Fuzzy radon hazard index assessment for stochastic environmental health risk evaluation of urban scale building

Radon gas emission is emerging phenomenon that poses potential danger to human health as a result of modern lifestyles. Thus, it is critical to conduct stochastic evaluations of the amount of this hazardous gas in urban areas and residential buildings to identify environmental health risks. To assess statistical radon environmental health risks, this research proposes two novel fuzzy radon hazard indices (FRHIs), FRHI1 and FRHI2.. FRHI1 can contribute to every standard, while FRHI2 can be compared to geogenic radon potential or geogenic radon hazard indices. The output indices FRHIs range from 0 (no hazard) to 100 (the highest degree of hazard). The proposed approach can serve as a circumstantially integrated standard for stochastic radon risk assessment and management, so that fuzzification can bring innovation in stochastic standards in this field. In this study, radon concentration was measured in an urban building and natural radon and emission zoning maps were created using ArcGIS software at urban and geological scales. A residential building unit located in a critical area was selected and some corrective actions were adopted to reduce radon in urban building units. The FRHI Assessment for stochastic environmental health risk evaluation showed that the initial fuzzy level for the mean value of FRHI is hazardous (for an FRHI value equal to 60.1), indicated by red. However, the Maximum FRHI level for 48 h after the installation was rather hazardous (for an FRHI value equal to 44.8), indicated by orange. After steady-state installation, the maximum statistical environmental health risk would fall into an improved category. Identifying critical areas can provide exceptional control at the urban scale building that reduces the risks of natural radon.


Introduction
Natural radon gas is formed as a byproduct of materials breakdown in rocks. It is emitted from the subsoil and is most concentrated in enclosed spaces (Meyer 2019). Sinceadon-222 has a half-life of about 3.82 days, it can be stored in closed structures and remain in the air for many days (Chilingarian et al. 2021). Therefore, homes and workplaces must be adequately ventilated to remove any residual randon (Mainardi and Redlich 2018). Natural elements are responsible for three-quarters of the radioactivity in the environment (Udovicic et al. 2020) and radon is the most abundant natural radioactive source (McGrath James and Byrne 2020). The public health issues caused by the high concentration of this gas in the buildings and drinking water necessitate the constant evaluation of such materials concentration in the area (Alonso et al. 2019).
Radon decays through ionizing radiation, penetrating matter (Usikalu et al. 2017), and usually draws electrons from the surrounding atoms in ionization mechanisms (Boerma et al. 2016). When the material is a biological structure with high water content the ionization of water molecules can produce so-called free radicals with a high degree of chemical activity, enough to damage essential molecules found in living organism's cells (Ravana and Douki 2021;Blundell 2015). These damages include chemical changes in DNA and the crucial organic molecule that are part of the cells that make up our bodies (Magalhães et al. 2003;Brenner 1994) and may have biological consequences such as irregular cell growth (Stanley et al. 2017;Gesell Thomas 1983). The severity of damages depends on the radiation dosage (Abaszadeh Fathabadi et al. 2020). Randon inhalation in closed spaces poses the most severe hazard of all exposure. Radon gas releases particles that cannot migrate through lung tissues (Curado et al. 2020) and settle on them and cause damage (Nguyen et al. 2021). In order to minimize radon accumulation, adequate air circulation and old building renovation have attracted attention to buldings with people in them (Kladder Douglas 1995;Yarmoshenko et al. 2021). However, if the pollutants accumulation values are high, further disciplinary steps can be taken. This radioactive gaseous element is present in nearly all building materials and the soil where buildings are installed (Nastro et al. 2018;Rizo-Maestre and Echarri-Iribarren 2020). Various radon measurement instruments are available. Some are operational, demand energy, and continuously record radon gas concentration and variations throughout the measurement time (Li et al. 2019). Others are passive, requiring no electricity to run in the sampling area. Radon detectors, alpha detectors, electrical ion detectors, and continuous controllers can measure radon in suburban areas (Sainz et al. 2018;Bekteshi et al. 2017). This study uses a sensor made of activated carbon (coal) for short-term calculation (Sainz et al. 2018). Since the maximum radon concentration is observed while the space in question is devoid of air ventilation (for example, when all windows and joints are closed), radon concentration measurements should be performed in such condition (Ahmad et al. 2017).
