A Review of Chronological Evolution of Air Quality Indexing Systems (1966 To 2021)

Air quality index (AQI) also known as air pollution index (API) is the way of describing ambient air quality to assess the health risk associated with pollution. With the advent of time, there have been several air quality indexing systems starting from the first air Quality Index developed in 1966 by Marvin H. Green and various modifications have been made ever since to improve the accuracy of measurement. Such systems can assess the air quality by several factors like the concentration of different pollutants or by various empirically established formulas based on past experiences. In this review article, an effort has been made to chronologically evaluate the AQI system developed across the world from 1966 to 2021. Every indexing system has its own unique method for air quality determination and each method has its own merits and demerits. This pape rcovers various parameters, empirical relationships, standards, merits, and demerits, which in hind sight will help to develop an amalgamation of various indexing systems that can be used as a standard method for monitoring the quality of air. This paper also covers the AQI systems that prevail in India. A fuzzy logic system is very helpful in handling the uncertainty in air quality assessment. So, fuzzy-based air quality indexing systems developed from 2010 to 2017 have also been reviewed. The review of articles established that the results obtained through fuzzy-based AQI aremore reliable than the other methods. Out of all the above describing methods, fuzzy synthetic evaluation-based AQI system and fuzzy air quality health index (FAQHI) are more powerful tools to describe the air quality. But till 2017, thereis no development of AQI systems based on fuzzy logic, considering PM2.5 as one of the pollutants. So, there is a need to develop the fuzzy-based AQI system considering PM2.5 as a pollutant with other air pollutants. CONTACT Dipsha Paresh Shah dipsha.shah@gmail.com Ganpat University, Mehsana, Gujarat, India. © 2021 The Author(s). Published by Enviro Research Publishers. This is an Open Access article licensed under a Creative Commons license: Attribution 4.0 International (CC-BY). Doi: http://dx.doi.org/10.12944/CWE.16.3.5 Article History Received: 04 June 2021 Accepted: 09 December 2021


Introduction
The presence of harmful chemicals or compounds in the air such as particulate matters (PM 10 , and PM 2.5 ), CO, O 3 , SO 2 , NO 2 , which not only lowers the quality of air but also deteriorates human health and overall quality of life is defined as air pollution. It is the most unusual scenario for sulfur It is the most unusual scenario and it is rarely dioxide to reach or exceed 1. 5 ppm. attained therefore it is considered the most dangerous case.
After industrialization, globalization and modernization have drastically changed the living standards with the introduction of gadgets like motorcycles, air conditioning systems which have made life simpler but also increased the pollution levels.
As per the estimation done by the World Health Organization (WHO), in developing countries, about 25% of all deaths may be due to environmental pollution. Due to increasing industrial development air pollution and its resultant adverse health impacts increases. A study by World Health Organization also revealed the possibility of risk of air borne diseases due to constant exposure to air pollution over a long time (WHO, 2009). Therefore, awareness of air pollution is necessary among citizens which leads to an increasing need for communication to the common public about the pollution levels. The simplest way to report the status of air quality to people is the AQI system. Around the world, various indexing systems have been established, but there is no universal indexing system, which can be used globally, in all conditions. The development of the indexing system starts in 1966 with considering only two pollutants; coefficient of haze (COH) and sulfur dioxide (SO 2 ).The latest development in the air quality indexing system in the year 2021, six pollutants have been considered. This indexing system is based on the impact of contaminants on human health. Fuzzy set theories are very important to decide uncertain environmental conditions. Many researchers also developed the fuzzy modelingbased air quality indexing system, which is reviewed in a separate section in this paper. This present paper attempts to review these Air Quality Indexing Systems with its strength and limitations.

