A comparative assessment of flood susceptibility modelling of GIS-based TOPSIS, VIKOR, and EDAS techniques in the Sub-Himalayan foothills region of Eastern India

In the Sub-Himalayan foothills region of eastern India, floods are considered the most powerful annually occurring natural disaster, which cause severe losses to the socio-economic life of the inhabitants. Therefore, the present study integrated geographic information system (GIS) and three comprehensive and systematic multicriteria decision-making (MCDM) techniques such as Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), Vise Kriterijumska Optimizacijaik Ompromisno Resenje (VIKOR), and Evaluation Based on Distance from Average Solution (EDAS) in Koch Bihar district for comparative assessment of the flood-susceptible zones. The multi-dimensional 21 indicators were considered, and multicollinearity statistics were employed to erase the issues regarding highly correlated parameters (i.e., MFI and long-term annual rainfall). Results of MCDM models depicted that the riparian areas and riverine “chars” (islands) are the most susceptible sectors, accounting for around 40% of the total area. The microlevel assessment revealed that flooding was most susceptible in the Tufanganj-I, Tufanganj-II, and Mathabhanga-I blocks, while Haldibari, Sitalkuchi, and Sitai blocks were less susceptible. Spearman’s rank (rs) tests among the three MCDM models revealed that TOPSIS-EDAS persisted in a high correlation (rs = 0.714) in contrast to the relationships between VIKOR-EDAS (rs = 0.651) and TOPSIS-VIKOR (rs = 0.639). The model’s efficiency was statistically judged by applying the receiver operating characteristic-area under the curve (ROC-AUC), mean absolute error (MAE), mean square error (MSE), and root mean square error (RMSE) techniques to recognize the better-suited models for mapping the flood susceptibility. The performance of all techniques is found good enough (ROC-AUC =  > 0.700 and MAE, MSE and RMSE =  < 0.300). However, TOPSIS and VIKOR have manifested an excellent outcome and are highly recommended for identifying flood susceptibility in such active flood-prone areas. Thus, this kind of study addresses the role of GIS in the construction of the flood susceptibility of the region and the performance of the respective models in a very lucid manner.