The earth is the main source of radon in isolated structures or on the ground floor of buildings. Radon concentration in the ground ranges between 10 and 50 Bq/ m 3 , with the possibility of far higher values, with an average value of approximately 40 Bq/m 3 (Fard et al. 2021). Radium-226, as well as its soil permeability, determine the radon level that reaches a building from the earth in the subsoil (Maestre and Iribarren 2018). Many countries have radon content predictive charts, which primarily reflect the igneous makeup of the soil (Cambeses et al. 2016;Bochicchio et al. 2014;Spengler and Adamkiewicz 2009). Sweden, for example, has created maps focused on the calculation of radon's geo-genic potential, which shows the danger level by zone based on the concentration of radon in the ground at a depth of 1 m (Maestre and Iribarren 2018). Similarly, the utility of the approaches dependent on other factors, such as soil radio-226 concentration, has been investigated. For example, the national map in France was created using geological maps and each geological unit's average natural radon elements content (Bard 2017;Kemski et al. 2001). The Germany and Czech Republic maps were both created using Radon's geo-genic ability. Both radon gas predictive maps show granitic soils as the most dangerous in concentrations (Neznal et al. 2004;Francisco et al. 2017). Various theories and strategies for hazard identification and risk analysis can focus on safety (Sarkheil and Rahbari 2016a, b;Sarkheil et al. 2016) as well as health and environmental aspects (Sarkheil et al. 2020;Sarkheil 2021). By considering them, the risk of hazards arising from natural radon emissions would considerably decrease.
Because of the role of this gas in community health, the amount of natural radon gas released from various geological rocks and its impact on population distribution and on the residents of investigated areas in the case study were explored in this research. A location is surveyed and multiple natural radon inhibition procedures are investigated, with the findings interpreted and compared. Classic studies like Petermann and Bossew (2021), Nenzel and Nenzel (2005), Haruna et al. (2020), Bossew et al. (2020), Aghdam et al. (2022) and Szabo et al. (2014) in this field define and assess conventional indices of geogenic radon potential (GRP) and geogenic radon hazard identification (GRHI), which are mainly related to geological aspects of radon radiation. However, many gaps exist for novel studies defining and assessing health and environmental indices. On the other hand, a few studies have utilized artificial intelligence methods for developing environmental radon measurement and assessment. Hence, creating a Fuzzy radon hazard index based on artificial intelligence and environmental health is crucial.

Natural radon data collection in the case study
To investigate the natural radon emission in the case study region, we performed measurements of radon concentration on an urban scale ( Fig. 1) due to the case study's social and economic importance. The harvests were conducted under almost identical conditions as described below. Data collection was carried out for 3 months during fall. The data were collected from enclosed spaces with constant temperature and humidity conditions. The temperature was between 12 and 18°C, and the humidity percentage was very low due to the case study's climate, ranging from 10 to 17%. The case study's urban scale consists of 145 neighborhoods, and we conducted at least one harvest in each neighborhood. We collected all data from the basements of residential, commercial, or office units in various city parts. Some basements were related to existing parking lots, while others were in buildings. In this study, we tried to select public places where people are inevitably present and the situation is beyond their control.
We collected data about critical buildings and underpasses beneath them multiple times, focusing on the essential measurements. The map of the different neighborhoods of the case study is shown below. Radon concentration was measured using a KATA Radon-Box/10 device, which has an acceptable accuracy and has been used to measure radon concentrations in different parts of the city. The Radon-Box is a metal container filled with activated carbon, which can be placed in a room for 7 days to collect radon. The device is then analyzed using the analysis software available in the DGM-1500 (Sarén et al. 2016) and the final result shows the amount of radon in Bq/m 3 .
Natural radon distribution zoning maps for urban areas were obtained using Arc GIS software and the geostatistical analysis tool (Pulido-Bosch et al. 2015). To achieve the most optimal radon gas zonation, Kriging, Areal, IDW, and co-kriging techniques were used (Gong et al. 2014) and parameters such as mean error and root mean square error (RMSE) were employed for comparison (Ć alasan et al. 2020).

