Air quality assessment using weighted interval type-2 fuzzy inference system

Accepted Manuscript Air quality assessment using weighted interval type-2 fuzzy inference system

Joy Debnath, Debasish Majumder, Animesh Biswas PII: DOI: Reference:

S1574-9541(18)30035-9 doi:10.1016/j.ecoinf.2018.06.002 ECOINF 863

To appear in:

Ecological Informatics

Received date: Revised date: Accepted date:

15 February 2018 13 May 2018 7 June 2018

Please cite this article as: Joy Debnath, Debasish Majumder, Animesh Biswas , Air quality assessment using weighted interval type-2 fuzzy inference system. Ecoinf (2018), doi:10.1016/j.ecoinf.2018.06.002

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ACCEPTED MANUSCRIPT

Air quality assessment using weighted interval type-2 fuzzy inference system

Joy Debnath1 [email protected], Debasish Majumder2 [email protected] and Animesh Biswas 3,* [email protected] 1

Department of Mathematics, JIS College of Engineering, India

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Department of Mathematics, University of Kalyani, India

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Corresponding author.

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Abstract. This paper presents an integrated model based on interval type-2 fuzzy reasoning approach and interval type-2 fuzzy analytic hierarchy process for assessment of air quality in urban areas. In the proposed model, interval type-2 fuzzy reasoning approach is employed to determine impacts of different air pollutants to describe complex relationship between air pollutants and air quality index by considering individual weights of different air pollutants through the aggregation of toxicological impacts and concentration level of different air pollutants using interval type-2 fuzzy analytic hierarchy process. The proposed approach is advantageous over its counterparts to model the inter-personal and intra-personal uncertainties involved in classification of air quality index. Finally, the developed air quality assessment model is applied on the historical data set collected from ambient air quality monitoring stations operating near by the Victoria memorial, in Kolkata Metropolitan area. The study shows that the air quality index increased significantly during the festive season due to extensive fireworks in those areas.

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Keywords: Air quality assessment, interval type-2 fuzzy logic system, interval type-2 fuzzy analytic hierarchy process; air quality index. 1. Introduction

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In the era of expanding economies and urbanization, air pollution becomes one of the most impenetrable environmental challenges that almost all countries around the world are facing today. Due to the presence of harmful or poisonous substances in the air, the environment is becoming polluted day by day. As a consequence the earth is gradually becoming unhygienic for the living beings. Over the decades, numerous studies established the fact that exposure to air pollution affects human health, specially, cardiovascular diseases, respiratory diseases, etc. [7]. As per the estimation of World Health Organization (WHO) urban air pollution (UAP) in developing countries has resulted in more than 2 million deaths per annum along with various cases of respiratory illnesses [5, 6, 41, 42]. People living in India are facing an apocalypse right now due to unhealthy air, killing 1.8 million Indians every year which includes 1,250,296 deaths due to household air pollution and 621,137 deaths due to ambient air pollution and costing the economy an estimated 3% of GDP [10]. Most of these deaths are due to non-communicable diseases caused by pollution such as acute lower respiratory disease (ALRI); chronic obstructive pulmonary disease (COPD), lung cancer; is chaemic heart disease (IHD) and stroke (see Table 1). The report shows that deadly air pollution is not now confined only to Delhi-NCR (National Capital Region) or even to India’s

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metros - it becomes a national problem. Virtually no place in India, except few places in southern India which complied with National Ambient Air Quality (NAAQ) standards only, is complying with WHO and NAAQ standards, and the entire nation is experiencing a public health crisis due to high air pollution levels [10]. Due to the exposure of particulate matter size equal to or less than 10 micron (PM10 ), respiratory and cardiovascular diseases are aggravated and may trigger carcinogenic effects. Breathing air with a high concentration of carbon monoxide (CO) mainly indoors or in other closed environments can cause dizziness, confusion, unconsciousness and death. On breathing air containing ozone (O 3 ), is particularly very harmful for those who are already suffering from respiratory and asthmatic problems. Children are at greatest risk from exposure to air containing O 3 because their lungs are still developing and they are more likely to be active outdoors when ozone levels are high. Longer exposures to elevated concentrations of nitrogen di oxide (NO2 ) may cause the development of asthma and potentially increase susceptibility to respiratory infections. Exposure to sulfur di oxide (SO2 ) can affect the respiratory system, especially for people with asthma. The 2017 State of Global Air report, published by the Health Effects Institute, shows that air pollution-related deaths in India rose by almost 150% in between 1990 and 2015 surpassing China as the deadliest in the world [15]. Table 1

Number of deaths

Household air pollution

ALRIa

COPDb

102,149

409,172

Lung cancerb

IHDb

Strokeb

Total

24,048

395,160

319,767

1,250,296

26,334

249,388

195,001

621,137

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Air pollution

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Burden of disease due to air pollution in India.

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Ambient air pollution 39,914 110,500 a Age group includes less than 5 years old. b Age group includes 25 years and above.

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1.1. Air Quality Index: Indian Scenario

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India’s growing pollution crisis is becoming so severe in the present scenario that it is very much essential to develop proper air quality monitoring systems for receiving timely information about the changes of different pollutants in the air. It has already been proved that increasing public awareness of air quality and the health impact of various air pollutants is a fundamental step in reducing air pollution and improving public health. Thus, it is important to put up information on air quality in public domain using simple linguistic terms that is easily understandable by common people to increase awareness in society. Air Quality Index (AQI) is a tool for informing people about air quality status in simple linguistic terms. It transforms complex air quality data of various pollutants into a single number (index value) characterizing linguistic hedges and colours. The standard of AQI varies with the nations. Different countries adopted different air quality assessment system [38]. In India, National Air Monitoring Programme (NAMP) was introduced by the Central Pollution Control Board (CPCB) along with State Pollution Control Boards covering 240 cities of the country with objectives to monitor and regulate the standard spectrum of air pollutants, including tiny, dangerous particles known as particulate matter size equal to or less than 2.5 micron (PM2.5 ), O3 , CO, NO2 , and others [8, 9]. In Kolkata, during the study period the annual average concentration of the pollutants PM10 was 75.09 𝜇𝑔/𝑚3 , CO was 1.06 𝑚𝑔/𝑚3 , O 3 was 8.77 𝜇𝑔/𝑚3 , NO2 was

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39.94 𝜇𝑔/𝑚3 , SO 2 was 5.7 𝜇𝑔/𝑚3 . The ministry of environment, forests & climate change outlined the AQI, as ‘One Number- One Colour-One Description’ for the common man to get informed about the air quality within his vicinity as a continuation of the initiatives under Swachh Bharat Mission envisioned by the Hon’ble Prime Minister. There are six AQI categories, viz., Good, Satisfactory, Moderately polluted, Poor, Very Poor, and Severe. Each of these categories is decided based on ambient concentration values of air pollutants and their likely health impacts (known as health breakpoints). In the present study the AQI is calculated using Indian AQI (IND-AQI) assessment method specified by CPCB and is considered as the standard method for determining AQI in India. The detail mathematical derivation of IND-AQI [14] evaluation process is described in Appendix I. Despite of the fact that more than 60 cities are presently under the programme, exact data collection method remains unclear [4]. Moreover, one of the common mistakes, which often mislead, is the biasness towards a particular activity or environment and representing city air quality based on single station value or single hour data. As per international guidelines, correct way to identify one AQI for a city is to consider different microenvironments, and develop the methodology for the same based on scientific knowledge. It requires a systematic approach to understand pollution levels regularly and take action accordingly. To ass ist people in keeping fit and improving the quality of their lives, the development of a robust, accurate, yet simple, air quality monitoring system is highly desirable. 1.2. Fuzzy Air Quality Index