Review of Chronological Evolution of Air Quality Indexing Systems
The chronological evolution of air quality indexing systems since 1966 is discussed in this section along with the number of pollutants considered, salient features of indexing systems, methods adopted for index formulation, and its limitations.
Green's Index, 1966 1 Green's Index is the first air Quality Index developed in 1966 by Marvin H. Green. This pollution index is based on only two parameters: i. Sulfur dioxide and ii. Smoke shade. The reasons for selecting these two parameters were that the quality index developer observed a strong correlation between these two parameters during New York's air pollution episodes and also both the pollutants' concentrations were observed very high during air pollution episodes. In this research, the hypothesis was that "there are certainly very high concentrations of sulfur dioxide in theair, which, when reacted with a similarly high concentration of particulate matters as represented as smoke shade measurements, can increase the death expectancy in the exposed population. "Three different categories concerning pollutants concentration are shown in table 1.
The author developed the equations to convert the pollutants' concentration to index value based on power function. The conversion from pollutant level to the index number is done by the power function represented as Eq. 1 and Eq. 2. To qualify the air based on two pollutants combined index was formed using equation 3.
Combined Index = 0.5* (Sulfur dioxide Index + Smoke Shade Index) ... (3) This index is only relevant and applicable in winter (colder season). Based on the above-mentioned equations, 3 Alerts must be issued. The first alert, second alert, and third alert were issued by the control agency's chief administrator at an index value of 50, 60, and 68 respectively. Limitations of this index are that it includes only two pollutants; SO 2 and COH. It is ambiguous and eclipsing in nature. This indexing system was for activating regulating actions during air pollution episodes rather thanair quality data reporting to the people. The index level along with the description is tabulated in    6 In August 1976, the US EPA evolved the pollutant standards index (PSI). The linear inter polation method was used in the development of the index, in which the concentrations of air pollutants were converted to a standard number, known as a sub-index.The maximum sub-index value of pollutants was reported as the overall index of air quality. The index is a maximum operating function

-50
Advisory, the first alert is issued. An order may be issued by the minister to major source contributors to curtail their activities.

-75
Issue of the second alert. The minister may mandate sources for further restriction in operations.

-100
The threshold level for air pollution episode, restrictions of all sources not important for the health of people,orsafety may be required.

IAPI=
... (13) The limitation of this index is that by nature, it is ambiguous, which may lead to false alarms when calculated to be hazardous. To eliminate this limitation, Swamee and Tyagi (1999) developed a quantitative tool-based air pollution index through which air pollution status can be conveyed consistently. They introduced ambiguity and eclipsing free aggregating function for the air pollutants sub-indices as shown in Eq. 14. After extensive study, an exponent value p = 0.4 was derived and given in the aggregation function to eliminate the ambiguity.

I=
... (14) and colors are shown in table 10. The breakpoints for the pollutants sub-indices are tabulated in table 11.
The main objective of modifications in the US EPA index was to rein force the index system's health implication, particularly for the population sensitive to poor air quality. World widely, this system has been adopted due to its simplicity and accuracy. Yellow Fair air quality, adverse effect unlikely, the effect on nature and material.

-150
Orange Safe air quality, the possibility of adversarial effects on sensitive people, noticeable effects on materials and vegetation.

>150
Red Possibility of adversarial effectson sensitive people. Marked effect on flora, fauna, and materials.   11 If the index is based on linear sum and root sum square form, it suffers from ambiguity. To omit the ambiguity of the Integral Air pollution Index (IAPI), this index was developed. While the maximum operating function-based index does not consider the change in the remaining pollutants. Therefore,

Revised Air Quality Index, 2004 12
This index was developed by joining Shannon's entropy function and pollutant standard index (PSI). It is a contextual mean entropy and arithmetic index.
Combining entropy function rectifies the deficiency of PSI that it identified only one pollutant level at a time, hence it was difficult to as certain that whether more than one pollutant exceeds standards or not. Therefore, this index with comparative index function was developed which allows more diffusion and makes it simpler to find the biggest index value.
The formula developed as RAQI is represented as Eq. 16.
... (16) In the RAQI, five pollutants had been considered and compared: PM 10 , SO 2 , NO 2 , O 3 , and CO. In the equation, the first factor represents the maximum value of each sub-index, i.e. maximum operating function is used in the first factor. The maximum operating function has been considered in the equation to reduce the eclipsing irregularity. In the second factor, the numerator is the summation of the daily arithmetic mean of each sub-index, while the denominator is the yearly mean multiplied by the summation of the daily mean. The third factor is the background arithmetic average entropy index value. Log 10 of the entropy function is defined as the maximum operating function of I 1 ...I n .
The entropy function is a modifier that helped to stop mathematical deviation to extremely large values.
As compared with PSI, the RAQI value is always greater than the PSI value. RAQI poorly predicts the short-term health impact or short-term air quality. This index is more useful to predict long-term health impacts and long-term air quality.

