[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Elsevier - PMC COVID-19 Collection logoLink to Elsevier - PMC COVID-19 Collection
. 2021 Jun 2;109:107540. doi: 10.1016/j.asoc.2021.107540

Status evaluation of provinces affected by COVID-19: A qualitative assessment using fuzzy system

Bappaditya Ghosh 1, Animesh Biswas 1,
PMCID: PMC8169225  PMID: 34093096

Abstract

The outbreak of COVID-19 had already shown its harmful impact on mankind, especially on health sectors, global economy, education systems, cultures, politics, and other important fields. Like most of the affected countries in the globe, India is now facing serious crisis due to COVID-19 in the recent times. The evaluation of the present status of the provinces affected by COVID-19 is very much essential to the government authorities to impose preventive strategies in controlling the spread of COVID-19 and to take necessary measures. In this article, a computational methodology is developed to estimate the present status of states and provinces which are affected due to COVID-19 using a fuzzy inference system. The factors such as population density, number of COVID-19 tests, confirmed cases of COVID-19, recovery rate, and mortality rate are considered as the input parameters of the proposed methodology. Considering positive and negative factors of the input parameters, the rule base is developed using triangular fuzzy numbers to capture uncertainties associated with the model. The application potentiality is validated by evaluating Pearson’s correlation coefficient. A sensitivity analysis is also performed to observe the changes of final output by varying the tolerance ranges of the inputs. The results of the proposed method show that some of the provinces have very poor performance in controlling the spread of COVID-19 in India. So, the government needs to take serious attention to deal with the pandemic situation of COVID-19 in those provinces.

Keywords: COVID-19, Fuzzy inference system, Triangular fuzzy number, Qualitative assessment

Graphical abstract

graphic file with name fx1_lrg.jpg

1. Introduction

The word ‘Corona’ is one of the most widely used words in the recent time. The spread of novel coronavirus disease which is termed as COVID-19 was started from the city of Wuhan, China since late December of 2019 [1], [2], [3], [4], [5]. Fever, fatigue, cough, problem of breath, loss of taste and smell, etc., are the common symptoms of COVID-19 [6], [7]. The primary symptoms of COVID-19 and common flu are almost the same, which makes this virus more dangerous. When a person comes to know that he is COVID-19 positive, some other people had already been infected by him/her, unknowingly. As on the end of 2020, it was reported that among the active COVID-19 cases, majorities are found in mild symptoms, in India [8], [9], [10], [11], [12]. The time of exposure of symptoms takes around four to five days and may remain up to fourteen days [13], [14]. Corona virus mainly infects the lungs which may causes cardiovascular, gastrointestinal, nervous system, liver, kidney and ocular damages [15], [16], [17].

Most of the countries declared COVID-19 crisis as a national disaster. The outbreak of COVID-19 has already shown its harmful impact on mankind, especially on global economy, health sectors, cultures, education systems, politics, etc. The local and global marketing systems, manufacturing sectors are being hampered, significantly, which resulted a large unemployment of man powers all over the world. The major impact of this pandemic is being observed in health sectors. The inclusion of new COVID-19 hospitals has reduced the scopes of admission of the common people to the hospitals due to other major health issues. So, people are being deprived of their regular treatments from the hospitals due to the lack of doctors, nurses and other health workers. The increasing number of COVID-19 cases reduces the number of beds for common people in several hospitals. Many senior citizens were facing several mental health problems due to their loneliness during the lockdown periods. The art and cultural sectors including film and entertainment industries were temporarily closed due to the pandemic of COVID-19. All the major sport events have been either partially postponed or cancelled indefinitely. The pandemic also established its harmful impact on education system, globally. All the government, and private schools and educational institutes are either partially opened or indefinitely closed or running on virtual mode due to this pandemic which are adversely affecting the learning processes of the learners, worldwide. Lastly, the world political systems were also affected due to rescheduling of elections, death of politicians, lack of campaigning due to social distancing, etc.

Up to 30th November, 2020, around 6,36,09,507 people were found as COVID-19 positive, globally. Among them, around 4,39,83,871 people were recovered from this disease; whereas, around 14,74,186 people died due to this pandemic. USA was facing the worse effect of this pandemic at that time as it covered about 22% of total COVID-19 positive cases in the world. Around 1,66,904 new COVID-19 cases were found in USA; whereas, about 1,39,26,349 people were found as infected, of which around 82,24,314 people were recovered from this disease, and about 2,74,369 people died. According to the statistics of worldwide COVID-19 report on 30th November, 2020, India stood second in terms of number of COVID-19 positive cases. According to the data provided by the Department of Ministry of Health and Family Welfare (MoHFW), Government of India on 30th November, 2020, around 94,31,691 people were infected, of which about 88,47,600 people were recovered, and around 1,37,139 people lost their lives due this pandemic in India. These facts reflected very serious concern to the Government of India in controlling the spread of COVID-19. On 26th March, 2020, Nirmala Sitharaman, the finance minister of India, announced an incentive package of Inline graphic crore in the purpose of helping the people affected by the lockdown. Most of the states and union territories (UTs) of India are facing the worse effect of COVID-19. But, as per the available report of MoHFW as on 30th November, 2020, one UT, viz., Lakshadweep remained free from COVID-19; and consequently, the administration of Lakshadweep requested to the central government to provide the permission of reopening the schools; but, other states and UTs were still hesitating to reopen in that circumstances.

It is the fact that most of the news channels, survey institutes or some other organizations are estimating the fight of a country or state against COVID-19 on the basis of confirmed corona positive cases. But, as per the recent report of World Health Organization (WHO), majority of the active COVID-19 cases are found either asymptomatic or in mild symptoms. Therefore, a country or state having large number of population or performing huge number of COVID-19 tests would obviously situate in the group of large number of positive COVID-19 cases. Thus, some other factors such as population, population density, number of COVID-19 tests, recovery rate, mortality rate, etc., are needed to be considered in assessing the fight of a country or state against COVID-19.