Introduction
Rapid-onset geophysical hazards have always wreaked havoc on human beings, their property, and their possessions (Kron et al. 2021). It accounted for nearly one-third of all geophysical hazards and almost 31% of all economic damages in the world (Matheswaran et al. 2019). Flood is further grouped into three sub-types: river floods, flash floods, and storm surges or coastal floods (Yang and Liu 2020). Riverine floods in any region ensue when a river's capacity is exceeded by a large amount of rain (Lund 2012;Liu et al. 2018). Every year, floods in different parts of the world take a massive, devastating toll on society (Shah et al. 2020;Teh and Khan 2021). It has become more common worldwide over the last 40 years (Vanolya and Jelokhani-Niaraki 2019), owing to the growing effects of changes in climatic parameters, land use, and other anthropogenic activities . Nearly 90% of flood-related disasters and 95% of related losses occur in developing nations, particularly on the Asian continent (Mirza 2011). Hence, flood risk estimation and flood control are vital issues for understanding flood-prone sites and preventing flood damage by taking the necessary actions (Hagen and Lu 2011).
Susceptibility is a quality that can be used to indicate a system's weakness to a threat (Birkmann, 2007). The susceptibility of a human settlement to being impacted by a hazardous phenomenon as a result of its placement in the effect region of the phenomenon and insufficient physical protection (Cardona 2013). The word vulnerability refers to the impacts (harm) that could result from an occurrence. Vulnerability is defined as the conditional likelihood that the hazard event causes destruction provided the existence of the threat incident (Fischer et al. 2016). The vulnerability of human settlement is inextricably linked to many social activities (Cardona 2013). In certain circumstances, although not all, susceptibility and vulnerability can be employed interchangeably. Being vulnerable implies that you are weak and open to being attacked. Susceptibility alludes to the quality of recurrence over time and succumbing to circumstances. Few recent studies (Monte et al. 2021;Feldmeyer et al. 2021) have clearly highlighted that vulnerability is socioeconomic constraints of the hazardous event while susceptibility is physical environment oriented in nature. Risk can be described as the sum of susceptibility factors, the likelihood that an outcome will happen, how exposed you are to it, and the results (negative effects) if the event does happen (vulnerability) (Kaplan and Garrick 1981). The framework for determining the risk assessment is created by the susceptibility and vulnerability of multiple elements.
Flood hazard mapping studies are essential for any region, and they have witnessed significant analytical advancements in recent years (Shafapour Tehrany et al. 2017). Several scholars believe multicriteria decision-making (MCDM) and geographic information system (GIS) procedures to be highly versatile in terms of giving methodologies and strategies for assessing any decision-making situations with incomparable criteria (Rahmati et al. 2016;Idowu and Zhou 2021). The MCDM has been proven to be useful in resolving conflicts between tangible and intangible parts in the machine tool selection (Li et al. 2020). It has been observed that various scholars used MCDM techniques in their work to delineate flood hazard zonation (Das 2018), flood susceptibility mapping , flood vulnerability mapping (Atijosan et al. 2021), flood risk mapping (Radwan et al. 2019), flash floods analysis , and flood forecasting (Teh Noranis et al. 2019). In contemporary studies, the MCDM techniques, viz., analytical hierarchy process (AHP) Das and Gupta 2021), fuzzy analytical hierarchy process (Hasanloo et al. 2019), discrete choice analysis (Wassenaar and Chen 2003), Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) (Sari 2021), preference ranking organization method (Chen 2021), Vise Kriterijumska Optimizacijaik Ompromisno Resenje (VIKOR) (Wang et al. 2019), Evaluation Based on Distance from Average Solution (EDAS) (Ghorabaee et al. 2017(Ghorabaee et al. , 2015, and multi-objective optimization on the basis ratio analysis (Karande and Chakraborty 2012), take a dominant role to handle flood hazard susceptibility and vulnerability mapping. In this study, the researchers have attempted to manifest the flood susceptibility modelling of the region using the TOPSIS, VIKOR, and EDAS MCDM methods, which have become preferably and frequently used in regional flood studies (Pathan et al. 2022;Ameri et al. 2018;Arabameri et al. 2019;Khosravi et al. 2019;Sari 2021;Mandal et al. 2022;Rafiei-Sardooi et al. 2021;Bera et al. 2021;Stanujkic et al. 2018). All the MCDM methods are selected due to their high efficiency in making the decision based on multiple criteria (Song and Chung 2016; Stanujkic et al. 2018).