Pollution Index (PI), 2004 13
Two different pollution indexes had been established and implemented in Naples city (Italy). For the development of the index, data was collected and analyzed from nine monitoring stations in 2003.
One background station, two stations in residential areas, four stations in high traffic regions, and two stations that monitored photochemical pollution were among the nine monitoring stations.The aim of the development of the pollution index (PI) was to evaluate the air pollution status with its consequence on the health of human beings. The pollution index is a modified version of US EPA AQI, considering the standards governing in Europe.The pollution index (PI) was re-evaluated considering the aggregation of air pollutants.
The pollution index range is from 0 to 100, divided into five different categories instead of six categories of the US EPA AQI. The breakpoint concentration of different pollutants along with pollution category, pollution index range, and pollution categories definition is shown in table 12. The pollution index was determined by linear interpolation among the The formula to calculate the pollution index of i th pollutant on the j th station is represented as eq. 17. The highest value of the pollutant's sub-indexwas represented as the pollution index of that site as shown in eq. 18.
... (18) The pollution index has been developed for single pollutants. In a mixture, pollutants may have synergetic or additive effects on human health. Synergistic effects of pollutants have not been developed yet. In the pollution index determination procedure, other pollutants do not contribute to the estimation of the index. The pollution index value may be higher than that obtained by the maximum operating function and would represent the actual situation if synergistic effects would be considered.
To consider the synergistic effects of pollutants, Murena tried to modify the pollution index as shown in Eq. 19, based on the procedure that applied in industrial hygiene for validating thres hold values in the scenario of air pollutants' mixture.