In this article, an effort is made for estimating the strategies which were taken by the states and UTs in India to combat against COVID-19. In this purpose, a methodology is developed to evaluate the performance score to control the spread of COVID-19 corresponding to each state and UT in India. The data were collected from the official website of MoHFW, Government of India. But, such a highly populated country like India, it is very difficult to find exact figures of relevant inputs, such as population of a state or UT, number of tests, confirmed cases, recovery rate, mortality rate, etc. Therefore, some sorts of uncertainties or inexactness are unavoidably occurred in collecting data. Thus, the inclusion of fuzziness in the process of data collection becomes very much essential. The concept of fuzziness was successfully implemented by Togacar et al. [18] for detection of COVID-19. Later, Govindan et al. [19] used fuzzy inference system to develop a decision support system for demand management in healthcare supply chains concerning COVID-19 outbreaks. Mardani et al. [20] proposed an extended approach based on hesitant fuzzy sets to rank the key challenges of digital health interventions in controlling COVID-19 outbreak. Mahmoudi et al. [21] developed a fuzzy clustering method for comparing the infection rate of COVID-19 in countries with high risks. Behnood et al. [22] used adaptive neuro-fuzzy inference system in determining the infection rate of the COVID-19 in U.S. Later, Ly [23] developed a methodology using adaptive neuro-fuzzy inference system for forecasting COVID-19 cases in United Kingdom. A decision making approach was proposed by Singh and Avikal [24] for prioritizing the preventive activities against COVID-19. Further, Ocampo and Yamagishi [25] performed an intuitionistic fuzzy DEMATEL analysis to develop a model of lockdown relaxation protocols concerning the COVID-19 pandemic under the Government of Philippine. The concept of hesitant fuzzy sets was used by Ren et al. [26] in selecting the medicines for the patients having mild symptoms of COVID-19. Li et al. [27] developed a consensus model for managing non-cooperative behaviours of individuals in group decision making problems during the pandemic of COVID-19. Shaban et al. [28] introduced a strategy for detecting COVID-19 patients using fuzzy inference engine and deep neural network. Further, Aggarwal et al. [29] proposed an approach to compare the criterion in decision support system for COVID-19. Ghorui et al. [30] used hesitant fuzzy multi-criteria decision making method to identify the risk factors involved with the spread of COVID-19. To select drugs for the patients with mild symptoms of COVID-19, a decision-making framework using hesitant fuzzy sets was introduced by Mishra et al. [31]. Later, Ecer and Pamucar [32] proposed a technique under intuitionistic fuzzy environment for ranking the performance of insurance companies during COVID-19 pandemic. In the recent past, Sharma et al. [33] developed a meditative fuzzy logic model to provide the relation between the growths of COVID-19 cases with respect to time. But no method has been developed yet to evaluate the status of provinces affected by COVID-19 on the basis of the factors influencing the pandemic situation of COVID-19 using fuzzy systems. Getting informed about the recent status through this method, the concerned governing bodies might think about starting intra-state, and inter-state public transport services, reopening educational institutes, theatres, cinema halls, and museums, supplying medical equipment, declaring economic packages, awarding role model against COVID-19, building up strategies for equitable distribution of COVID-19 vaccines, and others.

In the proposed study, a Mamdani fuzzy inference system (MFIS) [34] is generated to evaluate the state wise performance score to combat against COVID-19 in India. The score value of all the input factors, such as population density, number of COVID-19 tests per million, number of confirmed case per million, recovery rate, mortality rate corresponding to all the states and UTs in India are fuzzified to capture the uncertainties associated with the collected data. Here, linear type fuzzy numbers are used to represent the membership functions (MFs) for input and output parameters of the proposed MFIS. To establish the application potentiality and validity of the proposed methodology, Pearson’s correlation coefficient [35] is evaluated between the final results and recovery rate of COVID-19. Later, a sensitivity analysis is also performed to observe the changes of final output by varying the tolerance ranges of the input values.

2. Data collection and analysis

In the proposed methodology, all the factors such as projected population in 2019, population density, number of COVID-19 tests, confirmed cases of COVID-19, recovery rate, mortality rate, etc., are considered as inputs for assessing the performance of all the states and UTs in India to combat against COVID-19. The projected population in 2019 and population density in 2011 of all the states and UTs were collected based on the census report of India which was conducted by National Commission on Population in 2011 [36]. The data regarding other inputs, such as number of tests, confirmed cases, recovered cases and deceased cases of COVID 19, as shown in Fig. 1, were collected from the official website of MoHFW, Government of India [37] and from another website [38]. But, it is very difficult to assign exact number against each of the above mentioned inputs for such a highly populated country like India due to continuous spread of COVID-19. Also, due to several issues like complexity in accounting exact figures of comorbidity, migratory cases, lack of communication between central and state governments, etc., a deviation up to 2% in the input values available on the website of MoHFW is inevitable. Therefore, the occurrence of uncertainties or inexactness associated with the data collection is unavoidable. Thus, all the crisp inputs for the proposed methodology are fuzzified into suitable fuzzy numbers to capture imprecision associated with the collected data. Since, the uncertainties or inexactness in collected data are found as a deviation of about 2% from the exact value, the triangular fuzzy numbers (TFNs) [39] are used for fuzzification of crisp input values.

Fig. 1.

Fig. 1

Cumulative graph of number of (a) tests (b) confirmed cases, recovered cases, and deceased cases of covid-19.

Thus, if a be a crisp input of the proposed method, then it is fuzzified into a TFN as

N=1la,a,(1+l)a;l>0

with the following membership function

Nx=x1laa1la,1laxa(1+l)ax(1+l)aa,ax(1+l)a0,otherwise (1)

3. Proposed methodology

MFIS [34] is a systematic formulation of pre-defined if-then rules which interprets human perceptions. In the proposed method, a MFIS is generated to evaluate the performance of all the states and UTs in India to prevent the pandemic situation of COVID-19. The proposed methodology is described as follows:

Step 1: Selection of input and output parameters

The proposed MFIS consists of five input parameters, viz., PopulationDensity(PD), NumberofTestsperMillion(NTM), Confi rmedCasesperMillion(CCM), RecoveryRate(RR), and MortalityRate(MR) in the respective universe of discourses, X1, X2, X3, X4, and X5 and one output parameter, viz.,

PerformanceScoreagainstCOV ID19(PSC) in the universe of discourse Z. To capture the uncertainties associated with the collected data, the MFs of both input and output variables are represented by TFNs.

Step 2: Development of rule base

The rule base of MFIS characterizes the relationship between the input and output parameters. The ith(i=1,2,,m) rule of a MFIS [39], [40] is of the following form:

Ri:Ifx1 is FiPDandx2 is FiNTM andx3 is FiCCM and x4 is FiRR and x5 is FiMR then z isFiPSC, (2)

where FiPD,FiNTM,FiCCM,FiRR,FiMR,andFiPSC are TFNs representing the qualitative descriptors of PD,NTM,CCM,RR,MR,and PSC, respectively, for the ith rule; xiXi(i=1,2,,m), and zZ.

Here, three linguistic terms are considered corresponding to each input and output parameter. Thus, the rule base contains a total number of 35=243 if-then fuzzy rules by combining all the possible outcomes corresponding to input–output parameters. It is to be noted here that in forming the rules, three input parameters, viz., PD, NTM, RR are considered as the positive factors and CCM, MR are considered as the negative factors for the evaluation of PSC.

