proposed method is presented in Section 3. Finally, discussion and conclusion are given in Section 4.

Fuzzy Logic provides artificial intelligence methods that resemble human reasoning for handling the various type uncertainties. Fuzzy Inference Systems produce an output by processing incomplete, ambiguous fuzzy inputs of a problem that can be defined by linguistic parameters. Fuzzy inference system consists of a fuzzification interface which transforms the crisp inputs into degrees of match with linguistic values; a rule base containing a number of fuzzy IF-THEN rules; a database defining the membership functions of the fuzzy sets used in the fuzzy rules; a decision-making unit performing the inference operations on the rules; and finally a defuzzification interface which transforms the fuzzy results of the inference into a crisp output (Fig. 1) . More information about this concept can be found in the literature, [42] [43] [44] [45] .

A fuzzy set à in a universe of discourse X is defined by a membership function such that it associates a real number giving a membership degree of each element x in the range [0, 1] . Fuzzy numbers are special fuzzy sets satisfying the following conditions (Fig. 2) ;

for all ∈ (0, 1] and x 1 , x 2 ∈ X , then à is a convex fuzzy set.),

1} ≠ ∅ , then à is normalized.), • It's membership function is piecewise continuous, • It is defined in the real number.

There are different classes of fuzzy numbers suh as Triangular, Trapezoidal, Gaussian, S-shaped, G-bell, Z-shaped, Sigmoidal fuzzy numbers, which appear in real-world problems. Fuzzy numbers are used in fuzzification interface of an inference system; namely, inputs are described by fuzzy numbers in the system.

A fuzzy rule base consist of a set of fuzzy IF-THEN rules, which are the main theme of the FIS. All other components such as membership functions are used to implement these rules in a reasonable, realistic and efficient manner. A fuzzy IF-THEN rule generally assumes the form where, Ã 1 , Ã 2 and B are linguistic variables of the FIS defined by fuzzy numbers on input and output universes, respectively. Logical operators AND, OR are known as the fuzzy intersection or conjuction (AND), and fuzzy union or disjunction (OR), respectively and defined as follows:

After determining the rule base, we apply the process by which the fuzzy sets that represent the outputs of each rule are combined into a single fuzzy number (set), which is known as aggregation of rules. Aggregation could be done by different operators, such as Max, Sum or Probor. The Max operator is generally preferred when compensation between input variables is desirable. The Max operator is given by:

The last step is the defuzzification interface such that output fuzzy set obtained after the aggregation step is changed to a crisp number. Defuzzification techniques used in Mamdani based fuzzy inference system are generally Center of area or centroid (CoA), Bisector of area, Small of maxima (SoM), Mean of maxima (MoM), and Largest of maxima (LoM). The Mean of maxima (Fig. 3) gives a defuzzified crisp value x * as the element with the highest membership values such that the mean value of the maxima is taken when there are more than one element having maximum membership values.

All these mathematial operations explained above can be done using the MATLAB Fuzzy Logic Toolbox. In this paper, Mamdani type fuzzy inference system is used for the personal risk index of COVID-19, which is the most common in practice and in the literature. We apply max-min inference method for composition and minimum operator for implication. Gaussian Fuzzy numbers whose membership function is defined in (1) are used generally for the inputs and the aggregation is determined as the Max operator. As the defuzzifiation method, the Mean of maxima is taken for the proposed Mamdani type Fuzzy Inference Systems discussed below.

∶ If 1 isà 1 AND (OR) 2 isà 2 , THEN isB,

where c and are the parameters of the Gaussian fuzzy number, which determine the membership ship center (the peak of the curve) and the membership function width, respectively.

COVID-19 is a contagious pandemic with an estimated reproduction number of 2.87, [46] , and thus is spreading over multiple countries or continents. In order to know whether or not you have the virus, two types of tests are applied: molecular tests (also called PCR tests, viral RNA tests, nucleic acid tests) and antigen testing, [47, 48] . The decision on whether to test for COVID-19 can be made based on the individual applicant's verbal expression of whether he/she has symptoms of the virus and how severe the symptoms are. Therefore, an inference system bringing out appropriate human reasoning capabilities can be developed in order to support the decision of whether to test or not, in order to further clarify the virus symptoms of the person, in order to make them numerical data and to obtain comparative results, and in order to better manage growing demand and make quick decisions. In this paper, we construct such a system based on the FIS, expert knowledge, related literature and last information from WHO for describing a personal risk index of COVID-19 pandemic.