PIs = Pollution index of a particular site Cp = Concentration of pollutant (P)
BPp, c = For pollutant P, the lower range of scale, corresponding to each category (C), as shown in table 12 PIbc = the lowest value of PI relating to maximum pollution category C With this assumption, Naples' air quality data had been re-described and pollution index (PIs) is re-calculated. There is a significant difference between the results generated due to the maximum operating function-based pollution index and the synergetic effect of the pollutants-based pollution index. The results showed that the additive effects of pollutants strongly influenced the air quality evaluation.
If air pollutants are in the same category, additive effects can be expected and have the same effects on the health of human beings. This is relevant to all five pollutants considered in the modified pollution index. So, the result obtained through a modified pollution index was over estimated than the actual pollution index.
Air Quality Depreciation Index (AQDI), 2006 14 An index was formed that measures ambient air quality deterioration ranging between 0 and -10.
The index was applied on monitoring data of ten different monitoring stations of coal mining areas of Kobra Industrial belt (approx. 530 square km coverage) for one year. AQDI measures air quality deterioration considering the amalgamation of factors that affect human health, aesthetic, and biophysical attributes on an absolute scale of environmental quality, which is not dependent on NAAQS. The value function graphs, which are based on long-term health impacts, are used in the development of AQDI. A value of index; 0 denotes the most desired air quality i.e. no decline in air quality. While a value of index-10 represented worst air quality or maximum deterioration. The index is formulated as shown in Eq. 20.
... (20) Where, In TWi computation, a weight ranging from 1 to 5 was assigned subjectively to HWi, AWi, and BPIWi by a team of experts. One was assigned to the least important factor and five was assigned to the most important factor. The calculation of the composite weight of different pollutants and assigned values are represented in Table 13.This index represents even small changes in air quality in a more simple and meaningful way and like AQI it doesn't simply make comparisons to NAAQS to assess air quality.
The index can be used to prepare a periodic air quality deterioration map representing the possibility of environmental damages. The AQDI is not geographically specific and can be used forthe number of pollutants. The index can also beused for various applications and situations.
An Aggregate Air Quality Index, 2007 15 George Kyrkiliset. al.developed an index considering aggregate effects of pollutants and European standards for Athens city, the capital of Greece. In Athens, there were serious air pollution problems. They considered five criteria pollutants: PM10, CO, O 3 , SO 2 , and NO 2 . Two different models were adopted to develop AQI for the Athens area; one was the maximum air quality index (AQI) model and second was an aggregate air quality index (AQI) model. In Athens, four stations were selected and all five pollutants were monitored. In the first model, the maximum operating function-based air quality index was calculated for each station. Then the median of maximum operating function based air quality index of four stations is considered to be the entire city's AQI.Due to the limited availability of data, the index creator imposed the constraint that, for a given station, the maximum operating function-based AQI value must be based on a minimum of three pollutants, two of which must be PM 10 and NO 2 . These two pollutants were selected, as both pollutants were needed in the aggregate index calculation. For the city's atmosphere, PM10 is considered severe problematic and NO 2 concentration was very high in the city and also it acts as an ozone precursor.   0  0  25  50  25  12  5000  50  25  12  60  5000  50  Low  26  51  26  13  5001  51  26  13  61  5001  51  50  100  50  25  7500  100  50  25  120  7500  100  Medium  51  101  51  26  7501  101  51  26  121  7501  101  75  200  90  50  10000  200  90  50  180  10000  300  High  76  201  91  51  10001  201  91  51  181  10001  301  100  400  180 100  20000  400 180  100  240  20000 500 Very High a >100 >400 >180 >100 >20000 >400 >180 >100 >240 >20000 >500 All pollutants concentration is in μg/m 3 a Anindexvalue above100 was notcalculatedbutreportedas">100"

New Air Quality Index (NAQI), 2009 17
The USEPA AQI gives a general assessment of the quality of air; without considering the synergetic effects of air pollutants. So, to overcome this limitation, the authors calculated the factor analysis aided by principal component analysis (PCA) based new air quality index (NAQI). In the development of the NAQI, the deficiencies of the US EPA method tried to be incorporated. The criteria pollutants: PM 10 , CO, and SO 2 had been considered for determining NAQI and US EPA AQI for Delhi. In November, three additional parameters were monitored: NO 2 , O 3 , and NO. Total ten sites were selected as a sampling site covering the whole area of Delhi, out of ten sites; four sites were situated on the inner ring road, another four sites were situated on the outer ring road and the remaining two sites were situated on JNU Campus, situated in south Delhi. The 2003 -04 years were divided into four seasons: monsoon (July -September), post-monsoon (October -November), winter (December -March), and summer (April -June). A total of eighteen representative days per season were selected for the study. The measurements for air pollutants were carried out continuously for 24 hours for the two sites of JNU. While the remaining eight sites, measurements were done for a period of four hours each in the evening and the next day morning for four hours for the same site. Automatic electronic monitors are installed in the mobile air pollution laboratory to monitor the air pollutants.

Seasonal Effect on NAQI Values Winter Season
In winter, the highest index values were observed due to prevailing climatological conditions in north India and due to less dispersion of pollutants. High pressure in winter, in this region, is responsible for atmospheric stability, which results in more stagnant air masses and less circulation of air.

Summer and Monsoon Season
Insummer, index values were observed high due to extreme dust storms covering Delhi's atmosphere. During monsoon, comparatively, the value of NAQI isvery small due to changes in wind direction, wash out of air pollutants due to precipitation, and dispersion of air pollutants due to high wind velocities.

Post-Monsoon Season
Air quality is comparatively better than summer and winter with exception of October which is mainly due to lighting crackers due to festivals of Diwali and Dussehra.

