Prediction System for Diagnosis and Detection of Coronavirus Disease-2019 (COVID-19): A Fuzzy-Soft Expert System

1  Introduction

In early December 2019, a new virus named “2019 novel coronavirus (2019-nCoV)” appeared in Wuhan, China. A novel epidemic disease (named “coronavirus disease-2019 (COVID-19)”) was announced by the World Health Organization (WHO) on February 11, 2020 [1]. Also, the WHO described that COVID-19 is of origin. It is transmitted between animals and humans [1,2]. Moreover, WHO showed that COVID-19 is the source of the disease as a severe acute respiratory syndrome in the Middle East [1]. The latest statistics showed that the number of cases of the disease reached 3,152,556 cases, 964,840 of which were recovered and 218,491 deaths, while the number of patients currently infected is 1,969,225, of whom 1,912,345 are in stable condition and 56,880 are in critical condition [3].

Newly, research works on COVID-19 are very active and developing rapidly: The relationship between the severe acute respiratory syndrome coronavirus 2 (for short, SARS-CoV-2) and COVID-19 was discussed [4]. Characteristics of human coronaviruses (COVID-19 infection) were presented [5]. COVID-19 was discussed as belonging to other coronaviruses and it was from the platoon Bedside [6,7]. Further, it was published that there are diseases that increase the weakening of the body’s immunity and the speed of the infection with COVID-19 (for example, diabetes, hypertension cases, and cancers) [8]. The relationship between COVID-19 and rheumatoid disease was shown and studied [9]. The effect of COVID-19 on several diseases, such as dialysis renal histopathological and hemodialysis patients was studied [10,11]. The relationship between epilepsy and fever COVID-19 and neurological convulsions in the human body were studied [12]. COVID-19 is an unusual virus because it reduces the percentage of white cells in the human body, especially of the type lymphopenia. As for the rapid spread of the disease, there was a study that shows that infection with COVID-19 is possible not only through respiratory droplets, but also possible through urine or stools, and the fecal-oral route [13,14]. On the other side, about COVID-19 and its relationship to climate, there was a study examining four climatic factors related to high and low infections: Temperature, Humidity, Wind Speed, and UV rays [15]. On the other hand, a final review was undergone for the COVID-19 prediction models that identified and evaluated twenty-seven studies, that statistically described thirty-one models [16].

Recently, COVID-19 has become one of the most dangerous viruses spread in the world and is an inspiration of the first death. To reduce the prevalence of COVID-19, we must find some appropriate solutions to keep people safe, which is to inform people about the dangers of COVID-19. Therefore, early detection of this virus (COVID-19) should be done through the medical expert systems or the design of a matching medical diagnostic system for expert physicians. There are several expert medical systems developed in medical diagnosis to detect the seriousness of the diseases (see [17-38]).

The present paper is arranged as follows: The basic notions of this paper are introduced in Section 2. The structure of the fuzzy-soft expert system is explained in Section 3. Experimental results are discussed in Section 4. A comparison between the present system and the fuzzy expert system is presented in Section 5. Finally, the conclusion is given in Section 6.

2  Preliminaries

2.1 Fuzzy Set, Soft Set, and Fuzzy Soft Set

Definition 2.1 (cf. [39–42]) For given set X, let 2X be the set of all subsets of X, [0,1]X (resp., [0,1]XI=([0,1]X)I) be the set of all mappings from X (resp., I) to [0, 1] (resp., [0,1]X). Then each element A∈[0,1]X will be called a fuzzy set on X, and each element A∈2X×I=(2X)I (resp., A∈[0,1]XI) will be called a soft set (resp., a fuzzy soft set) on X indexed by I.

The trapezoidal fuzzy numbers [x^,x^,y^⟩,⟨x^,y^,y^]∈[0,1]R~ (called fuzzy sets, R~ is the set of all real numbers), where x^≤y^ and also ⟨x^,y^,z^⟩∈[0,1]R~ (called fuzzy set), where x^≤y^≤z^ are used repeatedly in the present paper, are defined by

[x^,x^,y^⟩(u)={1,u≤x^,y^−uy^−x^,x^<u<y^,0,u≥y^;⟨x^,y^,y^](u)={0,u≤x^,u−x^y^−x^,x^<u<y^,1,u≥y^;⟨x^,y^,z^⟩(u)={u−x^y^−x^,x^≤u<y^,z^−uz^−y^,y^≤u<z^,0,otherwise.(1)

Example 2.2 Suppose that X={u1,u2,u3} be a set of three types of houses and I={i1,i2} a set of two parameters, where i1 is ‘price’, and i3 is ‘size’. This situation can be described by the following soft set:

A={{u1,u3}i1,{u2}i2}.