Fuzzy radon hazard index (FRHI)
In this study, a novel fuzzy attitude is conducted in continuation of these studies: , 2016a, 2016b, 2017, Sarkheil et al. (2018aSarkheil et al. ( , 2018bSarkheil et al. ( , 2019Sarkheil et al. ( , 2021aSarkheil et al. ( , 2021b and . This part proposes two comprehensive indices via two fuzzy inference systems for assessing health problems caused by radon gas emission. The most important notes around developing the FRHIs and their differences with literature are as follows: • The construction of the FISs is based on the most reputed standards in this field and the researcher's inferences and resolutions. • The main objective of the FRHIs is to cover health and human-environmental hazard assessments compared to classic methods, which deal mainly with geogenic aspects. • Two FRHIs are developed for areas with limited or unavailable permeability data. Also, FRHI1 can contribute to each of the respected standards, and FRHI2 can be compared to GRPs or GRHIs. • Computation of FRHIs is simple, quick, and inexpensive in contrast to conventional methods with timeconsuming torrents of hand calculations. • Applications of fuzzy sets theory can overcome the diverse statistical deviations and variances due to its nonlinear and intersectional nature. Fuzziness is helpful and advantageous for stochastic and chaotic statistical environmental radiation fields, while simplifying many problems.
This study's methodology, results, and discussion can be understood through the flowchart presented in Fig. 2.
Some essential studied criteria are, are listed in Table 1, and presented schematically in Fig. 3.
It should be noted that the curves are calibrated regarding the non-linearity of output FRHI. The primary attitude is overestimating, i.e., for levels above less hazardous, the FRHIs rise sharply just after the category start point (critical points recommended by standards) while smoothing down before the category endpoint. This notion satisfies the rigor required for an accepted worldwide standard. For non-hazardous and less hazardous levels, the pattern smooths after start points while accelerating before endpoints. As the lower amounts are not so crucial, the critical values are those close to higher bounds. This is a significant advantage of the novel fuzzy method introduced in this study. In fact, this fuzzy approach identifies the critical conditions well and can provide corresponding health recommendations.
The produced FIS for FRHI has 5 Gaussian membership functions (MFs) for both input and output, demonstrated in Fig. 4a and b. The prepared FIS can be found in ''Appendix 1''.
The membership functions are mainly Gaussian because they cover diverse statistical standard deviations. The corresponding fuzzy rules for this FIS are as follows: The output received by FRHI is very trustworthy because it is constructed upon the integration of four reputed international standards and can be widely accepted by many studies, just like the results of the present study in  the following. Fuzzy perceptions help researchers to conceptualize the fuzzy radon health risk better because the main body of hazards and health and environmental risks are non-linear and too complex. For cases with Soil Gas Permeability, a more comprehensive [Mamdani] FIS, naming FRHI2,with Radon Concentration (C R ) and Soil Radon Permeability (K) as inputs and FRHI2 as output are proposed. The arrangement of radon concentration and FRHI2 MFs are as those of FRHI1, and the Radon Permeability of [K MFs] is presented in Fig. 5.
As observed from Figs. 4 and 5, the MFs of inputs and output of both FRHIs are Gaussian. The reasons for this are explained in the following notes: • According to Central Limit Theorem, radon concentration, radon soil permeability, and radon hazard index are studied in very large sets and can be expressed in standard distribution form for their relative standard deviations (r). • The data for the Inputs and Outputs of FRHIs are very diverse and are mainly indicated by Box and Whisker plots. One effective statistical function for formulating these plots would be standard distribution. • These data can hardly be presented in levels for-Trapezoid MFs-and are mainly exhibited around typical or definite amounts. However, Triangular MFs cannot cover such a vast and diverse statistical population.
Fuzzy rules for FRHI2 are assigned as follows:

Management of radon risk
After conducting a comprehensive risk assessment, the focus should shift toward continuous risk management. The most critical risk management methods are generally stated as follows (Sarkheil and Rahbari 2016a, b): • Risk elimination/decrease.
• Risk control by engineering acts.
• Risk substitution. • Endorsing PPEs. 1 Amongst the above list, steps 1 and 2 are the most proper and effective methods for managing radon emission risk because radon emissions have natural radix and vary from site to site and time to time. Health masks are suitable only for temporary outdoor conditions and may not be helpful for indoor and long-term use.