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Over the last few years, numerous indices have been proposed to evaluate the quality of the air [19, 21, 37]. The traditional air quality assessment used a simple digital indicator as a dividing line each side of which indicates two different levels of pollution, and hence unable to capture the haziness of the boundaries of the classes. The evaluation of air quality, which is aimed at determining "the degree of pollution,” is a fuzzy concept, and it is difficult to find clear boundaries; thus, the evaluation classification standard of pollution levels should also be fuzzy [43]. Therefore, fuzzy logic appeared as a suitable tool for air quality assessment [1, 2, 12, 13, 46], and many air quality indices based on fuzzy systems have been proposed [12, 22, 34] in the past. Several other methodologies, viz., artificial neural networks [11, 28] associative memories [44], support vector machines [20, 31, 33, 35, 39] factor analysis [3], are also applied to analyze environmental pollution to increase accuracy of the results. However, due to lack of reasoning processes, all these models suffers from the drawback to handle properly the inherent uncertainty, subjectivity and the relative importance between the pollutants that are implicit in air quality parameter behaviors, abstaining evaluations process from right assimilation [30]. A fuzzy reasoning approach combining with analytic hierarchy process (AHP) provides a better air quality assessment process as it emphasizes on the pollutants with major health impacts and also, it increases the effectiveness of the assessment to generate more accurate evaluations that can be reflected in an AQI. However, in such approaches the main focus is on how to explain a behavior of a system linguistically or qualitatively [36]. The membership functions of the employed fuzzy sets are used to handle uncertainty or express vague concepts. However, human perceptions are not precise and vary over time; one’s intuitions and cognition of concept highly depends on the context, domain knowledge, individual sense, etc. [29]. Moreover, different individuals may perceive the same concept differently [32]. Although, as pointed out by Mendel [24, 27], the use of type-2 fuzzy sets (T2 FSs) is advantageous over type-1 fuzzy sets

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(T1 FSs), as type-1 membership functions are totally crisp whereas the type-2 membership functions are fuzzy themselves [25]. This eventually enables the fuzzy model to capture both inter personal and intra personal uncertainties in the meanings of the words those are used in the antecedents and consequents of rules. The aim of this paper is to propose a methodology that combines the inherent strengths of interval type-2 fuzzy inference system (IT2FIS) and interval type-2 fuzzy AHP (IT2FAHP) to capture the inter personal and intra personal uncertainties involved in the process of air quality assessment. Interval type-2 fuzzy reasoning process is used to determine impacts of different air pollutants to describe complex relationship between air pollutants and AQI. In the present study, the proposed model is applied for analyzing air quality of Kolkata and its metropolitan areas, where pollutants are assessed for establishing an indicator for good or bad air quality, generally. The rest of this paper is organized by incorporating a brief demographic description on the study area along with the air pollutants and their main characteristics for air quality assessment are explained in Section 2. Section 3 presents the proposed methodology for air quality assessment. In section 4, a case study is performed using real time air quality data in order to validate the proposed methodology, where the result is compared with other existing methods in literature to establish efficiency of the proposed model. Finally, Section 5 provides conclusions and few future research directions.

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2. Study Area

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Kolkata, previously known as Calcutta is the capital of a state, West Bengal, and is well known as the cultural capital of India. The Kolkata Metropolitan Area, located on the east bank of the holy river, Ganges (also known as Hooghly) and is spread over 1,886.67 km2 , is the educational hub of Eastern India. Moreover, the Port of Kolkata, the oldest operating port in India, and its only major riverine port established Kolkata as the most important commercial and financial hub of East and North-East India and home to India's oldest, and also India's secondlargest stock exchange, the Calcutta Stock Exchange. This leads to a lot of migrants from other states over the year. In 2017, the population of Kolkata metropolitan area is estimated to be 14.7 million which ranked Kolkata 3rd most populous metropolitan area in India. However, due to the recent urban boom, ever- increasing traffic, economic expansion, industrialization, and higher levels of energy consumption in the Kolkata metropolitan areas, air pollution, among the several other environmental issues, is affecting seriously its environment as well as public health. According to a very recent study, jointly conducted by the British Deputy High Commission, UKAID and Kolkata Municipal Corporation, reveals that air pollution level in Kolkata is highest in the country. Despite of the fact that New Delhi is reeling under severe air pollution, Kolkata has not only touched the country's capital city but have also surpassed the city quite a few days in terms of air pollution. A recent report published by WHO claims that Kolkata is the fourth most polluted ‘megacity’ in the world, just ahead of Mumbai, in terms of coarse dust particles - a byproduct of construction activities; while the report has placed Delhi at the top of the list, Cairo and Dhaka occupy the second and third positions respectively. According to the report the PM 10 level in Kolkata during this period was nearly seven times the limit prescribed by WHO. If one considers the Indian safety limits, which is less stringent, pollution level of PM10 in Kolkata is more than double. In addition, NO 2 levels exceed by close to two times. The major sources of air pollution include automobile exhausts which is about 50%, industrial emissions that is almost 48% and the

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rest 2% from cooking. The study also finds that around 70% of the city's 15 million inhabitants suffer from some form of respiratory problems caused by air pollution. However, the ambient air quality is monitored at three locations in Kolkata by National Environmental Engineering Research Institute (NEERI) under NAMP of CPCB (see Fig. 1). West Bengal State Pollution Control Board (WBSPCB) is also monitoring ambient air quality at large number of monitoring stations in Kolkata. Although, it is essential to have a robust monitoring of air quality across the country to know information in real time and using the data to arrive at strategies that would protect public health and reduce pollution levels. The strategies to reduce pollution should become an action plan which is time bound and has targets and penalties.

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3. Methodology

Development of IT2FIS for AQI assessment

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3.1.

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In this section, an integrated model based on an IT2FIS and IT2FAHP is proposed in order to provide good assessment of AQI. In the first phase, an IT2FIShas been developed for processing of air quality parameters based on their permissible limits. Then, based on the negative impact of different air quality parameters, weights are derived using IT2FAHP. Finally, the weights are used in the aggregation process of fuzzy reasoning; significantly affect the final AQI according to the air quality parameters with higher importance [30]. The proposed methodology has been described in the following subsections. Fig. 2, shows the architecture of the proposed integrated model used for air quality assessment.

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The building process of IT2FIS for AQI assessment is basically fuzzy system modeling, enabling it in describing the complex relationship of various air pollutants with the AQI using interval type-2 fuzzy logic which is advantageous over its counterpart type-1 fuzzy logic in capturing linguistic uncertainties-both inter personal and intra personal. The development process can be broken down into three phases, such as input-output parameters selection, determination of fuzzy classifier, rule-base generation.

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3.1.1. Input-output Parameter Selection The AQI assessment is based on air pollutant concentration levels, which causes negative effects in public health by their toxicity [40]. Depending on region and climatic conditions, the contribution of various air pollutants in AQI differs. However, national problem like air pollution needs to be addressed equally across the country. As per the guideline of NAMP, the three air pollutants viz., SO 2 , NO2 and PM10 , have been identified for regular monitoring across the country. Moreover, WBSPCB tracks air quality of Kolkata and it surrounding area, by monitoring of O 3 , CO along with other three air pollutants. For this reason, the five most influential air pollutants in Indian scenario, viz., PM10 , NO2 , O3 , CO, SO 2 , are considered as the input parameters in the proposed model for the assessment of air quality in terms of AQI, the output parameter. The impacts of these five pollutants on human health are shown in Table 2.

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Fig. 1. Location of the monitoring stations in Kolkata metropolitan area used for air quality measuring.

ACCEPTED MANUSCRIPT Data and information collection

Construction of fuzzy pair-wise comparison matrices for the air pollutants using IT2 fuzzy numbers

Input-output parame te r se le ction

Determination of fuz z y classifier

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Conversion of IT2 fuzzy numbers into equivalent defuzzified values

Development of fuzzy rule base

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Fuz z ification of inputs using IT2 FSs present in the antecedents of each rule

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Determination of firing intervals for each rule

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De te rmination of weighted firing intervals for e ach rule

Determination of centroids ofIT2 FSs in the consequent part of each rule using KM algorithm

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Evaluation of AQI by weighted IT2 fuzzy reasoning

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Construction of crisp pair-wise comparison matrices at different levels using defuz z ifie d values

Weight evaluation

Designing of IT2 MFIS

Ide ntification of influential air pollutants

Combining firing interval of each rule with the centroid of corresponding consequent IT2 FSs using center-of-sets type reducer

Defuzzification

Weighted AQ I

Fig. 2.Flowchart of the proposed model.

Is comparison matrix consistent?