It can also be described more precisely by the following fuzzy soft set:

A={{1u1,0u2,1u3}i1,{0.1u1,0u2,1u3}i2}.

Definition 2.3 (cf. [41,42]) For two fuzzy soft sets A∈[0,1]XI and B∈[0,1]XJ, define the fuzzy soft set A∨¯B∈([0,1]X)I×J (called “OR ” operation) by (A∨¯B)(i,j)=A(i)∨B(j)  (∀(i,j)∈I×J) (also can be written (A∨¯B)(i,j)=Ai∨Bj).

Example 2.4 (Continued from Example 2.2). Consider {A,B}⊆[0,1]XI, defined by

A={{0.5u1,0.4u2,0.3u3}i1,{0.7u1,0.1u2,0.9u3}i2}, B={{0.2u1,0.8u2,0.7u3}i1,{0.4u1,0.5u2,0.1u3}i2}.

then

A∨¯B={{0.5u1,0.8u2,0.7u3}(i1,i1),{0.5u1,0.5u2,0.3u3}(i1,i2){0.7u1,0.8u2,0.9u3}(i2,i1),{0.7u1,0.5u2,0.9u3}(i2,i2)}.

2.2 Five Symptoms of COVID-19

COVID-19 signs and symptoms may appear between 2 to 14 days after exposure to the virus. The data for our work in this paper is obtained from (Department of Respiratory, Nanjing Chest Hospital, China). We used the five important symptoms [43] (Shortness of Breath (ShB), Sore Throat (STh), Cough, Fever, Age). The symptoms of COVID-19 can range from very mild to severe. Some people may never have symptoms. Older people or those with medical conditions, such as diabetes, heart and lung disease, or a weakened immune system, may be more likely to develop severe disease. This is similar to other respiratory diseases, such as influenza. So, we have considered the five symptoms in designing our system.

3  Methodology of Proposed Fuzzy-Soft Expert System

The fuzzy-soft expert system gives diagnostic assistance related to COVID-19 where the final results of the sixty patients will be discussed by specialist doctors. The basic construction of our system has five steps illustrated in Fig. 1. As Fig. 1, these five steps are explained in detail as shown below.

Figure 1: Main construction of fuzzy-soft expert system

3.1 Classification of Data Set

We will explain the classification of data set according to membership functions as follows:

(1) ShB: have four membership functions (Low (L), Medium (M), High (H), Very High (VH)), where the range of L is less than 25, M is in between 23 to 49, H is in between 37 to 60, and VH is greater than 49. Trapezoidal represents ‘L’ and ‘ VH’, also triangular represents ‘M’ and ‘ H’.

(2) STh: have four membership functions (Low (L), Medium (M), High (H), Very High (VH)), where the range of L is less than 35, M is in between 35 to 60, H is in between 47 to 75, and VH is greater than 60. Trapezoidal represents ‘L’ and ‘VH’, also triangular represents ‘M’ and ‘H’.

(3) Cough: have four membership functions (Low (L), Medium (M), High (H), Very High (VH)), where the range of L is less than 14, M is in between 11 to 48, H is in between 33 to 65, and VH is greater than 59. Trapezoidal represents ‘L’ and ‘VH’, also triangular represents ‘M’ and ‘H’.

(4) Fever: have four membership functions (Low (L), Normal (N), Moderate (M), High (H)), where the range of L is less than 36.4, N is in between 36.5 to 37.5, M is in between 37.6 to 38.3, and H is greater than 38.4. Trapezoidal represents ‘L’ and ‘H’, also triangular represents ‘N’ and ‘M’.

(5) Age: have four membership functions (Young (Y), Mild (M), Old (O), Very Old (VO)) where the range of Y is less than 38, M is in between 33 to 45, O is in between 40 to 58, and VO is greater than 52. Trapezoidal represents ‘Y’ and ‘VO’, also triangular represents ‘M’ and ‘O’.

4  Experimental Results and Analysis

In the present work, we will give an exploratory study that includes sixty patients (i.e., forty males and twenty females) with symptoms similar to COVID-19 in (Department of Respiratory, Nanjing Chest Hospital, China), where forty males: p1,p3,p4,p6−p12,p14−p20,p23,p25,p30,p32−p37,p45−p50,p52−p59 and twenty females: p2,p5,p13,p21,p22,p24,p26−p29,p31,p38−p44,p51,p60. The data of sixty patients are illustrated in Table 1.