Therefore, to decrease health risk problems of radon emissions, it is highly recommended to decrease indoor radon concentration by engineering methods. The essential engineering methods are as follows: • Preventing radon entry to residential spaces after finding the primary source of natural emission. Most radon emissions happen through microscopic and macroscopic holes on the ground surface. It is recommended to use proper insulations for floors, usually made of rubber or slurry. • Utilizing proper free or forced ventilation for rooms by canals or fans. • Soil Suction from underground spaces by proper pipelines attached to the suction motor. • Reducing the emission driving force, pressurize the indoor space with suitable blowers, fans, ventilators, etc. • Using impermeable paints for walls.
A case study for proper ventilation is presented as follows. A 24-year residential unit with a total area of 224 m 2 and 178 m 2 of infrastructure constructed as a single-story building with a basement and a gabled roof. Materials and hand-mixed concrete were used to build this building. The window frames of this residential unit were made of metal, and single-paned glass is used for the doors and windows. This residential unit is located in the Kuh-e-sangi area, 20th Kuh-e-sangi street, No. 27 (located in the southern part of the city, an area with high radon pollution and worn texture), and at the time of this study four people were living in there. Radon concentration values were measured in ten points by the RadonBox-10 device to evaluate the radon concentration values in this residential unit. There are four ways to reduce radon concentration inside buildings: • Ventilate air rich in radon.
• Radon emission sources should be removed.
• Radon and its derivatives should be removed or eliminated somehow (Skeppström and Olofsson 2021).
Ventilation methods cause radon-laden air to escape and prevent radon accumulation. The quality of the walls and floor of a building also plays a vital role in preventing radon from entering to the building (especially cracks and holes found on the walls and floors) Theoretically, it is possible to pass indoor air through a filter so that radon and its derivatives are absorbed and separated from the indoor air (Cooper et al. 2011).
In order to eliminate radon in this residential unit, the method of reducing the pressure under the slab was used.
To evaluate the performance of the radon correction method, radon concentration values were recorded every 12 h four times.
To improve the efficiency of radon correction systems, using the method of reducing air pressure under the slab, a combination of radon absorption well drilling and repairing cracks in the body and foundation of the basement were employed. All cracks and crevices in the floor, walls, and corners of rooms and basements were identified and then were repaired using Faber concrete adhesive. The Faber concrete adhesive is a homogeneous water-free adhesive, with high tensile and flexural strength and is effective in gypsum and lime concrete durability improvement. The Faber concrete adhesive is used for various applications such as repairing superficial and deep damages. The most common use of concrete adhesive is for building maintenance and repair, because this material forms a compatible and homogeneous mixture with mortar, which prevents water seepage and separation of fine and coarse grains. The concrete adhesive is available in liquid form and has a milky color. The specific weight of Faber concrete adhesive is 3 gr/cm, and contains no chlorine (Fuente et al. 2019).

Stochastic evaluation of radon zoning
Based on the mean error values and RMSE, the kriging method was selected as the most optimal method. In this study, radon levels were measured in 145 neighborhoods and radon zoning was performed by four interpolation methods based on the measured values. The population density map of the city, the zoning map by kriging method, and the map of places and streets of the study area were used to evaluate the zoning results on an urban scale. The results are shown in Table 1. The FRHI column in Table 1 indicates the fuzzy radon hazard index values contrasted by predefined colors. As it is derived from FRHI columns for 159 stations, only nine stations (about 5.6%) are categorized in very hazardous level by purple, 89 stations (about 55.9%) are categorized in non-hazardous level by green, 45 stations (about 28.3%) are categorized in less-hazardous level by yellow, seven stations (about 4.4%) are   Table 2 shows the measured quantities of radon gas in each station.
The output results of FRHI2 were compared to two conventional indices of GRP (geogenic radon potential) and GRHI (geogenic radon hazard index). These indices were defined as follows: After inserting radon concentrations and Ks of various study area locations into the proposed FRHI2.FIS, the results were compared to GRP and GRHI. The gist of the results are shown in Table 2; and all the results are given in Table 7, Appendix No. 2.
The output FRHI2s are validated with GRHI. The results are shown in Fig. 7, with a correlation coefficient of about 0.75, expressing a rather proper fit.