The recommended system consists of three sub-fuzzy inference systems and a final system ( ( Fig. 3 The mean of maxima defuzzification Moreover, the First FIS has three sub-fuzzy inference systems, which are the Fever-Time, Cough-Time and Fatigue-Time Mamdani-type inference systems. The first system provides an inference on common and serious symptoms, the second gives an output on rare symptoms, and finally the third fuzzy inference system is built in which personal The inputs in the first and second fuzzy inference systems were created by evaluating the symptoms announced by WHO, [3] . The inputs in the third fuzzy inference system were determined as age, chronic disease and smoking-alcohol habits that affect the risk of COVID-19 disease transmission. The COVID-19 personal risk index is obtained by transforming the outputs of these sub-fuzzy inference systems into a single output in a final fuzzy inference system.

In this FIS, we aim to get a numerical output for the common and serious symptoms of COVID-19. There are five inputs in the system; fever-time, cough-time, fatigue-time, shortness of breath and chest pain/dysfunction. The structure of the First FIS is shown in Fig. 5 . Three membership functions are used for explaning linguistic variables of inputs-outputs. Paek et al. [49] formed a review study for better understanding of fatigue and also gave significant detection methods and systematic approaches to figure out the impacts and causes of fatigue such that it is explained that Karolinska sleepiness scale (KSS), a nine-point scale, has a different measure of fatigue for each point and is the most frequently used drowsiness and fatigue scale. In other study, [50] , subjective and objective tests to evaluate the sense of smell, whih are commonly used in patients, were discussed like Visual Analogue Scale (VAS, 0-10 scale).

On the other hand, Fontana and Widdicombe [51] investigated how to measure the cough intensity or frequency and concluded that there are many methods for measuring and assessing cough such that the choice of them, apart from practical and financial considerations, must depend on the question being asked. Therefore, we aim to collect data on the severity of pain by scoring the severity of pain in the range of 0-10, which is also called a Likert scale. The Table 1 gives the information about the linguistic variables and fuzzy membership functions of Common and Serious Symptoms. 17 rules, several of which are given in Table 2 For the fever, cough and fatigue, which are common symptoms, three separate corresponding sub-fuzzy inference systems were formed to include in the system how long a person Table 3 . Table 4 has some rules about fever-time sub-fuzzy inference system. There are 8 rules for this sub-fuzzy inference system and the defuzzification method is the mean of maximum. The surface view of the rule base of the fever-time is given in Fig. 8 . Similar sub-FIS can be formed for the cough-time and fatigue-time, which surface views of the rule base for them are shown in Figs. 9 and 10. As a result, we get the outputs for common symptoms: fever, cough and fatigue, by using the sub-fuzzy inference systems and then we reach the risk index for the common and serious symptoms by using the first FIS. 

In this FIS, we aim to get a numerical output for the rare symptoms of COVID-19. There are four inputs in the system; Loss of Taste/Smell, Body Aches, Conjuctivitis, and Nausea/Vomiting/Diarrhea. The Table 6 explains the linguistic variables of inputs-output and the corresponding membership functions of the fuzzy inference system. In total, 32 rules are formed for the rare symptoms, several of which are given in Table 5 . The mean of maximum (MOM) is chosen as the defuzzification method. Figs. 11 and 12 show the impact of the symptoms on risk evaluation in 3D form as a rule surface performed in MATLAB.

In this FIS, we aim to get a numerical output for the personal information affecting the risk value of COVID-19. There are three inputs in the system; Age, Smoke, and Comorbidities. The Table 7 explains the linguistic variables of inputs-output and the corresponding membership functions of the fuzzy inference system. In total, 13 rules are formed for the personal information, several of which are given in Table 8 . The mean of maximum (MOM) is chosen as the defuzzification method. Figure 13 illustrates the impact of the symptoms on risk evaluation in 3D form as a rule surface performed in MATLAB.

Now, we can obtain the COVID-19 personal risk value by combining the fuzzy inference systems explained above. We present a final fuzzy inference system whose inputs are the outputs obtained by the first, second and third fuzzy inference systems. There are 16 rules and the mean of maximum (MOM) is chosen as the defuzzification method. The Table 9 , Figs. 14, 15, and 16 give the structure of the final system like the previous ones. Then, we can discuss the performance of the proposed approach. The following questions can be asked to the person to determine the input values of the FISs in the proposed system. According to the input values obtained by the responses for these questions, we compute the outputs of the fuzzy inference systems and using the final inference system explained above, we get the final output that is the personal risk value for COVID-19 disease. The input values can be obtained by a person coming for testing, practically. Or, input information for helping the medical diagnosis can also be obtained by the patient's practical and quick response to the questions given above under the control of a physician in a digital environment. For example, the answers given by two people to the above questions may be as in Table 10 .