Step 3: Evaluation of firing strength of each rule

The fuzzy intersection method is performed to evaluate the firing strength, δi, of the ith(i=1,2,,m) rule as follows:

δi=min{max{NPD(x1)FiPD(x1)},max{NNTM(x2)FiNTM(x2)},max{NCCM(x3)FiCCM(x3)},max{NRR(x4)FiRR(x4)},max{NMR(x5)FiMR(x5)}}=min{max{α[0,1]:α=min(NPD(x1),FiPD(x1)),x1X1},max{α[0,1]:α=min(NNTM(x2),FiNTM(x2)),x2X2},max{α[0,1]:α=min(NCCM(x3),FiCCM(x3)),x3X3},max{α[0,1]:α=min(NRR(x4),FiRR(x4)),x4X4},max{α[0,1]:α=min(NMR(x5),FiMR(x5)),x5X5}}, (3)

where NPD(x1),NNTM(x2),NCCM(x3),NRR(x4), andNMR(x5) are the membership grades of the respective fuzzy inputs, NPD,NNTM,NCCM,NRR,andNMR in the form of TFNs. FiPD(x1),FiNTM(x2),FiCCM(x3),FiRR(x4), andFiMR(x5) are the membership grades of the corresponding qualitative descriptors, FiPD,FiNTM,FiCCM,FiRR,andFiMR of PD,NTM,CCM,RR,andMR, respectively, for the ith(i=1,2,,m) rule.

Step 4: Derivation of fuzzy output of each rule

The fuzzy output, PSCi, for the ith(i=1,2,,m) rule is derived as follows:

PSCi(z)=δiFiPSCz=min{δi,FiPSCz}, (4)

where FiPSC(z) is the membership grade of the qualitative descriptor, FiPSC of the output variable, PSC and zZ.

Step 5: Aggregation of fuzzy outputs

The fuzzy output, AGPSC, derived from all the rules are aggregated by operating fuzzy union as

AGPSC(z)=i=1mPSCiz=maxPSC1z,PSC2z,,PSCmz,zZ. (5)

Step 6: Defuzzification of the aggregated output

The aggregated output is defuzzified by operating the centroid of area method which gives the final output, PSC, as follows:

PSC=k=1nAGPSCzk.zkk=1nAGPSC(zk), (6)

where zkZ, k=1,2,,n are n quantization of Z.

It is to be mentioned here that the higher value of PSC corresponding to a state or UT signifies the better performance of that state or UT to combat against the pandemic of COVID-19.

The proposed methodology is presented through a flowchart as presented in Fig. 2.

Fig. 2.

Fig. 2

Flowchart of the proposed methodology.

4. Performance score of the states and UTs in India to combat against the pandemic situation of COVID-19

In this section, the performance score of 28 states and 7 UTs in India are assessed by means of their efficiency to tackle the pandemic situation of COVID-19 based on the data available up to 30th November, 2020. As per the census report of India, conducted by National Commission on Population in 2011, and information provided by the Department of MoHFW, Government of India, available on the websites as on 30th November, 2020 [36], [37], the crisp value of PD, NTM, CCM, RR, and MR are, respectively, found as 368, 1,06,046, 7,076, 93.81, and 1.45 in India. In the proposed methodology, the MFs of all the linguistic hedges representing the input parameters are defined by keeping those values near the centre point of the middle linguistic term of the respective input parameters. The crisp values of those input variables corresponding to all the states and UTs in India are presented in Fig. 3(a–e).

Fig. 3.

Fig. 3

Fig. 3

Fig. 3

Crisp value of (a) PD (b) NTM (c) CCM (d) RR (e) MR corresponding to each state and UT in India.

4.1. Selection of membership functions for input variables

PD: According to the census report of India conducted in 2011 [36], the PD of the states and UTs, under consideration, is presented through Fig. 3(a). Following the report, it is observed that the UT of Delhi is recommended as the most densely populated region in India with population density of 11,320 persons per square Kilometre. Thus, the universe of discourse of PD is considered as the closed interval 0,12000 on which three linguistic hedges, viz., Low, Average, and High are defined. Since, the average population density in India is 368 persons per square Kilometre [36], the respective TFNs are formulated as 0,0,400, 0,400,800, and 400,12000,12000 to represent those linguistic hedges, and are shown in Fig. 4(a).

Fig. 4.

Fig. 4

MFs representing the linguistic hedges of (a) PD (b) NTM (c) CCM (d) RR (e) MR (f) PSC.

NTM:NTM signifies the number of tests performed per million numbers of people of a state or UT. It is the most vital process to detect the positive COVID-19 patients. According to the data provided by the Department of MoHFW, Government of India [37] on 30th November, 2020 and the census report of India in 2011 [36], NTM of the states and UTs is presented in Fig. 3(b). According to that report, it is found that Andaman and Nicobar Islands had performed maximum number of COVID-19 tests per million with score value of 3,25,917. Thus, the universe of discourse of NTM is considered as 0,335000 on which three linguistic hedges, viz., Low, Average, and High are defined. Since, the average value of NTM in India were found as 1,06,046, the respective TFNs, viz., 0,0,100000, 0,100000,200000, and 100000,335000,335000 are considered to represent those linguistic hedges which are shown in Fig. 4(b).

CCM:CCM of the provinces represents the number of positive COVID-19 cases found in those provinces. The data provided by the Department of MoHFW [37], which are presented in Fig. 3(c), shows that Goa stood top in the table of confirmed COVID-19 positive cases per million numbers of people with score value of 31,042; whereas, the average score value of the confirmed COVID-19 positive cases per million numbers of people in India is found as 7,076. Thus, the universe of discourse of CCM is taken as 0,35000 on which three linguistic hedges, viz., Low, Average, and High, as shown in Fig. 4(c), are defined with the respective representation of TFNs as 0,0,7000, 0,7000,14000, and 7000,35000,35000.

RR:RR signifies the percentage of positive COVID-19 patients who had been recovered from this disease. The average value of RR in India is 93.81%. According to Fig. 3(d), in Dadra and Nagar Haveli and Daman and Diu maximum recovery rate with score value 99.28% is observed. Thus the TFNs, viz., 0,0,90, 80,90,100, and 90,100,100 are considered to represent the linguistic hedges, viz., Low, Medium, and High, respectively, defined on the universe of discourse, 0,100, as shown in Fig. 4(d).

MR:MR reflects the percentage of positive COVID-19 patients who died due to this disease. The data related to the MR of each state and UT under consideration which are available on the official website of MoHFW, Government of India [37] as on 30th November, 2020, is summarized in Fig. 3(e). Following the report, the highest value of MR is found in Punjab with score value 3.15%. Thus, the universe of discourse of MR is considered as the closed interval 0,4 on which three linguistic hedges, viz., Low, Medium, and High are defined. Since, the average value of MR in India is found as 1.45%, the respective TFNs, viz., 0,0,1.45, 1,1.45,1.9, and 1.45,4,4 are introduced to represent these linguistic hedges and are shown in Fig. 4(e).

It is to be mentioned here that only those states and UTs are considered in this study where at least one COVID-19 positive case was found up to 30th November, 2020. Hence, the UT of Lakshadweep is out of the consideration, as no positive COVID-19 case was found there up to that time.

For simplicity, a deviation of about 2% of the collected data is considered for deriving the TFNs as inputs. The TFNs corresponding to the inputs are presented in Table 1.

Table 1.

Fuzzified input values.