PCA
Principal Component Analysis (PCA) is a widely used factor analysis method. The main aim of PCA is to consider the total deviation amongst the 'n' number of variables (subjects) in p-dimensional space by creating anew set of orthogonal and uncorrelated composite variates. Consecutive composite random variables will consider a small portion of the whole deviation to generate linear combinations. The first principal factor (composite) will have the largest alteration; the second principal component will have alteration larger than the third but smaller than the first, and so on. To develop the composite (overall) AQI, if the first few composites (principal components) have more than 60% of the total variance, then there are no requirements of taking more principal components (PCs). The principal components method can be applied by using the original values of variables (X j 's) (where j = 1, 2, 3, ..., n) or the standardized variables; Z j = x j / S j (measured as the deviations X j 's from the means and subsequently divided by standard deviations), or their deviation from their means (x j = X j -x ̅ ). The authors used standardized variables Z j represented as eq. 24. ... (26) The Eigenvalues associated with Piare denoted by λ i . For the determination of NAQI, the considered pollutant parameters are PM 10 , CO and SO 2 . And the considered meteorological variables are wind speed and direction, temp. and RH.
There was a consideration of a maximum of the first three components (P1 or P1 +P2 or P1 +P2+P3), having a total variance of 60% or more. These components were calculated on the conditions that the eigenvalue should be greater than one. The NAQI was calculated by the formula given as Eq. 27, after finding the principal components (PCs),.
Air Quality index= ... (27) Three principal components; P 1 , P 2 , P 3 are considered to have an aggregate variance of more than 60%. Since there are no guidelines available for characterization of the environment in terms of 'Good', 'Moderate', 'Unhealthy', etc. associated with the values of pollution indices determined from factor analysis employed in the present study, it is not possible to draw conclusive inferences about the air-quality in absolute terms. To overcome these limitations, an approach, which involves a comparison between factor analysis-based AQI and the USEPA-based AQI, had been adopted.

Pollutants Trends with Temperature
Correlation between pollutants concentration and temperature was studied, and it was established that ozone concentration increased with an increase in temperature and the maximum was noted during the afternoon. The highest Ozone concentration was observed during spring and summer because solar radiation is highest during that time. Ozone levels decreased from September to December, due to a decrease in ambient temperature. The concentration of Nitrogen Dioxide was decreased with an increase in ambient temperature. There was no significant comparison between major pollutants such as benzene and CO and temperature.

Correlation Analysis
A correlation between nitrogen dioxide and tropospheric ozone was found. There was a negative correlation coefficient = -0.85 between the two pollutants. A positive correlation coefficient of 0.85 between particulate matter and nitrogen dioxide. Positive correlations were also obtained between particulate matter and benzene, carbon monoxide, and benzene respectively. The analysis revealed that there was no strong correlation between carbon monoxide and particulate matter.

The Pollution Index Method
In this index assessment of air quality is done on basis of many pollutants critical in Italian urban areas. The index represented the air quality trend in a certain urban zone. Its calculation is the mean of the two most critical pollutants' sub-index values.
The index scale is ranged from 1 to 7; with increasing the number; associated risk is also increasing. The index's highest value represents the highest level of air pollution. The pollution index was calculated as per the formula represented as Eq. 28. The sub-indexes I 1 and I 2 were determined for the two utmost significant pollutants, presenting maximum value. The sub-indexes of the pollutants were calculated as per Eq. 29.
I IQA = (I 1 + I 2 ) / 2 ... (28) ... (29) I X = Sub -index of the X pollutant = Maximum concentration of X pollutant during an hour V rifx = Hourly limit value of X Pollutant General Air Quality Health Index (GAQHI), 2021 33 The index is constructed in Beijing, China, considering the aggregation of pollutants. In this index, it is tried to overcome the limitation of other indexing systems, and efforts are made to incorporate the cumulative effects of multiple pollutants' exposure. The index is based on the excess risk estimation, as shown in eq. 30 and eq. 31.
... (30) ... (31) Where, β p = exposure-response relationship coefficient of air pollutant pfor its expected health outcomes ER it = Excess risk in the ith city at time t x tp = Average 3 hrs. the concentration of pollutant p at time t ER max = Maximum value of ERit throughout the study period a = standardization coefficient varies between 0 to 10, a = 10 value is recommended GAQHI i = General air quality health index of the city i This index cannot be applied to all the cities is the limitation of this index. As β p value is different for different cities. This index is based on the impact of pollutants on human health and considers all major pollutants simultaneously. But this index cannot be used to show real-time air quality status.