FRHI exhibits more certainty because it deals with the standard distribution and fuzzy inferences. The most important reasons for deviations from the proposed FRHI with classic GRHI are explained below: • GRHI is confined to geogenic emissions and does not take into account the healthcare problems. • GRHI has a logarithmic notion, while FRHI has an inference-based nature so that it can overcome statistical deviations more effectively. • FRHI focuses more on concentration rather than permeability, while GRHI is more sensitive to K. Radon concentration is the most important factor for environmental and healthcare recommendations. • GRHI is dependent on Maximum and Minimum GRPs, so it is very sensitive to locations of sampling and the data statistics. In other words, GRHI varies harshly from one case study to another, while FRHI is dependent on fuzzy rules and inferences and independent of case studies. • GRHI is based on GRP, which indicates the potential of radon emissions. At the same time, FRHI is directly dependent on concentration and permeability. • FRHI is a more efficient index because it works with the standard distribution for fuzzy categorization of nonlinear inputs and outputs. However, GRHI first works with the median or average of Box and Whisker plots and second cannot cover the nonlinear aspects of the input-output spaces.
The regions with the highest levels of radon pollution in the city are region 8 in areas 1 and 2, region 12 in area 2, region 12 in area 3, region 6 in area 3, and region 5 in area 3. The reasons for the high radon concentration in region 8 in areas one and two are as follows: being located within the shrine's traditional and old texture, not meeting urban planning principles requirements, and poor air conditioning in these areas. Region 12 in area 3 includes the Asian Highway, the busiest entrance road to the city from Tehran. Also, in this zone, geological formations naturally emit high amounts of radon. Region 12 in area 2 is located near an industrial estate, which is likely to have high radon levels due to the many industrial units in the area. Region 6 in area 3 is located adjacent to a power plant. Radon released from its activity is the primary possibility for high amounts of radon and can be the main reason for observing higher radon levels in this area. The rest of the study area is within the radon limit. The cleanest areas are region 9 in area 2, region 11 in area 2, region 12 in area 1, region 7 in area 3, region 2 in area 5, area 6, and region 2 in area 6. Also, in area 2 and region11 in area 2, there is the Great National Park, which has caused the radon values in this zone to remain much lower than the permissible limit.
Radon concentration values are very high around region 12 in area 1, but in the middle of this area, due to green space (Vakilabad Park), radon concentration values are within the permissible range. In region 7 in area 3, Tough Forest Park is the main factor in the permissibility of radon gas. In region 2 in areas 5, 6, and region 6 in area 2, due to very low population density and its geological structure, radon values are within the allowable range (Fig. 8).
Four interpolation methods were utilized to model spatial variations, including areal, IDW, Kriging, and Co-Kriging (Table 4). Kriging and Co-kriging methods rely on the definition of the variogram, and the method's success depends on selecting the appropriate or optimal variogram model. The IDW method only determines weights based on the distance between known and unknown points without considering the distribution of points around the estimated point. Nearby points are given more weight, while farther points are given less weight. R2, ME, and RMSE indices were used to compare the accuracy of kriging, Co-kriging, IDW, and Areal interpolation methods (Warrick et al. 1990).

Implementation of the method in the selected residential unit
After repairing the cracks, an absorption well was dug in the building area at 1.5 m from the foundation sidewall, with a depth of 3 m and a diameter of 30 cm to hold the fan steady. A 20-W blowing shaft fan with an airflow rate of 100 m 3 /h was used. The proper chamber was covered with aluminum foil and a 7.5 cm hole was made in the center to expel the air. The area around the well was covered with concrete adhesive, and the perimeter of the PVC pipe was covered with glass adhesive to prevent air leakage. A hole was dug to a depth of 25 cm below the slab and a diameter of 7.5 cm in the corner of the main corridor of the basement using a Hilti device. It was connected to the air transfer pipe installed outside the building by an elbow pipe. Holes were made under the slab at 1-cm intervals in the first 30 cm of the buried pipe to facilitate air flow. The PVC pipe was continued to the roof level and connected to the suction system installed on the roof using a flexible plastic pipe, transferring the air-containing radon out of the building. The suction system includes two 15-W axial suction fans with an efficiency of 85% (''Appendix 2'').
Measurements were taken at each harvest point for approximately 10 min every 12 h, up to 48 h after installing the radon disposal system. A total of 50 measurements of radon gas were taken in this residential unit. The maximum registered value was 219 Bq/m 3 for the basement, while the minimum was 86 Bq/m 3 for the attic. As in previous sections, the radon limit was 147 Bq/m 3 (EPA). Table 5 shows the measured values.