State/UT PD NTM CCM RR MR
Andaman and Nicobar Islands 45,46,47 319399,325917,332435 11612,11849,12086 94.52,96.45,98.38 1.27,1.3,1.33
Andhra Pradesh 303,309,315 188750,192602,196454 16284,16616,16948 96.27,98.23,100 0.79,0.81,0.83
Arunachal Pradesh 17,17,17 234003,238779,243555 10601,10817,11033 92.55,94.44,96.33 0.32,0.33,0.34
Assam 390,398,406 151865,154964,158063 6076,6200,6324 96,97.96,99.92 0.45,0.46,0.47
Bihar 1084,1106,1128 120240,122694,125148 1920,1959,1998 95.21,97.15,99.09 0.53,0.54,0.55
Chandigarh 9067,9252,9437 118304,120718,123132 14415,14709,15003 89.99,91.83,93.67 1.56,1.59,1.62
Chhattisgarh 185,189,193 87465,89250,91035 8052,8216,8380 88.25,90.05,91.85 1.18,1.2,1.22
Dadra and Nagar Haveli
and Daman and Diu
951,970,989 73996,75506,77016 3405,3474,3543 97.29,99.28,100 0.06,0.06,0.06
Delhi 11094,11320,11546 311008,317355,323702 28026,28598,29170 90.37,92.21,94.05 1.57,1.6,1.63
Goa 386,394,402 222009,226540,231071 30421,31042,31663 93.87,95.79,97.71 1.41,1.44,1.47
Gujarat 302,308,314 112887,115191,117495 3005,3066,3127 89.13,90.95,92.77 1.87,1.91,1.95
Haryana 562,573,584 122074,124565,127056 7948,8110,8272 89.02,90.84,92.66 1.01,1.03,1.05
Himachal Pradesh 121,123,125 71064,72514,73964 5370,5480,5590 75.26,76.8,78.34 1.56,1.59,1.62
Jammu and Kashmir 74,75,77 223781,228348,232915 8154,8320,8486 91.96,93.84,95.72 1.5,1.53,1.56
Jharkhand 406,414,422 109492,111727,113962 2856,2914,2972 95.21,97.15,99.09 0.86,0.88,0.9
Karnataka 313,319,325 165349,168723,172097 13165,13434,13703 93.97,95.89,97.81 1.3,1.33,1.36
Kerala 843,860,877 174725,178291,181857 16729,17070,17411 87.06,88.84,90.62 0.36,0.37,0.38
Ladakh 5,5,5 311316,317669,324022 28105,28679,29253 86.41,88.17,89.93 1.35,1.38,1.41
Madhya Pradesh 231,236,241 44704,45616,46528 2440,2490,2540 89.28,91.1,92.92 1.56,1.59,1.62
Maharashtra 358,365,372 87098,88875,90653 14602,14900,15198 90.51,92.36,94.21 2.54,2.59,2.64
Manipur 125,128,131 132754,135463,138172 7867,8028,8189 84.19,85.91,87.63 1.08,1.1,1.12
Meghalaya 129,132,135 73449,74948,76447 3568,3641,3714 90.66,92.51,94.36 0.93,0.95,0.97
Mizoram 51,52,53 123420,125939,128458 3146,3210,3274 88.11,89.91,91.71 0.13,0.13,0.13
Nagaland 117,119,121 51528,52580,53632 5086,5190,5294 87.87,89.66,91.45 0.56,0.57,0.58
Odisha 265,270,275 132502,135206,137910 7143,7289,7435 95.82,97.78,99.74 0.53,0.54,0.55
Puducherry 2546,2598,2650 264108,269498,274888 24067,24558,25049 95.11,97.05,98.99 1.62,1.65,1.68
Punjab 540,551,562 104802,106941,109080 4974,5075,5177 89.81,91.64,93.47 3.09,3.15,3.21
Rajasthan 196,200,204 55955,57097,58239 3366,3435,3504 86.53,88.3,90.07 0.84,0.86,0.88
Sikkim 84,86,88 92386,94271,96156 7358,7508,7658 90.61,92.46,94.31 2.13,2.17,2.21
Tamil Nadu 544,555,566 156138,159324,162510 10105,10311,10517 95.14,97.08,99.02 1.47,1.5,1.53
Telangana 306,312,318 143590,146520,149450 7104,7249,7394 93.84,95.75,97.67 0.53,0.54,0.55
Tripura 343,350,357 129228,131865,134502 8026,8190,8354 95.11,97.05,98.99 1.11,1.13,1.15
Uttar Pradesh 812,829,846 84168,85886,87604 2361,2409,2457 92.16,94.04,95.92 1.4,1.43,1.46
Uttarakhand 185,189,193 117895,120301,122707 6540,6673,6806 89.84,91.67,93.5 1.61,1.64,1.67
West Bengal 1008,1028,1049 59392,60604,61816 4863,4962,5061 91.32,93.18,95.04 1.71,1.74,1.77

4.2. Selection of membership functions for output variables

The universe of discourse of PSC is considered as the closed interval 0,100 on which three linguistic hedges, viz., Poor, Ordinary, and Excellent are defined. The MFs corresponding to these linguistic hedges are represented by the respective TFNs, 0,0,50, 30,50,70, and 50,100,100 as shown in Fig. 4(f).

4.3. Formation of fuzzy rule base

Here, each input and output parameter consists of three linguistic terms. Thus, combining all the possible outcomes corresponding to input–output parameters, the rule base of the proposed MFIS contains a total number of 35=243 if-then fuzzy rules which are presented in Table 2.

Table 2.

Fuzzy rule base.

graphic file with name fx2_lrg.gif

4.4. Evaluation of PSC

After, forming the fuzzy rule base, the values of PSC of the states and UTs in India under consideration are evaluated through the processes as described in Step 3 to Step 6 of Section 3 and executed through the software MATLAB (Ver. R2014a); and the achieved results are presented in Table 3. As for visual representation, a snapshot of the MATLAB programming for the evaluation of PSC of Andaman and Nicobar Islands is presented in Fig. 5.

Table 3.

Achieved results through the proposed methodology.

State/UT PSC Rank
Andaman and Nicobar Islands 46.8497 23
Andhra Pradesh 60.6695 10
Arunachal Pradesh 74.6466 5
Assam 75.0416 4
Bihar 75.7746 1
Chandigarh 55.9679 13
Chhattisgarh 41.1934 25
Dadra and Nagar Haveli and Daman and Diu 75.6282 2
Delhi 53.6759 17
Goa 22.5984 32
Gujarat 40.3565 27
Haryana 68.0894 8
Himachal Pradesh 34.2012 29
Jammu and Kashmir 56.3987 12
Jharkhand 66.9933 9
Karnataka 41.0502 26
Kerala 75.5097 3
Ladakh 19.6694 35
Madhya Pradesh 31.3055 30
Maharashtra 21.5832 33
Manipur 49.8450 22
Meghalaya 52.6629 18
Mizoram 55.8357 15
Nagaland 45.3849 24
Odisha 70.9396 7
Puducherry 59.7758 11
Punjab 27.9819 31
Rajasthan 50 19
Sikkim 21.5425 34
Tamil Nadu 55.9669 14
Telangana 72.1552 6
Tripura 54.5099 16
Uttar Pradesh 50 20
Uttarakhand 36.3188 28
West Bengal 50 21

Fig. 5.