In India, during the monsoonal season, floods occur when the water level exceeds the danger level (1 m above the warning level) at that specific location. Tropical disturbances like cyclonic storms, depressions, and low-pressure systems envelope the country throughout the summer monsoon season. The uncertainty of the monsoon causes severe rain and floods in the country (Dhar and Nandargi 2003). Almost 40 million hectares of land in India is flood-prone, and about 8 million hectares of land is flooded each year (Ray et al. 2019). West Bengal is India's most flood-prone state, with floods affecting 42.55% of the state's landmasses. Several researchers have made a great contribution to the assessment of flood hazards, vulnerability, and risk in the Sub-Himalayan region of the state, viz., Chakrabortty et al. (2021), Chakraborty and Mukhopadhyay (2019), Ghosh and Kar (2018), Roy et al. (2021), Sinha et al. (2008), Ghosh et al. (2022), Bandyopadhyay et al. (2016), Sahana and Patel (2019), and Samanta et al. . Flood hazard management and mitigation measures in the state are at risk (Annual Flood Report 2019). The southern front of the Darjeeling-Bhutan Himalaya acts as the first orographic constraint to the southwest monsoon in the Sub-Himalayan part of the state. In this region, the annual rainfall is usually 3000-6000 mm. It also receives torrential rainfall of up to 800 mm day −1 (Prokop and Walanus 2017). As a corollary, the Himalayan foothills are a well-known flood-prone region in the state (Ghosh and Ghosal 2020). The Koch Bihar district is situated in India's eastern Himalayan foothills. The upper catchment area of the rivers in this region received a large quantity of rainfall throughout the rainy season, resulting in flood disasters in the riparian areas of the lower sections of the rivers. Essentially, the soil of this region resides in the transition area between Himalayan foothills and Bangladesh plains, culminating in flash flood events annually. The physiographic condition and tendency towards torrential rainfall in the upper catchment area have introduced flash flooding tendency in this region. Historically, flash floods are a common phenomenon in the study area, and 1993, 2006, 2007, 2008, 2009, 2010, 2017, 2019, and 2020 are demarcated as devastating flash flood years. During these years, flash flood hazards affected 60%, 30%, 25%, 45%, 20%, 35%, 50%, 15%, and 20% of the area respectively, in the district (DDMPKD 2021(DDMPKD -2022. Previous studies show that flooding has significantly impacted the lifestyle of the inhabitants in the district, both socially and economically (Chakraborty and Mukhopadhyay 2019;Choudhury et al. 2022). Due to its historical prominence, riverine flooding is the most sensitive issue in the Sub-Himalayan Koch Bihar district. However, the region is faced with frequent flooding phenomena. The frequency of floods and interruption of human settlements has significantly grown due to climate change in the Indian subcontinent (Mirza 2011;Pattnaik and Dimri 2020;Ahammed and Pandey 2021). The existing literature depicted the flood risk zones of Koch Bihar district with only the AHP method (Choudhury et al. 2022;Chakraborty and Mukhopadhyay 2019). There are certain restrictions on the choice of the conditioning factors in the case of the existing method but there are none in the case of TOPSIS, VIKOR, and EDAS because they maintain order when evaluating alternatives with more choices (Rafiei-Sardooi et al. 2021). Hence, in the present study, multi-dimensional susceptibility parameters have been taken into consideration. There is also lacking of multicollinearity assessment studies in this region for the removal of the highly interrelated flood conditioning factors. The multicollinearity issues regarding the highly correlated parameters have been fixed throughout the study. However, systematic research that studies the flood susceptibility at the microlevel of the district in the wake of recent challenges is lacking. Therefore, there are also significant research gaps in the application of multiple models and their correlation and cross-verification analyses for the comparison study of flood modelling. Therefore, the novelty of the research has prevailed in the utilization of multi-dimensional conditioning parameters for the comparative assessment of three MCDM techniques for flood susceptibility modelling. The approach of the study can be useful for demarcating the susceptible zones through a comparative discussion of different MCDM models for such kinds of active flood-prone regions. The main goals of the research are as follows: • To prepare the flood susceptibility models (TOPSIS, VIKOR, and EDAS) of Koch Bihar district by integration of GIS and MCDM approaches The region has been selected for mapping flood susceptibility based on literature reviews (Chakraborty and Mukhopadhyay 2019;Choudhury et al. 2022) and field observations (2019-2022). High intensifying rainfall during the monsoon season is a common phenomenon over here, viz., in 2020, the district received 6673.20 mm of rainfall, which is the highest in the last 10 years. The district has 12 community development blocks, and all blocks are susceptible to floods. Mostly in all blocks of the district, the seasonality of flood hazards varies from July to September. The gauge height of the river is tremendously increasing during monsoon time, viz., in 2020, the maximum gauge reading of the Torsa (at Keshab Ashram), Raidak-I (at Tufanganj), and Mansai (at Mathabhanga) was observed at 42.20 m (on July 11), 35.96 m (on July 13), and 48.57 m (on July 22), respectively. The region has a long history of occurrences of devastating floods and related damages to the socio-economic life of the people, viz., in 1993, floods affected directly and indirectly about 40% of inhabitants of the district, while in 2006 affected 20% of inhabitants, 2007 affected 10% of inhabitants, 2008 affected 30% of inhabitants, 2009 affected 15% of inhabitants, 2010 affected 20% of inhabitants, 2017 affected 30% of inhabitants, 2019 affected 5% of inhabitants, and 2020 affected 20% of inhabitants (DDMPKD 2021(DDMPKD -2022. The location map and flood condition of the study area are depicted in Fig. 1