Discussion
Up to 1970, many researchers tried to develop the air quality indexing system in different countries, considering only two to three air pollutants such as SPM or COH, CO, and SO2. In 1971, the oak ridge air quality index was developed in which five pollutants (photochemical oxidants, SO 2 , NO 2 , CO, and SPM) were considered. From 1972 to 1975, there was not much research on developing air quality indexing systems. Then in 1976, US EPA suggested an index which was known as pollutant standard index (PSI). This index is based on maximum operating function and is widely used by many countries. Again there was no significant development in the air quality indexing system from 1977 to 1992, and from 1994 to 1998. In 1993, two indexing systems were developed: i. Integral air pollution index (IAPI) which was based on maximum permissible concentration and developed for Russian cities, ii. A simple air quality index was developed for Finland which was based on linear interpolation and maximum operating function but considered WHO standards as breakpoint concentration. In 1999, US EPA modified the air quality index. The name changed from pollutant standard index (PSI) to air quality index (AQI). Instead of TSPM, PM 10 and PM 2.5 were incorporated in the calculation of AQI, and breakpoint values of pollutants were modified. In 1999, Swamee and Tyagi also developed an aggregate index.
After almost four years in 2004, two indexing systems: i. Revised air quality index (RAQI), and ii. A pollution index (PI) was developed. RAQI is based on entropy function and is more useful to predict long-term health impact and long-term air quality. The pollution index (PI) was developed for the city of Itlay. It is a modified version of US EPA AQI, in which European standards were considered in breakpoint values of pollutants. Murena et. al. developed the pollution index by considering maximum operating function as well as synergetic effects of pollutants. Based on the results obtained it was concluded that additive effects of pollutants strongly influenced the air quality evaluation. In 2006, the air quality depreciation index was developed which is based on value function graphs, and the index measures the deterioration in air quality. In 2007, two different air quality indexing methods were developed: i. An aggregate air quality index, and ii. CITEAIR's Common air quality index (CAQI). An aggregate air quality index was developed by George Kyrkilis et.al. for the Athens city, and also compared this index with US EPA-based AQI. Based on the comparison the researcher concluded that the aggregate index estimated more effectively the impacts of the pollutants to the population as contrasted to US EPAbased AQI.The CAQI under the CITEAIR project was developed for European cities which is based on the US EPA formula. This index also showed a significant difference between city background stations and traffic stations. In 2009, two indexing systems were developed: i. New air quality index (NAQI), and ii. Pollution index (PI). Principal component analysis (PCA) and factor analysis based new air quality index (NAQI) was developed in India. It was developed to incorporate the deficiencies of USEPA based AQI. The index developer also developed the NAQI with US EPA-based AQI. The comparison between the two indexing systems concluded that when NAQI and US EPA AQI values plotted against time, both index values followed the same trend lines, but when meteorological parameters were incorporated in NAQI, vast differences were observed between the two trend lines. The NAQI values were always less than the US EPA values, but NAQI values were in a wider range proved superiority.The sub-index of the pollution index is the ratio of hourly pollutant concentration to its corresponding standards. It was calculated by taking the average of the two most critical pollutants' sub-index values. From 2010 to 2017, there is a development of a fuzzy-based air quality indexing system. In 2021, a human health impact-based general air quality health index is developed in Beijing, China. But this index cannot be used universally. A fuzzy logic system is very suitable for addressing subjective environmental issues, which usually involve a degree of uncertainty. The fuzzy sets theory is very helpful in handling the uncertainty in the assessment of air quality. Keeping the importance of flexibility of the fuzzy sets theory in an imprecise environment and the decision-making process, many researchers tried to develop the fuzzy-based air quality indexing systems, which are reviewed and compiled in separate section 3.