Fig. 5

A snapshot of MATLAB programming for the Evaluation of PSC of Andaman and Nicobar Islands.

It is important to note here that the PSC of each state and UT is evaluated according to the data provided by the Department of MoHFW, Government of India available up to 30th November, 2020, which may differ, in future.

5. Results and discussions

It is found from the derived results, as presented in Table 3, that Bihar positioned at the top of the table in case of taking preventive measures against COVID-19 with PSC of 75.7746. In spite of being densely populated state, Bihar, recorded low number of confirmed COVID-19 cases (1959 per million) along with very high recovery rate of 97.15% and low mortality rate of 0.54%. Also, it is the fact that the Assembly election was held in Bihar in October, 2020. So, it might be assumed that the state government of Bihar tightened up the grip over the pandemic of COVID-19; and as a result, a downfall in the active cases and mortality rate of COVID-19 was recorded in Bihar. It is also the fact that the recovery rate from COVID-19 was also found high in Bihar due to the increase of corona-dedicated beds and ICUs in the hospitals.

In Result Table 3, the UT in the western India, Dadra and Nagar Haveli and Daman and Diu, ranks just below the rank of Bihar with PSC of 75.6282. Though, Dadra and Nagar Haveli and Daman and Diu is a densely populated region in India, but the facts behind this ranking might be very low number of confirmed COVID-19 cases (3474 per million) along with highest recovery rate of 99.28% in India and very low mortality rate of 0.06%. The administrative bodies in Dadra and Nagar Haveli and Daman and Diu recognized the people as ‘Corona Warriors’ who have completely maintained the lockdown rules. Also, the administration built up a large number of quarantine centres and got successes in isolating the COVID-19 positive people by performing free and rapid COVID-19 tests.

The first COVID-19 positive case was found in Kerala. The state government of Kerala was performing very significant jobs both in administrative and ground level for fighting against COVID-19 during the complete lockdown periods. As a result, Kerala became one of the most progressing states in India for adapting preventive strategies against COVID-19. But, in the last week of August, Kerala celebrates the festival, called “Onam”; and after that a significant jump in the active COVID-19 cases was found. It is suspected that there might be an effect of celebrating that festival, in which gathering of a large number of people took place. As a result, Kerala faced worse effect of COVID-19 during that time. According to the Result Table 3, Kerala remains at the upper side of the table as rank 3rd position with PSC of 75.5097.

In spite of performing a high number of COVID-19 tests, an average number of confirmed COVID-19 cases (6200 per million) along with very high recovery rate of 96.99% and very low mortality rate of 0.46% were found in a state of eastern India, viz., Assam. Considering those facts, Assam belongs to the upper side of Table 3 as 4th, with PSC of 75.0416. More than 1000 medical teams had been appointed in Assam for screening and monitoring the people having seasonal fevers. Further, the accredited social health activists and multi-purpose workers regularly monitored the home quarantined patients. The Government of Assam launched the mobile app ‘COVASS’ and ‘COVID Suraksha’ to spread the information related with COVID-19 and to monitor the patients who had suggested staying under home quarantine, respectively.

Further, Arunachal Pradesh, another state in the eastern India, also shows good fight against COVID-19 with PSC of 74.6466. Having conducting a high number of COVID-19 tests (2,38,779 per million) by the Government of Arunachal Pradesh, very low mortality rate of 0.33% were found there.

The state, Telangana, had performed a high number of COVID-19 tests. From the collected data, it is seen that this state recorded an average number of COVID-19 cases (7249 per million) along with very high recovery rate of 95.75% and very low mortality rate of 0.54%. Thus, Telangana remains at the top side of Table 3 with PSC of 72.1552. Proper face mask utilization, early detection and isolation of COVID-19 patients might also be the reasons for the improvement of COVID-19 situations in Telangana.

Odisha, situated in the eastern coast of India, is habituated for tackling natural disasters, which are frequently faced by this state. This state had shown its proficiency in managing the pandemic situation of COVID-19 as like other disasters. The PSC for this state is evaluated as 70.9396. From the data it is clear that the state Government of Odisha had performed a high number of COVID-19 tests (1,35,206 per million) to isolate the COVID-19 positive people. As a result, a high recovery rate of 97.78% and low mortality rate of 0.54% were found in Odisha.

Further, the state of Haryana, Jharkhand and Andhra Pradesh had also shown significant performances in controlling the spread of COVID-19 having PSC of 68.0894, 66.9933 and 60.6695, respectively. The input data corresponding to those states reflects higher ranking in the Result Table 3. So, those states and UTs can be considered as role model to others in fighting against the pandemic of COVID-19.

On the contrary, the UT of Ladakh which is situated at the north most region of India has the least PSC of 19.6694 in controlling the spread of COVID-19. Though, this state is least densely populated area of India, but it had a high number of confirmed COVID-19 cases (28,679 per million) with recovery rate of 88.17%. The deficiency of COVID-19 hospitals and medical facilities might be one of the primary reasons for this low scoring.

Sikkim, one of the north-eastern states of India, had also faced the worse effect of COVID-19 pandemic in the recent times having PSC of 21.5425. A large number of health workers were found as COVID-19 positive in Sikkim; and hence, the healthcare sectors of Sikkim faced major shortages of workforce during that times. As a result, high mortality rate of 2.17% were recorded in Sikkim.

The state of Maharashtra, situated in the western part of India, has also scored poor PSC of 21.5832 in controlling the spread of COVID-19. According to the COVID-19 statistics on 30th November, 2020, in Maharashtra around 20% of total COVID-19 positive cases and about 34% of total deceased cases of India were found. The city of Mumbai which is the capital of Maharashtra is also the financial capital of India. People from all the states and UTs in India come to Mumbai for their livelihood; and hence most number of migrated COVID-19 cases are found in Maharashtra. For that reason, it became difficult for Maharashtra to control the spread of COVID-19.

The pandemic situation of COVID-19 is worsening rapidly with an increase of confirmed COVID-19 positive cases (31,042 per million) in Goa, a state on the south-western coast in India. The government and private hospitals faced problems in increasing the beds for COVID-19 patients. As a result, Goa was showing poor performance in controlling the spread of COVID-19 with PSC of 22.5984.

Further, the PSC corresponding to Punjab, Madhya Pradesh, Himachal Pradesh, and Uttarakhand are evaluated low, i.e., those states performed poorly in fighting against COVID-19. So, those states and UTs have lots of works to do for controlling the spread of COVID-19.

The validation of the proposed method is performed in the next section.

6. Validation of the proposed method and sensitivity analysis

To test the validity of the proposed model, Pearson’s correlation coefficient is evaluated between the final results and recovery rate of COVID-19 corresponding to each state and UT, and is presented in Table 4. The value of Pearson’s correlation coefficient is found as 0.4284. The positive value of Pearson’s correlation coefficient establishes the consistency and steadiness of the processes followed in the proposed methodology.

Table 4.

Pearson’s correlation coefficient between the Achieved results and recovery rate of COVID-19.