Flood inventory map
For an accurate assessment of flood susceptibility maps, a flood inventory map must be developed (Ghosh et al. 2022). It is basically necessary to validate the MCDM techniques, i.e., TOPSIS, VIKOR, and EDAS. This study produced a flood inventory map using the West Bengal Disaster Management and Civil Defence Department portal (http:// wbdmd. gov. in/ pages/ distr ict_ dm_ plan.aspx) and thematic services of Bhuban Portal (Government of India) (https:// bhuvan-app1. nrsc. gov. in/ thema tic/ thema tic/ index. php). The flood inventory of the district consists of historical flooded data from 1999 to 2010 and 2018 to 2020. Figure 1c depicts the flood inventory of the district with the incorporation of 332 flood points and 211 non-flood points. The web map service (WMS) function in ArcMap was used to retrieve the locations that were flooded and those that were not. Areas that experienced flooding at least once during the periods from 1999 to 2010 and 2018 to 2020 have been taken into consideration. For extracting the nonflood points, firstly, the clustered effective flood records were mapped, and then outside areas were extracted using reclassify tool in ArcGIS. Secondly, non-flood points were randomly created, followed by Boots and Getis (1988).

Spatial database construction on the GIS platform
The flood susceptibility analysis basically follows several parameters. These parameters have distinct footprints on the susceptibility mapping. Therefore, it is a serious task to find out the best parameters through extensive literature reviews, expert opinion on the study area, and field observation. Several studies (Arabameri et al. 2019;Ali et al. 2020;Nachappa et al. 2020;Das and Gupta 2021;Saha et al. 2021) indicate the significant factors related to flood susceptibility mapping. Table 2 depicts the source of different applied factors for the flood susceptibility modelling. Over the last 20 years, GIS techniques have been extensively used to reliably and effectively estimate hazards, vulnerability, and risk (Ali et al. 2020;Das and Gupta 2021). At first, this study prepared the spatial database of 21 flood conditioning parameters to create the thematic layers in the GIS platform. The SRTM DEM (30 m spatial resolution) and LANDSAT-8 data were downloaded using the USGS (United States Geological Survey) Earth Explorer website and processed in ArcGIS 10.4.1 software. The obtaining SRTM DEMs were composited using the "Mosaic To New Raster" tool of "Data Management Tools," clipped and filled using the "Hydrology" tool of "Spatial Analyst Tools." The SRTM DEM is used to prepare the elevation, aspect, slope, curvature, TWI, drainage density, TPI, terrain ruggedness index, SPI, STI, and roughness layers. The satellite images are radiometrically corrected in the GIS platform and employed for computing the parameters LULC, NDVI, and mNDWI. The rainfall data was compiled from  the IMD (India Meteorological Department) website and were used to generate the long-term annual rainfall, MFI, and rainfall deviation map of the study area. To delineate the influence area of a rain gauge station, at first, Thiessen polygons were created using the "Proximity" tool of "Analysis Tools" in ArcGIS. All the rainfall indices were computed in Microsoft Excel 2019, and based on the assigned values, thematic layers have been produced in ArcGIS. The thematic layers for lithology, lineaments, and geomorphology were framed by obtaining data from the Bhukosh GSI (Geological Survey of India) website. The thematic layers of soil were produced from the data of the FAO (Food and Agriculture Organization) soils portal. For multicollinearity analysis, ArcGIS software was also used to generate and extract the random points in all thematic layers. After fixing the problems of multicollinearity, a total of 20 thematic layers have been taken into consideration. Finally, all layers were resampled into 30-m spatial resolution and further incorporated according to the methodology of the TOPSIS, VIKOR, and EDAS to finalize the susceptibility zonation of the region. The methodological framework ascertained for this research has been manifested in Fig. 2.

Flood conditioning parameters
The magnitude of the flooding events is dependent on topographical, geological, climatic, hydrological, lithological, and anthropogenic parameters. In the present study, 21 flood conditioning parameters were initially considered to develop the models, which are discussed below:

Elevation
Water tends to accumulate as it descends from higher to lower heights. Simultaneously, due to rainfall accumulation in the lower elevated lands, these areas are regarded as the most flood susceptible (Waqas et al. 2021). This parameter sustains an inverse relation with flood susceptibility (Ali et al. 2020). The elevation map was prepared from SRTM DEM in ArcGIS platform, and the region has varied from − 38 to 115 m in altitude (Fig. 3a).

Curvature
Several studies (Shafizadeh-Moghadam et al. 2018;) examined curvature as an important variable in flood susceptibility mapping. Curvature represents the three units, i.e., concave, flat, and convex. Convexity is associated with the pixels having positive values, while concavity indicates the negative value, and the flat area is expressed as zero. The curvature value varied from − 7.48 to 6.69 in this region (Fig. 3b).

Slope
The slope is considered an essential flood triggering parameter (Shafizadeh-Moghadam et al. 2018;Ali et al. 2019). It determines the flow velocity and affects the surface runoff rate and infiltration capacity (Ali et al. 2020). The filled DEM was used for slope analysis, and using the "Raster Surface" tool of "3D Analyst Tools," a slope map was generated for the study area. The produced slope map in Fig. 3c varies between 0 and 43.95°. The low-sloping lands are more susceptible to floods.