Evolution of Fuzzy Based Air Quality Indexing
System: Air Pollution Monitoring Using Fuzzy Logic, 2010 20 The authors applied a real-time fuzzy logic system using Simulink to calculate AQI. The fuzzy logic control process consisted following steps: i. Defining the input variables -they used five pollutants as input variables; SO 2 , NO 2 , PM 10 , O 3 , and CO. In this step, pollutants are categorized into five groups; good, moderate, poor, very poor, and severe based on their respective standards, ii. Fuzzification: it is the process to transform crisp values into membership grades for fuzzy sets language. In the fuzzy logic process, fuzzification is the first stepin which the crisp inputs are converted to fuzzy inputs by determining the membership function for each point. iii. Fuzzy inference rules: in which, the information related to the given problem is expressed as a set of fuzzy inference rules. iv. Defuzzification: in the MATLABFLC module, to get a crisp output, the center of gravity method is used. The authors applied their suggested model to compute AQI and concluded that the model produce acceptable simulation outcomes. The weight of individual pollutants was determined through an analytical hierarchical process (AHP).
The researcher attempted to combine the analytical hierarchical process (AHP) and fuzzy synthetic evaluation model for risk assessment of air pollution. The main characteristics of fuzzy logic are its uncertainty, which can be quantified by fuzzy sets theory. in terms of pollution index (PI) and exposure index (EI) respectively. The FAQHI matrix considered the pair-wise comparison between the PI matrix and EI matrix. For defining the uncertainty range, α cut was introduced in pollution index matrix, exposure index matrix, and FAQHI matrix and all three matrices were converted to fuzzy pollution index matrix (PIf), fuzzy exposure index matrix (EIf), and FAQHIf respectively. The PIf, EIf, and FAQHIf matrix converted to crisp comparison (PI', EI', and FAQHI') matrix using eq. 32.
Where, a iju and a ijl = upper and lower value of comparison element, The software MATLAB 7.10.0 was used to calculate the eigenvalues and eigenvectors from crisp matrices. Normalization of eigenvectors was done to determine the local weights of individual parameters, represented as PI w , EI w , and FAQHI w . Local weights are applied to determine the aggregate weights of different parameters. The triangular fuzzy membership function was used to determine the fuzzy membership function. After establishing the membership degree matrix (R), the defuzzification process was done. The advantage of this index is that it considered multi-pollutant parameters with subjective parameters. The index is helpful to estimate the health impact considering air quality as well as other local conditions.
Air Quality Indices using Fuzzy Logic: Feasibility Analysis, 2016 21 The researchers collected the air pollutant concentrations at industrial, residential, and sensitive areas of Bangalore. Three pollutants; RSPM, NO 2 , and SO 2 have been collected over six sites of Bangalore. Out of these, three sites were in the industrial zone, two sites were in a residential zone, and one sitewas in a sensitive zone. The data regarding pollutants concentration were obtained from, "Karnataka State Pollution Control Board (KSPCB), Bangalore" for the duration of five years; 2008 -2013. The Air Quality Indexes were calculated through linear interpolation formula and maximum operating function.The authors used a real-time fuzzy logic system with Simulink to compute AQ Iand reported that this system gives agreeable results. This system can also work under the continuous working mode, efficiently.
The authors concluded that the AQI model based on fuzzy rulesis a powerful tool to suggest to human beings about outdoor activities in a particular area. They also observed that the results obtained through the fuzzy approach were more efficient than the linear interpolation approach.

Fuzzy Inference System Based Air Quality
Indices, 2017 22 The authors used a Mamdani fuzzy inference system-based model to assess the air quality of Chennai. They considered three pollutants; SO 2 , NO 2 and RSPM. Data were collected from the Tamilnadu SPCB,Chennai for the year 2007 to 2015.
Four sampling stations, two in a commercial area, one in an industrial area, and one in a residential area were selected. The authors determined the membership function and fuzzy inference rules based air quality index. It was concluded that the results obtained through the fuzzy rules system were better than the results obtained through other methods.