Next, we will get the membership functions of every patient (i.e., forty males and twenty females) are illustrated in Tables 2-5.

4.1 Convert of Data Set and Reduction of Data Set

(1) Assume that P=Pm∪Pf,  where Pm={p1,p3,p4,p6−p12,p14−p20,p23,p25,p30,p32−p37,p45−p50,p52−p59} represents the forty patients from males, Pf={p2,p5,p13,p21,p22,p24,p26−p29,p31,p38−p44,p51,p60} represents the twenty patients from females, and I^ be the set consisting of 20 parameters as {ShB(L),ShB(M),ShB(H),ShB(VH),STh(L),STh(M),STh(H),STh(VH),Cough(L),Cough(M), Cough(H), Cough(VH), Fever(L), Fever(N), Fever(M), Fever(H), Age(Y), Age(M), Age(O), Age(VO)}. Further, assume that A^,B^,C^,D^,E^⊆I^ (i.e., have five fuzzy soft sets: LA^, MB^, NC^, QD^, RE^), where A^={ShB(L),ShB(M),ShB(H),ShB(VH)}, B^={STh(L),STh(M),STh(H),STh(VH)}, C^={Cough(L),Cough(M),Cough(H),Cough(VH)}, D^={Fever(L),Fever(N),Fever(M),Fever(H)},E^= { Age(Y),Age(M),Age(O),Age(VO)}.

(2) Reduce the following parameters: {ShB(L), ShB(M), ShB(H), ShB(VH), STh(L), STh(M), STh(H), STh(VH), Cough(L), Cough(M), Cough(H), Cough(VH), Fever(L), Fever(N), Fever(M), Fever(H), Age(Y), Age(M), Age(O), Age(VO)}. to {ShB(M),ShB(H),ShB(VH),STh(M),STh(H),.STh(VH),Cough(M),Cough(H),Fever(M),Fever(H),Age(M),Age(O),Age(VO)} according to the normal soft parameter reduction of fuzzy soft sets [44]. Therefore, we get on the five new fuzzy soft sets: UF^, VG^, WH^, XJ^, and YK^, where

F^={ShB(M),ShB(H),ShB(VH)}, G^={STh(M),STh(H),STh(VH)}, H^={Cough(M),Cough(H)},J^={Fever(M),Fever(H)}, K^={Age(M),Age(O),Age(VO)}.

4.2 Prediction Method for COVID-19

Through Kong et al.’s method [45] (i.e., as prediction method of COVID-19), we can predict which patient (forty male and twenty female) will suffer from COVID-19 as follows:

The first step: Input the following five new fuzzy soft sets (i.e., UF^, VG^, WH^, XJ^,YK^).

The second step: Calculate the fuzzy soft set TP^, for example, if we take “UF^ OR VG^” (i.e., ZO^=UF^∨_VG^, O^=F^×G^) (see Table 6), then we get on 9-element set of the form ϑ^ij, where ϑ^ij=πi ∨_ τj, (∀ i=j=1,2,3) (i.e., ϑ^11=π1 ∨_ τ1,ϑ^12=π1 ∨_ τ2,ϑ^13=π1 ∨_ τ3,ϑ^21=π2 ∨_ τ1,ϑ^22=π2 ∨_ τ2,ϑ^23=π2 ∨_ τ3,ϑ^31=π3 ∨_ τ1,ϑ^32=π3 ∨_ τ2,ϑ^33=π3 ∨_ τ3)  (where O^={ϑ^11,ϑ^12,ϑ^13,ϑ^21,ϑ^22,ϑ^23,ϑ^31,ϑ^32,ϑ^33}). Similarly, we can get on fuzzy soft sets ZO^, WH^, XJ^, and YK^ (i.e., TP^=ZO^∨_WH^∨_XJ^∨_YK^, P^=O^×H^×J^×K^). Then we can get on the 108-element set, where P^=O^×H^×J^×K^={ζ1,ζ2,ζ3,⋯,ζ108}.