In Table 5, the natural radon emission was measured at known points, and its values were assumed to be the initial values. After installing the radon reduction system, it was continuously measured every 12 h. Radon concentrations were reduced in all measurements, reflecting the positive effect of this corrective method.
As expected, the toilets had the highest recorded values. In contrast, the gables had the lowest due to their adequate where y, is the amount of radon over time X (one unit is half a day or 12 h). Implementing this correction method costs almost 100 USD, significantly less than radon-related therapeutic costs. The building owner uses a package and a wallmounted radiator instead of a heating system to reduce the amount of radon further.
More robust artificial ventilation should be used in the bathroom and the toilet area and doors and windows should be sealed in winter to improve natural ventilation. In some cases, it is recommended to open all the doors and windows to enhance air ventilation.  The diagrams in Fig. 9a-c show that the efficiency of the radon ventilation system will reach its maximum value after about 1 week. Auxiliary sensors should be used to optimize power consumption. For this purpose, a system can be used that starts working from a specific limit if the radon values rise and stay in standby mode when unnecessary.
It is important to note that the initial fuzzy level for the mean value of FRHI is Hazardous (for FRHI value equal to 60.1), determined by red. The Maximum FRHI level for 48 h after installation is rather hazardous (for FRHI value equal to 44.8), determined with orange. This indicates that the maximum statistical environmental health risk after steady-state installation would fall into an improved category exhibiting hazards. For mean values, this level would fall as less hazardous, meeting all three recommendations of ICRP, USEPA, and WHO.
The average of the initial recorded values was 146.9 Bq/ m 3 to evaluate the systems performance, which decreased radon values every 12 h after installing the system. Table 6 provides information on how the system efficiency increases. Within 48 h, the system's efficiency increased to 28%, which means that after 48 h, the amount of radon reached 72%. This value is expected to decrease to 50% in the long run and remain constant. Equation 1 of the fitting line provides the long-term radon values based on the measured values ( Table 6).
The interesting point in this case, is that building's owner initially opposed the installation of the system. Still, after learning about the very dangerous harms of radon gas and the relatively high amounts of radon in his home, he agreed to adopt this system and cooperated in all stages. Most people, even the educated, are not sufficiently aware of radon gas and its harm to human health. Therefore, providing people with proper education and information on such a delicate issue is of great importance to encourage individuals to adopt corrective methods to minimize health-related risks.

Conclusion
This study highlights the importance of stochastic assessment of radon gas in identifying environmental health risks in urban scale and residential buildings. The proposed fuzzy radon hazard indices (FRHI) cover health and human-environmental assessments, making them more efficient than classic methods that primarily focus on geogenic aspects. Two FRHIs are developed for areas where permeability data is limited and unavailable. Furthermore, FRHI1 can contribute to each standard, and FRHI2 can be compared to GRPs or GRHIs. Fuzzy sets theory applications can overcome diverse statistical deviations and variances due to their nonlinear and intersectional nature. Fuzziness simplifies many problems for stochastic and chaotic statistical environmental radiation fields. The GRHI is based directly on GRP, which indicates the potential for radon emissions. In contrast, the FRHI is based on concentration and permeability without intermediate. The FRHI is a more efficient index as it works with standard distributions for fuzzy categorization of nonlinear inputs and outputs. However, the GRHI first works with the median or average of Box and Whisker plots and cannot cover the nonlinear aspect of the input-output spaces. These fuzzy results indicate that this approach can serve as a circumstantially integrated standard for stochastic radon risk assessment.
The study also identifies critical zones with high radon emissions and provides insights into radon gas concentrations in different building areas. The findings emphasize the need to install correction systems in buildings with high radon levels to mitigate the risks of this natural gas. Overall, this study's approach can serve as a circumstantially integrated standard for stochastic radon risk assessment and help in developing special control measures for reducing radon gas risks in buildings.
It is widely recognized that subsurface rocks and fractures emit natural radon gas globally. As such, this research proposes techniques and standards that can be utilized to identify areas with elevated levels of radon emissions. By doing so, technical control measures can be implemented for local and site-specific buildings to mitigate the risks of this naturally occurring gas.
Appendix 1: The plans of a selected residential unit in the studied area See Figs. 10, 11, 12, 13 and 14.   Table 7.