State/UT Achieved result Recovery rate of COVID-19 Pearson’s correlation coefficient
Andaman and Nicobar Islands 46.8497 96.45 0.4284
Andhra Pradesh 60.6695 98.23
Arunachal Pradesh 74.6466 94.44
Assam 75.0416 97.96
Bihar 75.7746 97.15
Chandigarh 55.9679 91.83
Chhattisgarh 41.1934 90.05
Dadra and Nagar Haveli and Daman and Diu 75.6282 99.28
Delhi 53.6759 92.21
Goa 22.5984 95.79
Gujarat 40.3565 90.95
Haryana 68.0894 90.84
Himachal Pradesh 34.2012 76.8
Jammu and Kashmir 56.3987 93.84
Jharkhand 66.9933 97.15
Karnataka 41.0502 95.89
Kerala 75.5097 88.84
Ladakh 19.6694 88.17
Madhya Pradesh 31.3055 91.1
Maharashtra 21.5832 92.36
Manipur 49.8450 85.91
Meghalaya 52.6629 92.51
Mizoram 55.8357 89.91
Nagaland 45.3849 89.66
Odisha 70.9396 97.78
Puducherry 59.7758 97.05
Punjab 27.9819 91.64
Rajasthan 50 88.3
Sikkim 21.5425 92.46
Tamil Nadu 55.9669 97.08
Telangana 72.1552 95.75
Tripura 54.5099 97.05
Uttar Pradesh 50 94.04
Uttarakhand 36.3188 91.67
West Bengal 50 93.18

Further, a sensitivity analysis is performed to observe the changes of the values of PSC by varying the tolerance ranges, l of the input arguments in Eq. (1), and is presented in Table 5. It is seen from Table 5 that the proposed estimation is sensitive under the tolerance range, l and preserves the same rank of the provinces as like Table 3 up to l=0.025, which is a deviation of 2.5% from the exact values of the inputs. The changes of the values of PSC corresponding to different values of l are presented in Fig. 6.

Table 5.

Changes of the values of PSC for different values of l.

State/UT PSC
l=0.005 l=0.01 l=0.015 l=0.02 l=0.025 l=0.03 l=0.04 l=0.07 l=0.1
Andaman and Nicobar Islands 46.6741 46.6419 46.611 46.8497 46.8744 47.0302 47.3257 48.0787 48.6883
Andhra Pradesh 63.2689 62.4052 61.4657 60.6695 59.9843 59.4694 58.7555 56.9319 55.4817
Arunachal Pradesh 74.6310 74.6367 74.6415 74.6466 74.6495 74.6536 74.6577 74.6569 74.6377
Assam 75.2693 75.1928 75.1163 75.0416 74.9698 74.8996 74.7615 74.3845 72.6897
Bihar 75.7582 75.7637 75.7692 75.7746 75.7801 75.7855 75.7964 75.8289 75.8611
Chandigarh 55.42 55.626 55.8247 55.9679 56.2019 56.3849 56.7330 57.6690 58.4739
Chhattisgarh 41.137 41.1605 41.1841 41.1934 41.2366 41.2393 41.2578 41.3653 41.7488
Dadra and Nagar Haveli
and Daman and Diu
75.6140 75.6188 75.6237 75.6282 75.6334 75.6383 75.6479 75.6769 74.1079
Delhi 53.3223 53.4518 53.58 53.6759 53.83 53.9526 54.1907 54.8644 55.4855
Goa 21.6873 21.9942 22.3328 22.5984 23.0595 23.6026 24.6343 27.3492 29.6108
Gujarat 38.3986 39.3541 40.2263 40.3565 40.7522 40.9823 41.3545 42.3585 43.3654
Haryana 69.3681 68.9042 68.4645 68.0894 67.671 67.3146 66.6523 65.0681 63.9271
Himachal Pradesh 34.254 34.2363 34.2188 34.2012 34.1841 34.167 34.1333 34.0355 34.7909
Jammu and Kashmir 56.5329 56.4734 56.4164 56.3987 56.3045 56.2494 56.1409 55.6404 54.9794
Jharkhand 66.9605 66.9700 66.9792 66.9933 66.9975 67.0067 67.0247 67.0775 65.6925
Karnataka 38.4259 39.377 40.2475 41.0502 41.2301 42.4568 43.6608 46.4036 48.2471
Kerala 75.4967 75.5011 75.5054 75.5097 75.5143 75.5186 75.5273 75.4721 65.2688
Ladakh 19.1955 19.3398 19.4811 19.6694 20.7323 20.8625 21.1143 21.8589 22.5242
Madhya Pradesh 31.3025 31.3034 31.3045 31.3055 31.3065 31.3087 31.3092 31.3132 32.4368
Maharashtra 21.6454 21.6246 21.6038 21.5832 21.5631 21.5427 21.5025 21.3847 21.2782
Manipur 49.9823 49.9325 49.8884 49.8450 49.5035 49.2734 48.8741 47.9780 47.3412
Meghalaya 52.8786 52.798 52.7223 52.6629 52.5612 52.4921 52.3439 51.9474 51.5916
Mizoram 55.3128 55.5757 55.7028 55.8357 55.9621 56.1004 56.2428 56.6802 57.1256
Nagaland 45.3655 45.3712 45.3788 45.3849 45.4083 45.4157 45.4363 45.4798 45.5259
Odisha 71.2480 71.1431 71.0368 70.9396 70.8313 70.7298 70.5300 69.9589 69.4208
Puducherry 59.2286 59.4473 59.6547 59.7758 59.9533 60.2472 60.6115 61.5901 62.4188
Punjab 25.9868 26.8284 27.5462 27.9819 28.0222 28.0644 28.1421 28.3641 28.5739
Rajasthan 50 50 50 50 50 50 50 50 50
Sikkim 21.6307 21.5975 21.5649 21.5425 21.5001 21.4684 21.4057 21.3559 22.7267
Tamil Nadu 55.33 55.61 55.8134 55.9669 56.1113 56.2925 56.5111 57.3352 58.1232
Telangana 72.4909 72.3745 72.2584 72.1552 72.0368 71.9249 71.7094 71.0999 70.2683
Tripura 54.9080 54.81 54.6766 54.5099 54.4406 54.3261 54.1163 53.6008 53.2103
Uttar Pradesh 50 50 50 50 50 50 50 50 49.0732
Uttarakhand 36.0325 36.1320 36.2247 36.3188 36.4126 36.5059 36.6865 37.2093 37.6984
West Bengal 50 50 50 50 50 50 50 50 50

Fig. 6.

Fig. 6

The changes of the values of PSC by varying the tolerance ranges.

7. Conclusions

The results in Table 3 show that 14 states and UTs in India have scored less than 50. This is very alarming concern to the Government of India to fight against the pandemic situation of COVID-19. Considering the pandemic situation, the proposed study would become very much helpful to the authorities of both central and state governments to identify the district wise containment zones of COVID-19 within a particular state by evaluating the district wise PSC of that state. The proposed study would also be helpful to the government authorities in starting intra-state, and inter-state public transport services and reopening educational institutes, theatres, cinema halls, museums, etc., in those states and UTs having higher value of PSC. The states and UTs having higher PSC score could be considered as role models to others for taking preventive strategies to get rid of from the pandemic situation of COVID-19. Further, the proposed research work might also be helpful for the government authorities of India for performing fair and equitable distribution of the economic packages announced by the central Government of India, and also for supplying medical equipment to the states and UTs having lower PSC.