Yes Evaluation of fuzzy weights from fuzzy comparison matri x using geometric mean method Defuzzification of fuzzy weights Normalization of crisp weights

No

ACCEPTED MANUSCRIPT Table 2 Air quality parameters and their impacts on human health. Air quality parameters

PM 10 is a complex mixture of microscopic particles and liquid droplets that are so small that, once inhaled, these particles settles in the upper respiratory tract, often go very deep inside our lungs and penetrates the pulmonary alveoli, and some may even get into our bloodstream. As a result, it aggravates respiratory and cardiovascular diseases and may trigger carcinogenic effects. CO is a colorless, tasteless, odorless highly toxic gas, wh ich in prolonged exposures can be fatal. Breathing air with a high concentration of CO reduces the amount of o xygen that can be transported in the blood stream to critical organs like the heart and brain. At very high levels, mainly indoors or in other closed environments and not likely to occur outdoors, CO can cause dizziness, confusion, unconsciousness and death. However, the people already have a reduced ability for getting o xygenated blood to their hearts are especially vulnerable to the effects of CO when exercising or under increased stress, even for a short-term exposure to outdoors with elevated CO. O3 is a very o xidizing pollutant that is toxic to hu mans and vegetation because it o xidizes biological t issue .Ground level or "bad" ozone is not emitted direct ly into the air, but is formed by chemical react ions between oxides of nitrogen (NOx) and volatile organic co mpounds (VOC) in the presence of sunlight. On breathing air containing o zone, is particularly very harmful for those who are already suffering fro m respiratory and asthmatic problems. Children are at greatest risk fro m exposure to air containing ozone because their lungs are still developing and they are more likely to be active outdoors when ozone levels are high, which increases their exposure. Children are also more likely than adults to have asthma. NO2 is one of a group of gases called nitrogen oxides (NOx). Exposure to the air with a h igh concentration of NO2 , even for a short period of time, can exaggerate various respiratory d iseases, leading to respiratory symptoms, like coughing, wheezing or difficulty in breathing. Longer exposures to elevated concentrations of NO2 may contribute to the development of asthma and potentially increase susceptibility to respiratory infections. People with asthma, as well as children and the elderly are generally at greater risk for the health effects of NO 2 . SO2 is one of a group of highly reactive gases called sulfur o xides (SO X). Exposure to SO2 can affect the respiratory system, especially for people with asthma.

100 𝜇𝑔/𝑚3

2 𝑚𝑔/𝑚3

100 𝜇𝑔/𝑚3

SO2

80 𝜇𝑔/𝑚3

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PM 10

Permissible limit

Impact on human health

80 𝜇𝑔/𝑚3

3.1.2. Determination of fuzzy classifier As per the governmental standards, a sub- index, based on the concentrations of air pollutants and likely health impact, is designed for each of the five most influential air pollutants as well as the AQI, viz., Good, Satisfactory, Moderate, Poor, Very Poor, and Severe. As per the Indian standard, Classification levels for each of the five most influential air quality parameters and the AQI are described in Table 3. However, in order to build an integrated fuzzy AQI evaluation model, it is important to quantify the negative impacts of each air pollutant depending on its concentration level. This process of quantification predominantly suffers from both intra-

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personal and inter-personal uncertainties associated with different linguistic terms those are used to describe various classifiers. In order to capture these two types of uncertainties, the fuzzy classifiers are described by interval type-2 membership functions which, unlike type-1 membership functions which transform the input measurements into a crisp value within [0, 1], transform the input measurements into an interval within [0, 1]. As there is no such rule for building membership functions, they are built based on the problem context (triangular, trapezoidal and Gaussian). In the present study, trape zoidal membership functions are used for representing the Good and Severe concentration to be assessed; for intermediate levels of concentration, viz., Satisfactory, Moderate, Poor, Very Poor, triangular membership functions are used. A trapezoidal type IT2 FS, denoted by 𝐴̃, is characterized as (see Fig. 3)

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𝐴̃ = {((𝑥, 𝑢) , 1): ∀𝑥 ∈ 𝑋, ∀𝑢 ∈ 𝐽𝑥 ⊆ [0,1]}

(1)

where footprint of uncertainty (FOU) of 𝐴̃, denoted by 𝐹𝑂𝑈 (𝐴̃), is defined as

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𝐹𝑂𝑈 (𝐴̃) = {(𝑥, 𝑢) : 𝑢 ∈ 𝐽𝑥 ⊆ [0,1]}

(2)

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and the upper membership function, denoted by 𝜇̅𝐴̃ , and lower membership function, denoted by μ ̃ , associated with 𝐹𝑂𝑈 (𝐴̃) are defined as follows: 0 𝛼 ( 𝑥−𝑎𝑈 ) ( 𝑏 𝑈 −𝑎𝑈 )

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{

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𝜇̅𝐴̃ (𝑥; 𝑎𝑈 , 𝑏𝑈 , 𝑐𝑈 , 𝑑𝑈 , 𝛼) =

, 𝑎𝑈 ≤ 𝑥 < 𝑏𝑈

𝛼 , 𝑏𝑈 ≤ 𝑥 < 𝑐𝑈 𝛼 ( 𝑥−𝑑𝑈 ) , 𝑐 ≤ 𝑥 < 𝑑𝑈 ( 𝑐 𝑈 −𝑑𝑈 ) 𝑈 0

, 𝑥 > 𝑑𝑈

0,

𝑥 < 𝑎𝐿

( 𝑥−𝑎𝐿 )

𝛽(

𝜇𝐴̃ (𝑥; 𝑎𝐿 , 𝑏𝐿 , 𝑐𝐿 , 𝑑𝐿 , 𝛽) =

, 𝑥 < 𝑎𝑈

𝑏 𝐿 −𝑎𝐿 )

, 𝑎𝐿 ≤ 𝑥 < 𝑏𝐿

𝛽 , 𝑏𝐿 ≤ 𝑥 < 𝑐𝐿 ( 𝑥−𝑑𝐿 )

𝛽 (𝑐 {

𝐿 −𝑑𝐿 )

0

(3)

(4)

, 𝑐𝐿 ≤ 𝑥 < 𝑑𝐿 , 𝑥 > 𝑑𝐿

where 𝑥 is the input (pollutant), 𝑎𝑈 , 𝑏𝑈 , 𝑐𝑈 , 𝑑𝑈 , 𝛼 are the parameters of upper membership functions and 𝑎𝐿 , 𝑏𝐿 , 𝑐𝐿 , 𝑑𝐿 , 𝛽 are the parameters of lower membership functions which varies according to the defined limits of each pollutant (see Table 3). The triangular membership functions can be represented as trapezoidal membership functions where𝑏𝑈 = 𝑐𝑈 and 𝑏𝐿 = 𝑐𝐿 . Table 4 describes the membership function corresponds to each air quality parameter classification.

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Fig.3.Trapezoidal type IT2 FS.

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Table 3

Satisfactory 51-100 41-80 51-100 1.1-2.0 41-80 51-100

Classification levels Moderate Poor 101-250 251-350 81-180 181-280 101-168 169-208 2.1-10 10-17 81-380 381-800 101-200 201-300

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PM 10 (24 hr.) (𝜇𝑔/𝑚3 ) NO2 (24 hr.) (𝜇𝑔/𝑚3 ) O3 (8 hr.) (𝜇𝑔/𝑚3 ) CO (8 hr.) (𝑚𝑔/𝑚3 ) SO2 (24 hr.) (𝜇𝑔/𝑚3 ) AQI

Good 0-50 0-40 0-50 0-1.0 0-40 0-50

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Environmental parameters

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Classification levels for air quality parameters and AQI.