Discussion
The AQI system based on fuzzy logic has been evaluated since 2010. The fuzzy-based AQI is more reliable than the other methods. Out of all the above describing methods, fuzzy synthetic evaluationbased AQI and fuzzy air quality health index are more powerful tools to describe the air quality.

Air Quality Indexing Systems Existing in India
In India, presently two indexing systems prevail, i. Air Quality Index for India, and ii. National Air Quality Index, India. Both indexing systems are based on the US EPA formula and maximum operating function as shown in Eq. 34. As indicated in Eq. 33, for pollutant concentration (Cp), the sub-index (Ip) is determined using the "linear segmented concept." Where, Ip = Sub-index of pollutant P AQI=Max (I P ) ... (34) Where, P = 1,2,3………, n; denotes n pollutants Because the maximum operating function is devoid of eclipsing and ambiguity, it is used. Due to simplicity in maximum operating function, it is adopted by many countries. Both the indexing systems are studied in-depth and summarized as sub-section 4.1 and 4.2.  34 The air quality index for India was developed by IITM, Pune with the assistance of MoES as part of the SAFAR projectin August 2010. The SAFAR project can predict the air quality for the next three days. This indexing system has been implemented in four cities: Delhi, Mumbai, Pune, and Ahmedabad. The SAFAR -AQI system considered five pollutants: PM 2.5 , PM 10 , NO 2 , CO, and O 3 . The index range is from 0 to 500 and is distributed into six categories, from good to severe. The AQI categories and pollutants breakpoint values are shown in Table 18.

National Air Quality Index (NAQI), 2014 2
For the development of NAQI, CPCB has assigned the work to IIT -Kanpur. The index was launched in October 2014. An AQI's goal is to swiftly communicate news about real-time air quality. Eight Pollutants; PM 2.5 , PM 10 , SO 2 , NO 2 , O 3 , CO, NH 3 , and Pb having short-term norms have been studied. A scientific basis for meeting air quality standards, as well as dose-response relationships for specific pollutants, has been created and used to determine breakpoint values for each AQI class. Table 19 shows the air quality index categories with break point values of pollutants.

Discussion
The study of existing air quality indexing systems in India revealed that both indexing systems are based on maximum operating function and linear segmented principles. SAFAR-IITM AQI is implemented only in four metropolitan cities and considered only five pollutants. While NAQI has been adopted by CPCB and implemented in the whole country. During the development of NAQI eight criteria pollutants having short-term impacts have been considered. And the breakpoint values of the pollutants have been decided based on the impact of the pollutants on human health or the breakpoint values adopted by the US EPA.

Conclusion
From all the indexing systems listed above from 1966 to 202021, it can be concluded that there are always some draw backs and no system is entirely perfect. Attempts should be made to evolve the indexing system for the region because each area is different geographically and the index which may apply to one area may or may not apply to another. All the characteristics for the area should be carefully considered, major pollutants should be considered and only then the system should be finalized. An ideal indexing system is a system that is expandable, unambiguous, free from eclipsing, and understandable by a layman. Indexing should not be based on the maximum operating function, as this system does not reflect that whether more than one pollutant exceeded the standards or not. The ideal indexing system should consider the aggregation and synergetic effects of pollutants. It should be based on community data available from the local monitoring system, an arrangement shall be made such that in hazardous conditions an alarm is generated so that citizens are made aware.
Integration of all the above-stated indexes can be done to develop a global index, which not only helps to compare air quality but also protect the citizens from deteriorating air quality. When compared with other methods, the AQI system based on fuzzy logic is a more powerful instrument that produces more consistent findings. But till 2017, there is no development of a fuzzy-based AQI system in which fine particulate matter (PM 2.5 ) has been considered. So, there is a need to develop the fuzzy-based air quality indexing system considering PM 2.5 as a pollutant with other air pollutants.