It is clear now from the experiences of last few months that vaccine is the only solution for controlling the spread of COVID-19. But it is also becoming doubtful about the preventive power of the vaccines due to the appearance of different new strains of Corona virus. In fact, the world is now facing the challenges of second wave of COVID-19. In the month of July, 2020 WHO declared that 165 countries sharing up to 60% of the world population had signed an agreement of WHO COVAX plan in purpose of fair distribution of the licenced vaccines of COVID-19. But, for such a highly populated country like India, it might be difficult to organize fair and equitable distribution processes of the COVID-19 vaccines among the people. The proposed methodology would be helpful to build up the strategies for selecting the worse affected districts, states or UTs of India where the vaccines are needed to reach first than others, well in advance. Finally, the proposed research methodology may also be implemented in global interests by evaluating the PSC of each country which is affected by COVID-19 for taking preventive strategies, announcing economic packages, supplying medical equipment and distributing COVID-19 vaccines, etc. From that view point, the developed model is applicable for not only in India but also other countries for evaluation of their current COVID-19 status.

In spite of its usefulness in assessing recent situations and for building up strategies to prevent the spread of COVID-19, there are some potential limitations of the proposed study which are described as follows:

  • Although the proposed method possesses the input values as fuzzy numbers, but it is unable to provide the fuzzy outcomes. Other kind of inference system may be used for this purpose.

  • Here, the obtained results represent the current status of the provinces due to COVID-19. But, the proposed method is unable to provide any solution to overcome from that pandemic situation.

  • The proposed model is designed in the context of pandemic situation of COVID-19 in India. So, direct application of the methodology may not provide accurate results for other countries. However, modifications of the input variables, MFs, rule base may increase the reliability of the proposed method for assessing current pandemic scenario of different parts of a country.

Some future research scopes of this article are summarized as follows:

  • In this article, PSC of each state and UT in India is evaluated by generating the MFIS with five input parameters, viz., PP, NTM, CCM, RR, and MR. But depending on the context of research, some other factors such as daily new cases, serious or critical cases of COVID-19, rate of vaccinations, etc., can be considered as input parameters which may enrich the process of MFIS.

  • The proposed methodology can also be applicable in estimating the performance of a country, state or UT against other serious virus affected diseases like mumps, rubella, hepatitis, measles, etc., which will be helpful in taking preventive measures, well in advance.

  • The proposed method may also be extended in several branches of fuzzy environments, viz., q-rung orthopair fuzzy, intuitionistic fuzzy, Pythagorean fuzzy, and other domains.

Finally, it is expected that the proposed method would be helpful to identify the COVID-19 affected regions and to alarm that zone to take preventive measures, well in advance, so that the spread of COVID-19 can be minimized.

CRediT authorship contribution statement

Bappaditya Ghosh: Software, Formal analysis, Investigation, Data curation, Writing - original draft, Review. Animesh Biswas: Conceptualization, Methodology, Formal analysis, Investigation, Writing - review & editing, Supervision.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors remain very much grateful and appreciable to the learned reviewers for their constructive comments and helpful suggestions to improve the quality of the manuscript.