The third step: Compute si, (i=1,2,3,...,60). by Kong et al.’s algorithm [45] as follows: s1=−122.69, s2=124.81, s3=−28.5, s4=−19.8, s5=102.3, s6=100.7, s7=106.2, s8=−11.2, s9=111.8, s10=123.2, s11=123.8, s12=125.3, s13=−25, s14=132.4, s15=−15.7, s16=−24.8, s17=−13.5, s18=−22.5, s19=112.3, s20=110.2, s21=−16.7, s22=−14.9, s23=104.4, s24=125.8, s25=112.7, s26=−50.3, s27=115.3, s28=107.4, s29=109.3, s30=−31.2, s31=133.4, s32=−21.2, s33=101.4, s34=125.8, s35=−66.2, s36=123.7, s37=115.3, s38=113.2, s39=−15.4, s40=−30.4, s41=−45.3, s42=−61.2, s43=106.6, s44=123.9, s45=−70.3, s46=105.3, s47=−31.3, s48=−36.5, s49=120.8, s50=119.5, s51=−75.5, s52=−46.8, s53=135.9, s54=−44.6, s55=−20.2, s56=126.8, s57=130.5, s58=133.2, s59=129.7, and s60=127.2.

The fourth step: From the third step we can conclude that thirty four patients p2,p5−p7,p9−p12,p14,p19,p20,p23−p25,p27−p29,p31,p33,p34,p36−p38,p43,p44,p46,p49,p50,p53, and p56−p60 have high values of si. Therefore, these patients potentially suffer from COVID-19. All values of si  (i=1,2,3,..., 60) and its relationship to sixty patients (p1−p60) are shown in Fig. 2 and the diagnosis results are illustrated in Table 7.

Figure 2: The relationship between p1−p60 and si

5  Comparison Among the Fuzzy-Soft Expert System and the Fuzzy Expert System

5.1 Fuzzy Expert System

A fuzzy expert system is one of the known systems used for medical diagnosis. The main structure of the fuzzy expert system is illustrated in Fig. 3.

Figure 3: Main structure of the fuzzy expert system

The basic rules of COVID-19 data are inside the fuzzy expert system, though there are several insufficiencies in the above fuzzy expert system of COVID-19. Therefore,

(1) The fuzzy expert system depends on fuzzy rules (i.e., the input data of ShB have 4 membership functions (L, M, H, VH), the input data of STh have 4 membership functions (L, M, H, VH), the input data of Cough have 4 membership functions (L, M, H, VH), the input data of Fever have 4 membership functions (L, N, M, H), and the input data of Age have 4 membership functions (Y, M, O, VO)) which mean 4 × 4 × 4 × 4 × 4 = 1024 fuzzy rules; so the diagnosis results by a fuzzy expert system of COVID-19 according to several groups of fuzzy rules are contrary. For example,

(i) If the patient (p) has ShB (H) and STh (VH) and Cough (H) and Fever (H) and Age (O), then p have Coronavirus (COVID-19).

(ii) If the same patient (p) has ShB (M) and STh (M) and Cough (L) and Fever (N) and Age (Y), then p don’t have Coronavirus (COVID-19).

(2) The diagnosis results by a fuzzy expert system of COVID-19 are contrary to that of an expert physician.

If we apply a fuzzy expert system (according to 1024 fuzzy rules) by using the data from Table 1, then we can note that all the patients have Coronavirus (COVID-19).

According to the above discussion, our proposed system's diagnosis results (which is the same as the diagnosis results from expert physicians) are better than the diagnosis results from the fuzzy expert system. Therefore, our proposed system (which depends on the approach by Kong et al. [45] for the prediction of COVID-19) is evidence to present a remarkable improvement in the fuzzy expert system.

6  Conclusions

In this work, the fuzzy-soft expert system is better than the fuzzy expert system for the accuracy of diagnosis results. This method of our work is simple because it does not depend on programming software, as well as, unconventional medical analysis methods where the patient suffers from fatigue and the diagnosis appears after a long period of time. This proposed fuzzy-soft expert system will assist physicians and senior researchers who are interested in this emerging virus (COVID-19) in the rapid prediction of this virus diagnosis. Further, there is a study presented that some medical tests such as PCR to detect COVID-19 give inaccurate results [43,46]. In contrast, it is possible to use our system for accuracy and ease of implementation. In cooperation with the computer sciences department, the subsequent work will be the establishment of a program in hospitals, centers of diseases, and also at airports to limit the rapid spread of COVID-19 using this system.

Acknowledgement: The authors wish to express their appreciation to the reviewers for their helpful suggestions which greatly improved the presentation of this paper.

Funding Statement: The authors received no specific funding for this study.

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.

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