Very Poor 351-430 281-400 209-748 17-34 801-1600 301-400

Severe 430< 400< 748< 34< 1600< 401-500

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3.1.3. Rule-base generation In an IT2 FIS, the complex or nonlinear relationship between systems variables are described by a set of fuzzy IF-THEN rules, called fuzzy rule base, based on expert’s judgment [15]. The qualitative descriptors of input and output variables, as described in Eq. (1) and Eq. (2), are useful in handling subjectivity as well as both types of uncertainty - intra-personal and interpersonal involved in rule generation. In air pollution, it is important to identify all types of possible scenarios, presenting different contaminant concentrations that can be considered harmful for health. Thus, in an IT2 FIS with 𝑚 inputs and one output, if 𝑝 qualitative descriptors are used to cover input/output domains, then the number of all possible rules those can be defined is 𝑁 = 𝑝 𝑚 [16]. In the present study, for each of the five air pollutants as well as for AQI, six classification levels are considered and thus the number of all possible rules is 𝑁 = 66 . However, the system robustness depends on the number of rules - high number of rules leads to an immense computational burden; whereas, a low number of rules might not be able to reflect correctly all air quality situations. In the present study, at first the maximum and minimum concentration level of each pollutant over the study period is identified. On the basis of that range of concentration levels, all possible classifiers corresponding to each pollutant are recognized. Finally, all possible combination of those recognized classifiers are used to derive the rules. It has been found that the number of recognized classifiers are 4 for PM10 (viz., Good, Satisfactory, Moderate and Poor), 4 for CO (viz., Good, Satisfactory, Moderate and Poor), 1 for O 3 (viz., Good), 4 for NO 2 (viz., Good, Satisfactory, Moderate and Poor) and 1 for SO 2 (viz., Good). Thus, all possible combination of these recognized classifiers results in 4 × 4 × 1 × 4 × 1 = 64 rules. These 64 rules, as presented in Table 5, are the optimum set of rules required for the present study. Thus a set of N = 64 inference rules has been identified as enough to have good results; no significantly better response has been observed with more rules.

ACCEPTED MANUSCRIPT Table 4 Parameters of the membership functions corresponding to inputs and out put of the IT2 MFIS. Parameters of IT2 FSs (Trapezoidal) Classification levels Good Satisfactory [0,0,25,75;1] [25,75,75,175;1 ] PM 10 (24 hr.) [0,0,21,71;0.8] [29,75,75,171;0.8 ] [0,0,20,60;1] [20,60,60,130;1 ] NO2 (24 hr.) [0,0,16,56;0.8] [24,60,60,126;0.8 ] O3 [0,0,25,75;1] [25,75,75,134;1 ] Input (8 hr.) [0,0,21,71;0.8] [29,75,75,130;0.8 ] CO [0,0,0.5,1.5; 1] [0.5,1.5,1.5,6; 1] (8 hr.) [0,0,0.1,1.1; 0.8] [0.9,1.5,1.5,5.6; 0.8] SO2 [0,0,20,60;1] [20,60,60,230;1 ] (24 hr.) [0,0,16,56;0.8] [24,60,60,226;0.8 ] [0,0,25,75;1] [25,75,75,150;1 ] Output AQI [0,0,21,71;0.8] [29,75,75,146;0.8 ] ir pollution parameters

M oderate [75,175,175,300;1] [79,175,175,296;0.8] [60,130,130,230;1] [64,130,130,226;0.8] [75,134,134,188;1] [79,134,134,184;0.8] [1.5,6,6,13.5;1] [1.9,6,6,13.1;0.8] [60,230,230,690;1] [64,230,230,596;0.8] [75,150,150,250;1] [79,150,150,246;0.8]

D E

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E C

Poor [175,300,300,390; 1] [179,300,300,296;0.8] [130,230,230,340; 1] [134,230,230,336;0.8] [134,188,188,478; 1] [138,188,188,474;0.8] [6,13.5,13.5,25.5; 1] [6.4,13.5.13.5,25.1;0.8] [230,690,690,1200;1] [234,690,690,1196;0.8 ] [150,250,250,350; 1] [154,250,250,346;0.8]

Very Poor [300,390,390,470;1] [304,390,390,466; 0.8 ] [230,340,340,460;1] [234,340,340,456; 0.8 ] [188,478,478,1018;1 ] [192,478,478,1014;0.8] [13.5,25.5,25.5,42.5;1 ] [13.9,25.5,25.5,33.6;0.8] [690,1200,1200,2000;1] [694,1200,1200,1996; 0.8] [250,350,350,450;1] [254,350,350,446; 0.8 ]

C S

I R

M

A

U N

T P

Severe [390,470,500,500;1] [394,474,500,500;0.8] [340,460,500,500;1] [344,464,500,500;0.8] [478,1018,1200,1200; 1] [482,1022,1200,1200; 0.8 ] [25.5,42.5,50,50; 1] [25.9,42.9,50,50; 0.8] [1200,2000,2400,2400;1] [1204,2004,2400,2400;0.8] [350,450,550,550;1] [354,454,550,550;0.8]

ACCEPTED MANUSCRIPT Table 5 Rule base of the proposed model Rule no. Rule 1

:

Rules

:

If PM10 is Good and NO2 is Good and O3 Good and CO is Good and SO2 is Good then

Rule 2

:

Rule 3

:

Rule 4

:

Rule 5

:

3.2.

T

IP

CR

: :

If PM10 is Poor and NO2 is Poor and O3 Good and CO is Poor and SO2 is Good then

US

AQI is Severe.

AN

Rule 64

AQI is Good. If PM10 is Good and NO2 is Good and O3 Good and CO is Satisfactory and SO2 is Good then AQI is Good. If PM10 is Good and NO2 is Good and O3 Good and CO is Moderate and SO2 is Good then AQI is Satisfactory. If PM10 is Good and NO2 is Good and O3 Good and CO is Moderate and SO2 is Good then AQI is Satisfactory. If PM10 is Good and NO2 is Satisfactory and O3 Good and CO is Good and SO2 is Good then AQI is Good.

Weight evaluation process using IT2FAHP

AC

CE

PT

ED

M

The second phase of the proposed methodology is assigning a weight to each air pollutant using a priority analysis, based on an IT2F AHP which is advantageous over its counterparts AHP, Type-1 Fuzzy AHP (T1 FAHP) [2], in capturing intra personal and inter-personal uncertainties inherently present in weighting process. Each city has a different contemplation about the most challenging pollutant as the topography, sources of pollution and environmental obstacles are different in each place. In the present study, the Kolkata Metropolitan area has a distinguishing geography (see Section 2) that directly influences the air quality status. Thus, some pollutant concentrations are measured on real-time due to weather patterns, automobile emissions, or industrial activities. Moreover, as seen in Table 2, each air pollutant affects human health as well as the environment differently. These issues cannot be confined barely by the IT2FIS as it gives the same importance to each parameter while assessing the environment (tnorms and t-conorms compute the maxima or minimum value for all membership functions). Viewing this, it is indispensable to establish an importance level to each air pollution parameter based on its negative effect in the ecosystem. The relative importance of different air pollutants, based on expert’s judgment, is used to evaluate the weights and hence suffer from intra-personal and inter-personal uncertainties. In order to capture both types of uncertainties, IT2FAHP is proposed for evaluation of weights of different air pollutants associated with the construction site. The following method is used to determine the weights of each factor. The whole process of weight evaluation includes following steps. Step 1: Based historical data the pair wise comparison matrix of the criteria are formulated by experts’ using IT2 trapezoidal fuzzy comparison scale (Table 6) as follows

ACCEPTED MANUSCRIPT 𝐶̃11 ̃ 𝐶̃ = [𝐶̃𝑖𝑗 ] 𝐶21 ⋮ ̃ [𝐶𝑛1

𝐶̃12 𝐶̃22 ⋮ ̃ 𝐶𝑛2

𝐶̃1𝑛 ⋯ 𝐶̃2𝑛 , 𝑖, 𝑗 = 1,2, … , 𝑛 ⋱ ⋮ ̃ ⋯ 𝐶𝑛𝑛 ] ⋯

(5)

𝐶̃𝑖𝑗 = ((𝑎𝑈 , 𝑏𝑈 , 𝑐𝑈 , 𝑑𝑈 ; 𝛼(𝑏𝑈 ), 𝛼(𝑐𝑈 )), (𝑎𝐿 , 𝑏𝐿 , 𝑐𝐿 , 𝑑𝐿 ; 𝛽(𝑏𝐿 ), 𝛽(𝑐𝐿 ))) represents the quantified judgment on 𝑐𝑖 to 𝑐𝑗 and; 𝛼(𝑏𝑈 ) and 𝛼(𝑐𝑈 ) denotes the membership value of the elements 𝑏𝑈 and 𝑐𝑈 , respectively, in the upper trapezoidal membership function; and 𝛽(𝑏𝐿 ) and 𝛽(𝑐𝐿 ) denotes the membership value of the element elements 𝑏𝐿 and 𝑐𝐿 , respectively, in the lower trapezoidal membership function and

IP

T

where

CR

1 1 1 1 1 1 1 1 𝐶̃𝑗𝑖 = (( , , , ; 𝛼(𝑏𝑈 ), 𝛼(𝑐𝑈 )) , ( , , , ; 𝛽 (𝑏𝐿 ), 𝛽(𝑐𝐿 ))) 𝑑𝑈 𝑐𝑈 𝑏𝑈 𝑎𝑈 𝑑𝐿 𝑐𝐿 𝑏𝐿 𝑎𝐿

US

represents the quantified judgment on 𝑐𝑗 to 𝑐𝑖 and 𝑛 represents the number of criterion. It is worthy to mention here that, in the present study𝛼(𝑏𝑈 ) = 𝛼(𝑐𝑈 ) and 𝛽(𝑏𝐿 ) = 𝛽(𝑐𝐿 ) have been considered.