Aspect
As a topographic parameter, the aspect influences the occurrences of flood hazards . It indicates the direction of land and affects the precipitation, hydrological process, weathering, and levels of sunshine (Vafakhah et al. 2020). The aspect map was generated from filled SRTM DEM and using the "Raster Surface" tool of "3D Analyst Tools," It is shown in ten classes of the respective area in Fig. 3d.

Roughness
Roughness is another significant flood-inducing factor (Talukdar et al. 2020). The roughness of the region is calculated from the filled SRTM DEM using the "Focal Statistics" and "Raster Calculator" tools in the ArcGIS platform. The roughness is expressed as follows (Evans 1972; Mukherjee and Singh 2020): where FS mean is the focal statistics mean, FS min is the focal statistics minimum, and FS max is the focal statistics maximum. The roughness of the study area is varying in between 0.11 and 0.89 (Fig. 3e). Basically, the lower roughness value reflects the flooding areas.

Terrain ruggedness index
The terrain ruggedness index (TRI) affects the storage capacity of the surface, rate of runoff, and stream energy  (Rahmati et al. 2019). The heterogeneity of the topography is illustrated through the TRI map of the region in Fig. 3f. The TRI is calculated for every grid cell of the DEM by applying the "DOCELL" command in ArcInfo (Riley et al. 1999), as follows: (2) 2 where x ij is represents the elevation of each surrounding cell to cell (0, 0).

Topographic positioning index
The topographic positioning index (TPI) shows the altitudinal difference of the central point to the average heights of its surrounding cells within a certain radius (Weiss 2001;Fig Kanani-Sadat et al. 2019). It is also used to determine the slope position, categorize the landforms, and understand watershed characteristics (Weiss 2001). The TPI is calculated using Eqs. 3 and 4, where z 0 is the central point, z is the average elevation around the central point, and R is the predetermined radius.
The TPI map of the study area was derived by applying the "land facet corridor designer tool" in ArcGIS software (Jenness et al. 2013). TPI value varied from − 6.55 to 20.72, as illustrated in Fig. 3g. The positive value implies the higher elevated lands than the mean heights of its neighborhood and vice versa. Thus, flood-prone zones are associated with negative and zero TPI. Basically, negative TPI is the valleys, and zero TPI is the flat areas or constant-sloping lands (Weiss 2001).

Topographic wetness index
The topographic wetness index (TWI) governs the overland flow and is employed to determine the topographic influence on hydrology (Samanta et al. 2018;Ali et al. 2019Ali et al. , 2020Tehrany et al. 2019). The following equation was used to compute the TWI (Beven and Kirkby 1979): where a and B are used to describe the specific catchment area and slope of the region, respectively. Furthermore, a = A L , where A describes the total basin area, and L describes the length of the contour (Samanta et al. 2018). Using the "Raster Calculator" tool of "Spatial Analyst Tools," the TWI was produced for the study area. The TWI value ranges from 3.7 to 22.46, and the geographical variation of the wetness of the region is manifested by employing the TWI map, as illustrated in Fig. 3h.

Sediment transport index
The sediment transport index (STI) is also taken as a crucial flood susceptibility parameter. It is related to the runoff characteristics of any region. The region of higher susceptibility to floods is associated with lower STI and vice versa (Ali et al. 2020). In this region, the STI value varies from 0 to 3682.04 (Fig. 4a). The STI is employed by the following formula (Eq. 6), where F a and S are the flow accumulation and slope raster, respectively, derived from SRTM DEM, and x and y represent the constant.
All the function of Eq. 6 was performed using the "Raster Calculator" tool of "Spatial Analyst Tools" in ArcGIS.

Stream power index
The stream power index (SPI) depicts the erosive power of the stream flow (Vafakhah et al. 2020). It also demonstrates the soil-water content of the region, discharge degree, and flooding power of the river (Poudyal et al. 2010). A greater SPI value means the rivers of that region have more flooding power. The SPI is calculated using the following equation (Moore et al. 1991): where Ai represents the specific area and tan represents the gradient. For the generation of the SPI map of the region, the "Raster Calculator" tool of "Spatial Analyst Tools" has been employed. In the study area, the SPI value ranges from − 10.35 to 12.76 (Fig. 4b). The region with lower SPI is associated with more possibility of flooding, as water flow is in a slow movement or stagnant.

Lineament density
Lineaments are underground fractures that allow water storage and movement. Higher water movement persists in the areas with high lineament density (Periyasamy et al. 2018). The vector layer of the GSI was used to detect the presence of lineaments in the region. The lineament density map was prepared using the "line density" tool of "Spatial Analyst Tools" in ArcGIS, and the value varies from 0 to 0.55 km/km 2 (Fig. 4c).