References

  • 1.Behnood A., Golafshani E.M., Hosseini S.M. Determinants of the infection rate of the COVID-19 in the U.S. using ANFIS and virus optimization algorithm (VOA) Chaos Solitons Fractals. 2020;139 doi: 10.1016/j.chaos.2020.110051. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 2.Lahmiri S., Bekiros S. The impact of COVID-19 pandemic upon stability and sequential irregularity of equity and cryptocurrency markets. Chaos Solitons Fractals. 2020;138 doi: 10.1016/j.chaos.2020.109936. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 3.Sun T., Wang Y. Modeling COVID-19 epidemic in heilongjiang province, China. Chaos Solitons Fractals. 2020;138 doi: 10.1016/j.chaos.2020.109949. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 4.Velásquez R.M.A., Lara J.V.M. Forecast and evaluation of COVID-19 spreading in USA with reduced-space Gaussian process regression. Chaos Solitons Fractals. 2020;136 doi: 10.1016/j.chaos.2020.109924. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 5.Ribeiro M.H.D.M., da Silva R.G., Mariani V.C., Coelho L.D.S. Short-term forecasting COVID-19 cumulative confirmed cases: perspectives for Brazil. Chaos Solitons Fractals. 2020;135 doi: 10.1016/j.chaos.2020.109853. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 6.Rothan H.A., Byrareddy S.N. The epidemiology and pathogenesis of coronavirus disease (COVID-19) outbreak. J. Autoimmun. 2020;109 doi: 10.1016/j.jaut.2020.102433. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 7.Wang W., Tang T., Wei F. Updated understanding of the outbreak of 2019 novel coronavirus (2019-nCoV) in Wuhan, China. J. Med. Virol. 2020;92(4):441–447. doi: 10.1002/jmv.25689. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 8.2020. COVID-19: 99% active cases are with mild symptoms, Down To Earth. https://www.downtoearth.org.in/news/health/covid-19-99-active-cases-are-with-mild-symptoms-72757. (Accessed 11 August 2020) [Google Scholar]
  • 9.2020. Coronavirus now less fatal 90% patients have mild symptoms: AIIMS Director, Hindustan Times. https://www.hindustantimes.com/india-news/coronavirus-now-less-fatal-90-patients-have-mild-symptoms-aiims-director/story-axggNvvJwUkjRz9hTpYQ8N.html. (Accessed 3 June 2020) [Google Scholar]
  • 10.2020. Official website of World Health Organization. https://www.who.int/health-topics/coronavirus#tab=tab_1. (Accessed 30 November 2020) [Google Scholar]
  • 11.Wu Z., McGoogan J.M. Characteristics of and important lessons from the coronavirus disease 2019 (COVID-19) outbreak in China: summary of a report of 72314 cases from the Chinese center for disease control and prevention. J. Am. Med. Accoc. 2020;323(13):1239–1242. doi: 10.1001/jama.2020.2648. [DOI] [PubMed] [Google Scholar]
  • 12.Xia L., Chen J., Friedemann T., Yang Z., Ling Y., Liu X., Lu S., Li T., Song Z., Huang W., Lu Y., Schröder S., Lu H. The course of mild and moderate COVID-19 infections—The unexpected long-lasting challenge. Open Forum Infect. Dis. 2020;7(9) doi: 10.1093/ofid/ofaa286. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 13.Ye Q., Wang B., Mao J. The pathogenesis and treatment of the ‘Cytokine Storm’ in COVID-19. J. Infect. 2020;80(6):607–613. doi: 10.1016/j.jinf.2020.03.037. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 14.Murthy S., Gomersall C.D., Fowler R.A. Care for critically III patients with COVID-19. J. Am. Med. Accoc. 2020;323(15):1499–1500. doi: 10.1001/jama.2020.3633. [DOI] [PubMed] [Google Scholar]
  • 15.Hamming I., Timens W., Bulthuis M.L.C., Lely A.T., Navis G.J., van Goor H. Tissue distribution of ACE2 protein, the functional receptor for SARS coronavirus. A first step in understanding SARS pathogenesis. J. Pathol. 2004;203(2):631–637. doi: 10.1002/path.1570. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 16.Renu K., Prasanna P.L., Gopalakrishnan A.V. Coronaviruses pathogenesis, comorbidities and multi-organ damage - a review. Life Sci. 2020;255 doi: 10.1016/j.lfs.2020.117839. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 17.Ciotti M., Ciccozzi M., Terrinoni A., Jiang W.-C., Wang C.-B., Bernardini S. The COVID- 19 pandemic. Crit. Rev. Clin. Lab. Sci. 2020 doi: 10.1080/10408363.2020.1783198. [DOI] [PubMed] [Google Scholar]
  • 18.Togacar M., Ergen B., Z. Comert Z. COVID-19 detection using deep learning models to exploit Social Mimic Optimization and structured chest X-ray images using fuzzy color and stacking approaches. Comput. Biol. Med. 2020;121 doi: 10.1016/j.compbiomed.2020.103805. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 19.Govindan K., Mina H., Alavi B. A decision support system for demand management in healthcare supply chains considering the epidemic outbreaks: A case study of coronavirus disease 2019 (COVID-19) Transp. Res. E. 2020;138 doi: 10.1016/j.tre.2020.101967. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 20.Mardani A., Saraji M.K., Mishra A.R., Rani P. A novel extended approach under hesitant fuzzy sets to design a framework for assessing the key challenges of digital health interventions adoption during the COVID-19 outbreak. Appl. Soft Comput. 2020;96 doi: 10.1016/j.asoc.2020.106613. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 21.Mahmoudi M.R., Baleanu D., Mansor Z., Tuan B.A., Pho K.-H. Fuzzy clustering method to compare the spread rate of Covid-19 in the high risks countries. Chaos Solitons Fractals. 2020;140 doi: 10.1016/j.chaos.2020.110230. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 22.Behnood A., Golafshani E.M., Hosseini S.M. Determinants of the infection rate of the COVID-19 in the U.S. using ANFIS and virus optimization algorithm (VOA) Chaos Solitons Fractals. 2020;139 doi: 10.1016/j.chaos.2020.110051. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 23.Ly K.T. A COVID-19 forecasting system using adaptive neuro-fuzzy inference. Finance Res. Lett. 2020 doi: 10.1016/j.frl.2020.101844. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 24.Singh R., Avikal S. COVID-19: A decision-making approach for prioritization of preventive activities. Int. J. Healthc. Manag. 2020 doi: 10.1080/20479700.2020.1782661. [DOI] [Google Scholar]
  • 25.Ocampo L., Yamagishi K. Modeling the lockdown relaxation protocols of the philippine government in response to the COVID-19 pandemic: An intuitionistic fuzzy DEMATEL analysis. Socioecon. Plann. Sci. 2020;72 doi: 10.1016/j.seps.2020.100911. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 26.Ren Z., Liao H., Liu Y. Generalized Z-numbers with hesitant fuzzy linguistic information and its application to medicine selection for the patients with mild symptoms of the COVID-19. Comput. Ind. Eng. 2020;145 doi: 10.1016/j.cie.2020.106517. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 27.Li X., Liao H., Wen Z. A consensus model to manage the non-cooperative behaviors of individuals in uncertain group decision making problems during the COVID-19 outbreak. Appl. Soft Comput. 2021;99 doi: 10.1016/j.asoc.2020.106879. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 28.Shaban W.M., Asmaa H., Rabie A.H., Saleh A.I., Abo-Elsoud M.A. Detecting COVID-19 patients based on fuzzy inference engine and Deep Neural Network. Appl. Soft Comput. 2021;99 doi: 10.1016/j.asoc.2020.106906. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 29.Aggarwal L., Goswami P., Sachdeva S. Multi-criterion intelligent decision support system for COVID-19. Appl. Soft Comput. 2021;101 doi: 10.1016/j.asoc.2020.107056. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 30.Ghorui N., Ghosh A., Mondal S.P., Bajuri M.Y., Ahmadian A., Salahshour S., Ferrara M. Identifcation of dominant risk factor involved in spread of COVID-19 using hesitant fuzzy MCDM methodology. Results Phys. 2021;21 doi: 10.1016/j.rinp.2020.103811. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 31.Mishra A.R., Rani P., Krishankumar R., Ravichandran K.S., Kar S. An extended fuzzy decision-making framework using hesitant fuzzy sets for the drug selection to treat the mild symptoms of Coronavirus Disease 2019 (COVID-19) Appl. Soft Comput. 2021;103 doi: 10.1016/j.asoc.2021.107155. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 32.Ecer F., Pamucar D. MARCOS technique under intuitionistic fuzzy environment for determining the COVID-19 pandemic performance of insurance companies in terms of healthcare services. Appl. Soft Comput. 2021;104 doi: 10.1016/j.asoc.2021.107199. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 33.Sharma M.K., Dhiman N., Vandana R., Mishra V.N. Mediative fuzzy logic mathematical model: A contradictory management prediction in COVID-19 pandemic. Appl. Soft Comput. 2021;105 doi: 10.1016/j.asoc.2021.107285. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 34.Mamdani E.H., Assilian S. An experiment in linguistic synthesis with a fuzzy logic controller. Int. J. Man-Mach. Stud. 1975;7(1):1–13. [Google Scholar]
  • 35.Pearson K. Notes on regression and inheritance in the case of two parents. Proc. R. Soc. Lond. 1895;58:240–242. [Google Scholar]
  • 36.2020. Office of the Registrar General & Census Commissioner, India, Ministry of Home Affairs, Government of India. https://censusindia.gov.in. (Accessed 30 November 2020) [Google Scholar]
  • 37.2020. Ministry of Health and Family Welfare, Government of India. https://www.mohfw.gov.in. (Accessed on 30 November 2020) [Google Scholar]
  • 38.Worldometer K. 2020. info., COVID-19 coronavirus pandemic, Worldometers. https://www.worldometers.info/coronavirus. (Accessed on 30 November 2020) [Google Scholar]
  • 39.Majumder D., Debnath J., Biswas A. Risk analysis in construction sites using fuzzy reasoning and fuzzy analytic hierarchy process. Procedia Technol. 2013;10:604–614. [Google Scholar]
  • 40.An M., Chen Y., Baker C.J. A fuzzy reasoning and fuzzy analytical hierarchy process based approach to the process of railway risk information: A railway risk management system. Inform. Sci. 2011;181:3946–3966. [Google Scholar]

Articles from Applied Soft Computing are provided here courtesy of Elsevier

RESOURCES