AN

Table 6

PT

ED

M

Scale of relative importance for pair-wise comparison. Trapezoidal fuzzy number Linguistic variable (1, 1, 1, 1;1,1) (1, 1, 1, 1;1,1) Just equal (JE) (1, 2, 3, 4;1,1) (1.4,2.4, 2.6, 3.6;0.8,0.8) Weakly important (WI) (2,3,4,5;1,1) (2.4, 3.4, 3.6, 4.6;0.8,0.8) Between weakly and strongly important (BWSI) (3,4,5,6;1,1) (3.4, 4.4, 4.6, 5.6;0.8,0.8) Strongly important (SI) (4,5,6,7;1,1) (4.4, 5.4, 5.6, 6.6; 0.8, 0.8) Between strongly and very strongly important (BSVI) (5,6,7,8;1,1) (5.4, 6.4, 6.6, 7.6; 0.8, 0.8) Very strongly important (VSI) (6,7,8,9; 1, 1) (6.4, 7.4, 7.6, 8.6; 0.8, 0.8) Between very strongly and absolutely important (BVAI) (7,8,9,9; 1, 1) (7.4, 8.4, 8.6, 9; 0.8, 0.8) Absolutely important (AI)

CE

Step 2: After constructing initial comparison matrix 𝐶̃, its consistency of have to be checked. In order to check the consistency of 𝐶̃ , the equivalent crisp matrix 𝐶 corresponding to 𝐶̃ is evaluated using the defuzzification process of a trapezoidal IT2 fuzzy (DTraT) described as follows [17].

AC

( 𝑑𝑈 −𝑎𝑈 )+ (𝛼 (𝑐𝑈 ) .𝑏𝑈−𝑎𝑈 )+(𝛼( 𝑏𝑈 ).𝑐𝑈 −𝑎𝑈 ) ( 𝑑 −𝑎 ) + (𝛽 (𝑐𝐿 ).𝑏𝐿 −𝑎𝐿 ) +(𝛽 (𝑏𝐿 ).𝑐𝐿 −𝑎𝐿 ) +𝑎𝑈 + 𝐿 𝐿 +𝑎𝐿 4 4

𝐷𝑇𝑟𝑎𝑇 =

2

(6)

where 𝑑𝑈 is the largest possible value of the upper membership function; 𝑎𝑈 is the least possible value of the upper membership function of the IT2 FS under consideration (Fig. 4); 𝑏𝑈 and 𝑐𝑈 are the respective second and third parameters of the upper members hip function; 𝛼(𝑏𝑈 ) and 𝛼(𝑐𝑈 ) are the membership degrees of the second and third parameters, respectively, of the upper membership function; 𝑑𝐿 is the largest possible value of the lower membership function; 𝑎𝐿 is the least possible value of thelower membership function; 𝑏𝐿 and 𝑐𝐿 are the respective second and third parameters of the lower membership function; 𝛽(𝑏𝐿 ) and 𝛽(𝑐𝐿 ) are the membership degrees of the second and third parameters, respectively, of the lower membership function.

CR

IP

T

ACCEPTED MANUSCRIPT

Fig. 4.Descriptive examples of trapezoidal IT2 FS.

𝐶12 𝐶22 ⋮ 𝐶𝑛2

⋯ 𝐶1𝑛 ⋯ 𝐶2𝑛 ] ⋱ ⋮ ⋯ 𝐶𝑛𝑛

(7)

AN

𝐶11 𝐶 𝐶 = [𝐶𝑖𝑗 ] = [ 21 ⋮ 𝐶𝑛1

US

Thus, the equivalent crisp matrix is obtained as,



ED

M

It is to be noted here that a fuzzy comparison matrix 𝐶̃ is consistent only when the corresponding crisp comparison matrix 𝐶 is consistent. The consistency of the matrix 𝐶 is checked by performing the following steps. Compute the largest eigenvalue of the matrix as follows [45]. 𝐶𝑤 = 𝜆 𝑚𝑎𝑥

PT

(8)

where 𝑤 is principal eigenvector of the matrix

CE

The consistency of the comparison matrix is determined by the consistency ratio (CR), which is defined as

AC



𝐶𝐼

𝐶𝑅 = 𝑅𝐼

(9)

where CI is the consistency index which is computed as 𝐶𝐼 =

(𝜆𝑚𝑎𝑥 −𝑛)

(10)

(𝑛−1)

where 𝑛 denotes size of the matrix and RI is the random index, which is shown in Table 7. Table 7 Random indices for the different ordered reciprocal matrix. Order of Matrices RI

1 0

2 0

3 0.58

4 0.9

5 1.12

6 1.24

7 1.32

8 1.41

9 1.45

10 1.49

ACCEPTED MANUSCRIPT It is worthy to be mentioned here that if CR < 0.10, the consistency of the matrix 𝐶 i.e. of 𝐶̃ is acceptable, otherwise the pair-wise fuzzy comparisons should be revised. Step 3: In order to evaluate the fuzzy weights, at first the geometric mean (𝐶̃𝑖 ) of each row of the comparison matrix, 𝐶̃, are evaluated as 𝐶̃𝑖 = [𝐶̃𝑖1 ⊗ 𝐶̃𝑖2 ⊗ ⋯ ⊗ 𝐶̃𝑖𝑛 ]

1⁄ 𝑛

(11)

(12)

IP

̃ 𝑤 ̃ 𝑖 = 𝐶̃𝑖 ⊗ [𝐶̃1 ⊕ 𝐶̃2 ⊕ … ⊕ 𝐶̃𝑛 ]−1

T

Step 4: Now, the IT2 fuzzy weight of the 𝑖 𝑡ℎ criteria is evaluated as

CR

Step 5: Fuzzy weights are converted into crisp weights (𝑤𝑖∗ ) by using defuzzification method as defined in equation (6). Step 6: Crisp weights are normalized using the following equation as 𝑤𝑖∗

(13)

US

𝑤𝑖 = ∑𝑛

∗ 𝑖=1 𝑤𝑖

AN

where𝑤𝑖 is the weight of the 𝑖 𝑡ℎ criteria after normalization process.

3.3.