Drainage density
Drainage density represents the length of the drainage network per unit area (Waqas et al. 2021). It affects occurrences of peak flow (Rahmati et al. 2019), rate of runoff, and infiltration. The existing drainage networks in the study area were extracted from SRTM DEM. Several algorithms were performed in the "Arc Toolbox" to create the drainage map of the study area. After that, the drainage density map was prepared in the ArcGIS platform utilizing the "Line Density" tool, the same as the lineament density layer, as displayed in Fig. 4d. The drainage density value varies between 0 and 1.11 km/km 2 .

Lithology
Lithology is considered in this study as another flood conditioning parameter. It affects the hydrological processes (Miller et al. 1990), soil permeability (Oikonomidis et al. 2015), and characteristics of the drainage network of any region. The lithological characteristics of the study area have been depicted in Fig. 4e by obtaining the vector data from GSI.

Geomorphology
The area-specific geomorphological features contributed to the flood susceptibility analysis as one of the prime factors (Das and Gupta 2021). The geomorphological map of the area depicted that the region has predominance by a large number of abandoned channels, braid bar, channel bar, channel islands, cut-off meanders, active flood plains,  (e), geomorphology (f), soil (g) meander scars, paleochannels, and ox-bow lakes (Fig. 4f). The dominance of these low-lying lands is the primary driver that makes the district most susceptible to floods.

Soil
The characteristics of the soil of any region influence the hydrological behavior (Ali et al. 2020). The soil's texture, structure, porosity, density, aeration, cohesiveness, and permeability control the infiltration and runoff. The soil map of the region was delineated from the FAO soil map of the world and identified based on textural classes as sandy loam, loam, and clay (Fig. 4g).

Long-term annual rainfall
Rainfall is the key indicator for detecting flood-susceptible lands . It is observed that rainfall and flooding have a positive relationship. The torrential rains are accelerating the sub-surface hydrostatic level (Ali et al. 2020). Hence, an annual rainfall map was prepared as a crucial flood conditioning factor. The spatial distribution of long-term (1986-2020) annual rainfall of the region is shown in Fig. 5a. A high rainfall zone encompasses the area as the annual rainfall value varies from 2599 to 3536 mm.

Modified Fournier index
The variation in the rainfall intensity of the region was depicted using the modified Fournier index (MFI). It was considered a vital flood conditioning variable as a higher MFI value is associated with very high flood-susceptible areas (Souissi et al. 2020). MFI can be expressed as follows (Costache 2019;Souissi et al. 2020): here, Pi shows the mean monthly precipitation and P shows the mean annual precipitation. In the region, MFI values range between 520 and 648 mm/year (Fig. 5b).

Rainfall deviation
Rainfall deviation was used as an important causative factor for the flood susceptibility study since a positive deviation reflects adequate rainfall and potential of flooding, and vice versa (Ali et al. 2019). The rainfall deviation was derived taking the following formula (Ali et al. 2019): where Q represents the rainfall deviation, L represents the recorded rainfall, and Z represents the average rainfall. In the study area, rainfall deviation ranges from 96 to 184 (Fig. 5c).

Modified normalized difference water index
The modified normalized difference water index (mNDWI) is considered a flood conditioning parameter in place of the normalized difference water index (NDWI), as mNDWI appropriately retrieves water information. The mNDWI can successfully reduce the information on built-up lands when displaying the water feature in the areas with dominating build-up lands compared to the NDWI (Han-Qiu 2005). Therefore, mNDWI is computed using the following equation: where MIR is showing a middle infrared band. The mNDWI was computed using the "Raster Calculator" tool of "Spatial Analyst Tools" in ArcGIS. The mNDWI value in the case of the study area ranged from − 0.36 to 0.27 (Fig. 5d).

Normalized difference vegetation index
In this study, the normalized difference vegetation index (NDVI) is considered a significant flood triggering factor (Powell et al. 2014). Generally, NDVI is used to detect areas with vegetation and non-vegetation cover. Many researchers (Kanani-Sadat et al. 2019;Ali et al. 2020) exhibit the relationship between NDVI and occurrences of floods. It ranges from − 1 to + 1, and in the present study area, it lies between − 0.11 and 0.48 (Fig. 5e), employing the following equation: where NIR is the near-infrared band and RED is the red band. Using the "Raster Calculator" feature of the "Spatial Analyst Tools" in ArcGIS, the NDVI was calculated based on Eq. 11. The negative value demonstrates the probability of occurrences of flood havoc.