The outputs for the input values of the Table 10 are presented in the Table 11 . The results show that Person-1 should take the COVID-19 test and must quarantine herself/himself. Person-2 should be careful and don't need to take the test. As a result, the proposed system has a reasonable potential and usefulness and its performance is justified.

In this paper, a fuzzy logic inference system was proposed to get a numerical output on COVID-19 symptoms disease so that more specific data is obtained before testing for COVID-19. The data aimed to be obtained with the fuzzy inference system created in the study helps the segregation of individuals at risk of COVID-19 from the society. The data are obtained by evaluating the severity of symptoms mapped on Likert scale 0-10. The proposed approach has three sub-fuzzy inference system; namely, Common and Serious Symptoms, Rare Symptoms and Personal Information. In the last step, the data obtained from the sub-fuzzy inference systems are used for determinig the personal risk index by means of the final inference system.

The resulting numerical data can be used by health professionals and epidemiologists to make inferences about public health. Numerical output can also be useful in terms of self-control of an individual to help him/her make decisions about seeking appropriate medical care such as Centers for Disease Control and Preventation, 2021, [52] ; Columbia University 2021, [53] ; and John Hopkins Medicine 2021, [54] . In other words, the proposed approach can [55] proposed a deep learning framework for Covid-19 detection by using chest X-ray images by first enhancing the image by using fuzzy logic which improvises the pixel intensity and suppresses background noise. In addition, Al-ali et al. [22] implemented an (Adaptive Neuro-Fuzzy Inference System) ANFIS-Net based binary classification process for automatically detecting COVID-19 infection from chest X-ray images. Classifier outputs of these systems can also be used as an input-4 of our approach in the final system by refering to an X-ray image value in order to obtain more advanced and improved result for experts and physicians. This satisfies an evaluation that considers the symptoms and X-ray images together. On the other hand, in the studies [56] and [57] , a novel automatic cough frequency monitoring system combining a triaxial accelerator and a stretchable strain sensor AND the development of a machine learning-based analysis framework to connect multimodal wearable sensor data are presented for the cough and fatigue respectively. Based on these researches, we can obtain more measured and improved responses for the severity of fatigue and cough especially in the first FIS. Similary, smell-odor sensors and other techonological devices corresponding to the other inputs can be used to obtain more real and numerical results and to improve the efficiency of the proposed fuzzy approach.

Govindan et al. [28] proposed a similar decision support system based on physicians' knowledge and fuzzy inference system by considering the time as an input value for the most common symptoms. Also, users were divided into subgroups with respect to age and chronic disease. In our system, we consider other symptoms of COVID-19 and the severity of the symptoms in addition to the time of most common symptoms in the first FIS. Shatnawi et al. [21] represent a single FIS including the symptoms of COVID-19 that have two membership functions and this system does not include age, chronic disease and smoke. Also, constructing and updating a rule base are more difficult for such system having more inputs. However, the proposed system represents a practical and updatable fuzzy approach. On the other hand, we can also consider other important preventive, inhibiting factors and concepts affecting the spread of COVID-19 like immune response, mask use, social distance, nanoparticles, environmental factors and so on. Then, we can construct a final protection index system from COVID-19 pandemic using these factors and following similar structures. We can see some of the researches investigating such factors in [29, [58] [59] [60] . Abstract mathematical and statistical approaches, which can be seen some studies in [61, 62] , are another important ways for fighting COVID-19, as well.

In this paper, three membership functions have been considered for input variables where it is possible to promote the accuracy of the proposed system by increasing the number of membership functions. Another limitation is that some of the answers given by users to the questions mentioned in the Section 3.4 may not be absolutely correct.

What is already known on the topic? • Reliable and comparable information on the symptoms of COVID-19 virus is important. • Since linguistic concepts and variables are handled by physicians in deciding the diagnosis and prognosis, the medical area has a great compatibility with fuzzy logic technology and fuzzy logic is used in the medical decision-making process. What this study added to our knowledge? • A decision support system in fuzzy environment is being developed. This system consists of three sub fuzzy inference systems, Common-Serious symptoms, Rare Symptoms and Personal Information, and one main system combining the subsystems. • COVID-19 personal risk index of an individual is obtained by running the proposed inference system. • Results obtained from each subsystem and main system can assist healthcare professionals in a more detailed assesment of symptoms. Funding No funding was received to assist with the preparation of this manuscript.

Ethical approval Ethical approval or formal consent is not required for this manuscript.

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