M

Weights of all five air pollutants, viz., 𝑃𝑀10 , NO2 , O3 , CO, SO2 are calculated as 𝑤𝑃𝑀10 , 𝑤NO2 , 𝑤O3 , 𝑤CO , 𝑤SO2 , respectively, using above mentioned six steps sequentially. Evaluation of AQI by interval type-2 weighted fuzzy reasoning

ED

For an input vector 𝑥 ′ = (𝑥 𝑃𝑀10 , 𝑥 NO2 , 𝑥 O3 , 𝑥 CO , 𝑥 SO2 ), the computational process interval type-2

PT

weighted fuzzy reasoning involves the following steps: Step 1: Membership intervals of 𝑥 𝑃𝑀10 on 𝐴̃ 𝑛𝑃𝑀10 ,𝑥 NO2 on 𝐴̃𝑛NO2 ,𝑥 O3 on 𝐴̃𝑛O3 , 𝑥 CO on 𝐴̃𝑛CO and𝑥 SO2 on

CE

𝐴̃𝑛SO2 , are derived by Eq. (3) and Eq. (4) as [𝜇𝐴̃𝑛𝑃𝑀 (𝑥 𝑃𝑀10 ), 𝜇̅𝐴̃ 𝑛𝑃𝑀 (𝑥 𝑃𝑀10 )] , 10

[𝜇𝐴̃𝑛 (𝑥 NO2 ), 𝜇̅𝐴̃ 𝑛 (𝑥NO2 )] ,

[𝜇𝐴̃𝑛 (𝑥 O3 ), 𝜇̅𝐴̃ 𝑛 (𝑥 O3 )] ,

NO2

AC

NO2

[𝜇𝐴̃𝑛 (𝑥SO2 ), 𝜇̅𝐴̃ 𝑛 (𝑥 SO2 )] SO2

SO2

O3

,

[𝜇𝐴̃𝑛 (𝑥 CO ),𝜇̅𝐴̃ 𝑛 (𝑥 CO )]

O3

respectively,

10

CO

where

CO

𝑛 = 1, 2, … . , 𝑁

and and

𝐴̃𝑛𝑃𝑀10 , 𝐴̃𝑛NO2 , 𝐴̃𝑛O3 , 𝐴̃𝑛CO , 𝐴̃𝑛SO2 ∈ {Good, Satisfactory, Moderate, Poor, Very Poor,Severe}. Step 2: Firing interval of the 𝑛𝑡ℎ rule, 𝐹 𝑛 (𝑥 ′), is derived using min t-norm as follows: 𝐹

𝑛( ′)

𝑥 =[

𝑚𝑖𝑛 {𝜇𝐴̃ 𝑛

𝑃𝑀10

𝑚𝑖𝑛 {𝜇̅𝐴̃ 𝑛

(𝑥 𝑃𝑀10 ), 𝜇𝐴̃𝑛 (𝑥 NO2 ), 𝜇𝐴̃ 𝑛 (𝑥 O3 ), 𝜇𝐴̃𝑛 (𝑥CO ), 𝜇𝐴̃𝑛 (𝑥 SO2 )} , NO2 O3 CO SO2 ] (𝑥 𝑃𝑀10 ), 𝜇̅𝐴̃ 𝑛 (𝑥 NO2 ), 𝜇̅𝐴̃ 𝑛 (𝑥 O3 ), 𝜇̅𝐴̃𝑛 (𝑥 CO ), 𝜇̅𝐴̃𝑛 (𝑥 SO2 )}

𝑃𝑀10

𝑛

= [𝑓 𝑛 , 𝑓 ]

NO2

O3

CO

SO2

(14)

ACCEPTED MANUSCRIPT Step 3: Weighted firing interval of the 𝑛𝑡ℎ rule, 𝐹𝑤𝑛 (𝑥 ′ ), is derived by multiplying the weight 𝑤 𝑛 corresponding to the air pollutant whose membership function value defines the rule 𝑛

output [𝑓 𝑛 , 𝑓 ] as follows: 𝑛

𝑛

𝑛

𝐹𝑤𝑛 (𝑥 ′) = 𝑤 𝑛 ∗ [𝑓 𝑛 , 𝑓 ] = [𝑤 𝑛 ∗ 𝑓 𝑛 , 𝑤 𝑛 ∗ 𝑓 ] = [𝑓𝑤𝑛 , 𝑓𝑤 ]

(15)

T

where 𝑤 𝑛 ∈ {𝑤𝑃𝑀10 , 𝑤NO2 , 𝑤O3 , 𝑤CO , 𝑤SO2 }.

IP

For two or more air pollutants whose membership function value defines the rule 𝑛 output [𝑓 𝑛 , 𝑓 ] , the weight parameter with higher priority is used as 𝑤 𝑛 which

CR

guarantees that the output rule interval is influenced by the pollutant with the highest importance.

US

𝑛 Step 4: The primary variable of the IT2 FS, 𝐴̃𝐴𝑄𝐼 , present in the consequent of the 𝑛𝑡ℎ rule has

been discretized as 𝑦𝑡 (𝑡 = 1,2, … , 𝑀), where

AN

𝑛 𝐴̃𝐴𝑄𝐼 ∈ {Good, Satisfactory, Moderate, Poor, Very Poor, Severe} and the centroid of

that IT2 FS, 𝐶𝐴̃𝑛𝐴𝑄𝐼 = [𝑐𝑙𝑛 , 𝑐𝑟𝑛 ] has been determined as the optimal solutions of the

M

following interval weighted average problems [18, 26]as described below: =

𝑚𝑖𝑛

ED

𝑐𝑙𝑛

𝜃𝑡 ∊[𝜇 ̃̃ 𝑛

𝑐𝑟𝑛

=

𝐴 𝐴𝑄𝐼

PT

𝐴 𝐴𝑄𝐼

( 𝑦𝑡 ) ,𝜇 ̃̃ 𝑛

( 𝑦𝑡 )]

CE

𝐴 𝐴𝑄𝐼

( 𝑦𝑡 ) ,𝜇 ̃̃ 𝑛

𝐴 𝐴𝑄𝐼

=

𝑘 ∑ 𝑙 ̅ 𝜇 ̃𝑛 𝑡=1 ̃ 𝑛

𝐴 𝐴𝑄𝐼

( 𝑦𝑡 )]

∑𝑀 𝑡=1 𝜃𝑡

=

( 𝑦𝑡 ) 𝑦𝑡 +∑𝑀 𝑛 𝜇 ̃̃ 𝑛 𝑡=𝑘 +1 𝐴 𝑙

𝐴𝑄𝐼

( 𝑦𝑡 ) 𝑦𝑡

𝑘 ∑ 𝑙 ̅ 𝜇 ̃̃ 𝑛 ( 𝑦𝑡 ) +∑𝑀 𝑛 𝜇 ̃̃ 𝑛 ( 𝑦𝑡 ) 𝑡=1 𝐴 𝑡=𝑘𝑙 +1 𝐴 𝐴𝑄𝐼 𝐴𝑄𝐼 𝑛

∑𝑀 𝑡=1 𝑦𝑡 𝜃𝑡

𝑚𝑎𝑥

𝜃𝑡 ∊[𝜇 ̃̃ 𝑛

𝑛

∑𝑀 𝑡=1 𝑦𝑡 𝜃𝑡 ∑𝑀 𝑡=1 𝜃𝑡

𝑟 ∑𝑘 ̃𝑛 𝑡=1 𝜇 ̃ 𝑛

𝐴 𝐴𝑄𝐼

( 𝑦𝑡 ) 𝑦𝑡 +∑𝑀 𝑛 𝜇 ̅ ̃̃ 𝑛 𝑡=𝑘 +1 𝐴 𝑟

𝐴𝑄𝐼

(16)

( 𝑦𝑡 ) 𝑦𝑡

𝑘 ∑ 𝑟 ̅ 𝜇 ̃̃ 𝑛 ( 𝑦𝑡 ) +∑𝑀 𝜇 ̃̃ 𝑛 ( 𝑦𝑡 ) 𝑡=1 𝐴 𝑡=𝑘𝑛 𝑟 +1 𝐴 𝐴𝑄𝐼 𝐴𝑄𝐼

(17)

where the switch points 𝑘𝑙𝑛 and 𝑘𝑟𝑛 are determined by

AC

𝑦𝑘𝑛𝑙 ≤ 𝑐𝑙𝑛 ≤ 𝑦𝑘𝑛𝑙 +1

(18)

𝑦𝑘𝑛𝑟 ≤ 𝑐𝑟𝑛 ≤ 𝑦𝑘𝑛𝑟 +1

(19)

Step 4: The weighted firing intervals of the rules 𝐹𝑤𝑛 (𝑥 ′) and the corresponding rule consequent centroids, 𝐶𝐴̃𝑛

𝐴𝑄𝐼

= [𝑐𝑙𝑛 , 𝑐𝑟𝑛 ] have been combined by center-of-set (COS) type-reduction

method [23, 27], derived from the extension principle [46], as follows: 𝑛

𝐴𝑄𝐼𝑙 =

𝑚𝑖𝑛

𝑘∊[1,𝑁−1]

𝑛 𝑁 𝑛 𝑛 ∑𝑘 𝑛=1 𝑓 𝑤𝑐 𝑙 + ∑𝑛=𝑘+1 𝑓𝑤 𝑐 𝑙 𝑛

𝑁 𝑛 ∑𝑘 𝑛=1 𝑓 𝑤+ ∑𝑛=𝑘+1 𝑓𝑤

𝑛

=

𝑛 𝑛 ∑𝐿𝑛=1 𝑓 𝑤𝑐 𝑛 ∑𝑁 𝑙 + 𝑛=𝐿+1 𝑓𝑤 𝑐 𝑙 𝑛

𝑛 ∑𝐿𝑛=1 𝑓 𝑤 +∑𝑁 𝑛=𝐿+1 𝑓𝑤

(20)

ACCEPTED MANUSCRIPT 𝑛

𝑛 𝑛 𝑁 𝑛 ∑𝑘 𝑛=1 𝑓𝑤 𝑐 𝑟 +∑𝑛=𝑘+1 𝑓 𝑤𝑐 𝑟

𝐴𝑄𝐼𝑟 = 𝑚𝑎𝑥

𝑘∊[1,𝑁−1]

𝑛

𝑛 𝑁 ∑𝑘 𝑛=1 𝑓𝑤 +∑𝑛=𝑘+1 𝑓 𝑤

𝑛

=

𝑛 𝑛 𝑁 𝑛 ∑𝑅 𝑛=1 𝑓𝑤 𝑐 𝑟 + ∑𝑛=𝑅+1 𝑓 𝑤 𝑐 𝑟 𝑛

𝑛 𝑁 ∑𝑅 𝑛=1 𝑓𝑤 + ∑𝑛=𝑅+1 𝑓 𝑤

(21)

where the switch points 𝐿 and 𝑅 are determined by 𝑐𝑙𝐿 ≤ 𝐴𝑄𝐼𝑙 ≤ 𝑐𝑙𝐿+1

(22)

𝑐𝑟𝑅 ≤ 𝐴𝑄𝐼𝑟 ≤ 𝑐𝑟𝑅+1

(23)

and {𝑐𝑙𝑛 }𝑛=1,2,…,𝑁 and {𝑐𝑟𝑛 } 𝑛=1,2,…,𝑁 have been stored in ascending order, respectively.

IP

𝐴𝑄𝐼𝑙 + 𝐴𝑄𝐼𝑟 2

(24)

CR

𝐴𝑄𝐼 =

T

Step 5: Calculate the defuzzified output as:

4. Case study

AN

US

In this section, the developed model has been employed to evaluate the AQI in Kolkata Metropolitan area. Due to the presence of various influential air quality parameters, emitting from different sources, this part of the world is identified as one of the most troublesome metropolitan area in India. The detail of the computational process is presented in the following sub-sections.

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Concentration of PM10 (µg/m³)

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The historical data set is obtained from ambient air quality monitoring stations operating near by the Victoria Memorial, in Kolkata Metropolitan Area, over a period of 182 days, starting from 1st July, 2016 to 11th January, 2017.These monitoring centers emitted are port of air quality index on real-time. Daily variations in the concentrations of the five most influential air pollutants, viz., PM10 , CO, O 3 , NO2 and SO 2 are respectively shown in Fig. 5 - 9.

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Fig. 5. Daily variation in PM 10 concentration.

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Concentration of CO (mg/m³)

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Fig. 6. Daily variation in CO concentration.

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Fig. 7. Daily variation in O3 concentration.

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Concentration of NO2 (µg/m³)

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Concentration of SO2 (µg/m³)

Fig. 8. Daily variation in NO2 concentration.

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Fig. 9. Daily variation in SO2 concentration.

4.2 Air pollution parameter analysis In this section, an in depth analysis has been made on the daily variation in PM 10 , CO, O3 , NO2 andSO 2 concentrations using the collected database and the air quality classification levels (Good, Satisfactory, Moderately polluted, Poor, Very Poor, and Severe) for each one, defined by CPCB, in order to examine the main behaviors of those pollutants. In Fig. 5, PM10 concentrations present regular peaks in the second phase of the study period, locating mainly within Moderately polluted air quality level. In Fig. 8, NO 2 concentrations produce peaks frequently in the last part the study period indicating the sudden deterioration in air quality status. Such high

ACCEPTED MANUSCRIPT concentrations of NO 2 located between Moderately polluted and Poor air quality level. In Fig. 6, 7 and 9, CO, O3 , and SO 2 concentrations are located between good and satisfactory air quality level. This combination of air quality parameters is very harmful and alarming situation for the inhabitants living in the studied area. For this reason, they are considered as the most critical pollutants to be controlled and monitored. 4.3 Results & discussion

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Air quality assessments have been made using the integrated model as proposed in section 3. In order to infuse the priorities of the five air quality parameters during the process of IT2 weighted fuzzy reasoning, a pair-wise comparison matrix has been developed according to the scale of relative importance for pair-wise comparison as prescribed in Table 6. Table 8 present the comparison matrix developed for the present study. Table 9 presents the weights of PM10 , NO2 , O3 , CO and SO 2 evaluated using IT2 FAHP as described in section 3.2. Table 8

NO2 SO2

CO 𝐵𝑉𝐴𝐼 𝐽𝐸 𝑉𝑆𝐼 𝐵𝑆𝑉𝐼 1⁄ 𝑊𝐼

Weights of air quality parameters.

SO2 𝐴𝐼 𝑊𝐼

𝐵𝑊𝑆𝐼

𝐵𝑉𝐴𝐼

𝐽𝐸 1⁄ 𝑉𝑆𝐼

𝑉𝑆𝐼 𝐽𝐸

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𝐽𝐸 1⁄ 𝐵𝑊𝑆𝐼 1⁄ 𝐵𝑉𝐴𝐼

NO2 𝐵𝑆𝑉𝐼 1⁄ 𝐵𝑆𝑉𝐼

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Air quality parameter PM 10 CO O3 NO2 SO2

O3 𝑆𝐼 1⁄ 𝑉𝑆𝐼

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O3

PM 10 𝐽𝐸 1⁄ 𝐵𝑉𝐴𝐼 1⁄ 𝑆𝐼 1⁄ 𝐵𝑆𝑉𝐼 1⁄ 𝐴𝐼

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Pair-wise comparison matrix.

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Finally, the AQIs are evaluated from the collected data by the proposed model and the results are compared with the results obtained by its counterpart IND-AQI, T1 FIS, AHP-T1 FIS [30], T1 FAHP-T1FIS. In Figure 10, it is evidenced that while the behavior of the other methods are almost same, developed model endows significantly different results. This noteworthy variation in the result of proposed model as compared to other models is due to the novel weighment process used in the proposed model. While comparing with IND-AQI and T1 FIS AQI model, the result from the proposed model differs as none of those two AQI assessment models has incorporated the notion of weight to prioritize the air pollutants. Although, it is a completely known fact that these air quality parameters should be treated separately as they generates different problems on the health of people based on their toxicity level. On the other hand, in comparison with AHP-T1 FIS, T1 FAHP-T1FIS the result of the proposed model differs due to the inherent capability of IT2 FSs in order to capture both inter-personal and intra-personal uncertainties involved in subjective judgment during the pair-wise comparison of health- impact of the pollutants, which is already identified as better weight evaluation process in comparison with its counterpart AHP and T1 fuzzy weight evaluation process. Moreover, in any

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conventional weighted assessment process, the outputs obtained by FIS are synthesized with the weights using sum of product method; whereas in this model the pollutant that contributes in the rule output, weight of that pollutant is incorporated directly at the time of aggregation process, considerably affect the final score according to the environmental parameter with higher importance. Moreover, this combination of a reasoning system with a weighment process, will involve the importance of the pollutant with a potential crisis detection modelling, increasing the effectiveness of the assessment to generate more accurate evaluations that can be reflected in an air quality index (AQI) [30].

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Fig. 10.Comparison of AQI among the IND-AQI,T1 FIS, AHP-T1 FIS, T1 FAHP-T1 FIS and the proposed IT2

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Furthermore, Diwali is one of the most worrying days within the study period in India, especially in Kolkata, due to elevated execution of fireworks. In spite of restrictions and various environmental awareness campaigns, AQI rise up significantly during this festive session. In the present study, monitoring of AQI (Table 10) is performed on hourly basis during that festive season to assess the exact situation on those stipulated days. Table 10 reflects significant changes in AQI by proposed model in comparison with that of IND-AQI, T1FIS, AHP-T1 FIS [30], T1FAHP-T1FIS. Some results seems to have a higher deviation from the its counterparts because when a critical parameter presents high concentrations, the proposed model provides more weighment in the processing analysis, giving a higher score that tends to evaluate a worse air quality. Moreover, this result conveys that AQI level becomes high during night when most of fireworks are executed, although it lies between the permissible levels Satisfactory and Moderate, which indicates that the Victoria Memorial area are pretty much well maintained in terms of air pollution in India, even during period of festive season.

ACCEPTED MANUSCRIPT Table 10 Comparison of air quality assessments during Diwali (hourly basis). Time Date

Air quality parameters

AQI

29/10/2016

16:00:00

16:59:00

39.39

1.14

19.47

24.65

5.25

INDAQI 57

59.35

45.15

29/10/2016

17:00:00

17:59:00

39.85

1.63

14.4

29.09

5.49

82

61.41

63.10

62.99

49.74

29/10/2016

18:00:00

18:59:00

45.72

1.63

8.63

44.76

6

82

67.74

73.19

73.13

54.62

29/10/2016

19:00:00

19:59:00

61.92

2.39

7

40.63

6.15

105

104.45

105.55

105.48

82.79

29/10/2016

20:00:00

20:59:00

71.3

0.92

4.78

47.7

6.66

71

62.16

65.96

65.76

48.30

29/10/2016

21:00:00

21:59:00

96.91

1.3

1.95

47.11

6.91

97

106.27

105.90

105.91

97.98

29/10/2016

22:00:00

22:59:00

143.11

0.68

3.34

47.2

7.53

129

98.20

99.15

99.08

69.21

29/10/2016

23:00:00

23:59:00

182.11

0.68

2.64

50.28

8.02

30/10/2016

00:00:00

00:59:00

198.37

0.84

3.35

43.06

30/10/2016

01:00:00

01:59:00

190.69

1.07

2.21

34.73

30/10/2016

02:00:00

02:59:00

179.6

1.48

1.94

31.31

30/10/2016

03:00:00

03:59:00

161.53

1.05

30/10/2016

04:00:00

04:59:00

145.33

0.77

30/10/2016

05:00:00

05:59:00

114.04

30/10/2016

06:00:00

06:59:00

88.18

30/10/2016

07:00:00

07:59:00

82.38

30/10/2016

08:00:00

08:59:00

30/10/2016

09:00:00

09:59:00

30/10/2016

10:00:00

30/10/2016 30/10/2016

From

To

PM 10

CO

O3

NO2

SO2

D E

AHP-T1 FIS

T1 FAHPT1FIS

IT2 FAHPIT2FIS

56.10

59.30

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155

121.76

114.95

114.98

106.79

6.61

166

154.04

150.10

150.12

118.18

6.09

160

153.94

156.27

156.31

142.68

6.4

153

163.59

164.70

164.72

157.97

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TIFIS

2.22

28.5

7.15

141

129.77

134.36

134.13

110.37

2.27

24.13

5.52

130

106.29

106.80

106.74

75.73

2.49

31.84

5.63

109

97.65

99.98

99.84

69.95

2.16

28.93

5.35

88

88.91

92.78

92.83

82.98

3.99

23.07

5.38

82

75.46

78.63

78.68

61.62

0.42

3.44

15.69

5.68

70

27.84

32.99

32.69

26.24

48.9

1

6.53

17.21

4.76

50

65.73

71.79

71.88

46.60

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0.91

42.63

0.73

5.8

12.49

4.66

43

52.98

55.11

54.98

35.02

11:00:00

11:59:00

33.73

0.56

10.16

11.44

3.87

34

35.90

39.28

39.07

29.28

12:00:00

12:59:00

21.34

0.2

10.56

12.1

4.04

21

27.08

32.53

32.20

26.24

30/10/2016

13:00:00

13:59:00

26.64

0.36

16.43

19.29

3.67

27

27.32

32.68

32.36

26.24

30/10/2016

14:00:00

14:59:00

25.87

0.4

11.18

16.53

3.41

26

27.21

32.61

32.29

26.24

30/10/2016

15:00:00

15:59:00

20.34

0.23

16.91

18.8

2.7

24

27.08

32.53

32.20

26.24

30/10/2016

16:00:00

16:59:00

25.38

0.92

10.3

22.9

6.96

46

32.13

36.62

36.69

28.62

30/10/2016

17:00:00

17:59:00

39.11

1.63

3.93

36.49

7.01

82

64.21

67.51

67.47

49.84

C A

70.08

T P 0.77 1.05

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18:00:00

18:59:00

54.8

3.63

1.85

46.99

7.81

120

115.31

124.17

124.08

90.62

30/10/2016

19:00:00

19:59:00

74.84

4.77

2.27

44.33

8.72

135

142.58

146.76

146.55

132.27

30/10/2016

20:00:00

20:59:00

101.51

0.61

1.88

54.51

6.13

101

74.44

75.50

75.47

57.83

30/10/2016

21:00:00

21:59:00

134.58

0.91

2.24

35.49

6.05

123

111.67

115.45

115.24

79.88

30/10/2016

22:00:00

22:59:00

184.79

0.71

1.9

42.83

6.97

157

132.79

127.82

127.85

107.07

30/10/2016

23:00:00

23:59:00

226.62

0.84

2.29

42.86

6.94

184

169.64

168.40

168.40

122.72

I R

T P

C S

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U N

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In this paper, a new methodology has been proposed for air quality assessment employing IT2 FSs, enabling it to capture both intra-personal and inter-personal uncertainties involved in classification of air quality status based on concentration level and toxicity level of various air pollutants. Moreover, the use of proposed weighted interval type-2 fuzzy reasoning process in evaluation of AQI, provides a better way out of assigning priorities of air pollutants in AQI as the weight corresponding to air pollutant having membership value that define the firing interval of each rule. Finally, this model has been employed for evaluation of AQI in Kolkata Metropolitan area focusing five major air quality parameters based on their health impact. The study shows that, in Kolkata Metropolitan area, the air quality level was deteriorated drastically during the festive season, specially, during midnight of Diwali due to extensive fireworks. However, more in depth study has to be made in order to improve the model by optimizing the rule inference for a better assessment (adding or replacing rules). Also, an analysis about a fitted membership function type for a specific parameter is a question that has been planned. Additionally, a knowledgebase which introduces new rules based on parameter behaviors is a good idea for having an improved computational model.

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Acknowledge ments. The authors remain very much grateful to the anonymous reviewers for their insightful comments and valuable suggestions to improve the quality of the manuscript.

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IND-AQI: AQI at some specified monitoring location is determined by IND-AQI method which involves formation of sub-indices for each pollutant and aggregation of sub- indices. The subindices of each pollutant are calculated using the mathematical equation as follows: 𝐼 − 𝐼𝐿𝑂 𝐼𝑃 = ( 𝐻𝐼 × (𝐶𝑃 − 𝐵𝑃𝐿𝑂 )) + 𝐼𝐿𝑂 𝐵𝑃𝐻𝐼 − 𝐵𝑃𝐿𝑂 where 𝐼𝑃 is AQI for pollutant “𝑃” (Rounded to the nearest integer), 𝐶𝑃 is the actual ambient concentration of pollutant “𝑃”, 𝐵𝑃𝐻𝐼 is the upper end breakpoint concentration that is greater than or equal to 𝐶𝑃 , 𝐵𝑃𝐿𝑂 is the lower end breakpoint concentration that is less than or equal to 𝐶𝑃 , 𝐼𝐿𝑂 is the sub index or AQI value corresponding to 𝐵𝑃𝐿𝑂 ,𝐼𝐻𝐼 is the sub index or AQI value corresponding to 𝐵𝑃𝐻𝐼 and the breakpoints concentration of each pollutants are identified using their classification levels which is given in Table 3. After determining the sub- indices of each pollutant, the AQI of the monitoring area is evaluated as: AQI = max (𝐼1 , 𝐼2 , 𝐼3 , … , 𝐼𝑃 ) where𝐼𝑖 (𝑖 = 1, … , 𝑃) is AQI for pollutant “𝑖”.

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