Land use land cover
Land use land cover (LULC) has been regarded as a vital flood triggering parameter , as it affects the hydrological condition of the region, i.e., infiltration capacity, rate of evapotranspiration, evaporation, and runoff (Souissi et al. 2020;Vafakhah et al. 2020). The supervised classification technique has been adopted in ERDAS imagine software to prepare the LULC map of 2021. The map was produced with an 83% accuracy level. The study area manifested five distinct LULC categories: build-up area, waterbody, vegetation, river bed, and agricultural lands in Fig. 5f. The high potentiality of flood havoc is observed in the rivers, settlements, roads, and bare lands, while low potentiality is kept in the vegetation cover areas (Tehrany et al. 2013).

Multicollinearity checks
In flood susceptibility modelling, the multicollinearity test is regarded as an essential aspect that involves recognizing a linear relationship among the variables (Abedi Gheshlaghi and Feizizadeh 2021; Al-Juaidi et al. 2018; Tedla et al. 2022). In a multiple regression model, multicollinearity is a statistical issue, and a high degree of correlation persists between two or more independent variables (Mallick et al. 2021;Mukherjee and Singh 2020;Tang et al. 2021). It does not negatively affect the reliability and predictability of the model; hence, it was used as an effective tool. Several methods are applied to analyze the multicollinearity, and in the present study, the variance inflation factor (VIF) method is used to study multicollinearity in every flood triggering factor. The following formula was used to compute the VIF (Myers et al. 2010): where R 2 i represents the coefficient of determination of the regression equation. To fix the issues related to multicollinearity, firstly, random points were generated by employing

TOPSIS
The TOPSIS method of Hwang and Yoon (1981) generally depends on the euclidean distance among several available decision-making alternatives (Pathan et al. 2022;Ameri et al. 2018;Khosravi et al. 2019;Sari 2021;Mandal et al. 2022;Rafiei-Sardooi et al. 2021;Bera et al. 2021). It is an algorithm of straightforward procedure and an effective approach to solving MCDM problems (Song and Chung 2016). In this technique, ranking is constructed for the alternatives based on distance. It is basically the smallest distance from the positive ideal solution and the largest distance from the negative ideal solution (Li et al. 2022;Foroozesh et al. 2022;Opricovic and Tzeng 2004;Bağdatlı Kalkan et al. 2017;Jozaghi et al. 2018). This method consists of seven steps (Luu et al. 2019). In the present study, all steps were preciously done using extensive literature, professional viewpoints, and practical field knowledge. The steps are manifested as follows: Step I: Construction of the decision matrix D = d ij .
Step II: Standardization of the decision matrix. Here, vector normalization is applied for computing the r ij.
Step III: Set up a weighted standardized decision matrix through the multiplication of the attributes weight to each category.
where w j denotes the weight of the jth attributes.
Step IV: Determine the positive ideal solution ( A * ) and negative ideal solution ( A − ) depended on the weighted normalized values.
where J 1 represents a group of benefit attributes and J 2 represents a group of cost attributes.
Step V: Calculation of the separation from positive ideal value ( S + ) and negative ideal value (S − ) . The distance among the alternatives is computed through the n-dimensional Euclidean distance.
Step VI: Ascertain relative closeness to the ideal solution ( C i ).
Step VII: The relative distance C i can be ranked to get the final ranking of alternatives through sorting in descending order.
In this study, integration of TOPSIS with GIS has been conducted. Firstly, for the computation of TOPSIS, 15,000 random points were created using the "Sampling" tool of "Data Management Tools" for each thematic layer. After that, the values of these random points were extracted by employing the "Extraction" tool of "Spatial Analyst Tools" in the ArcGIS platform. Furthermore, with these values of 15,000 random points, calculation of TOPSIS has been performed in Microsoft Excel 2019. Then, beneficial (B) and non-beneficial (NB) conditioning parameters have been identified based on previous studies and expert's opinions, which along with weights were also assigned for all the thematic layers. After carrying out all the steps (Step I to Step VII), the values of S + , S − , and C i of 15,000 sample points were computed to prepare the flood susceptibility map.

VIKOR
The VIKOR method is another useful MCDM optimization and the robust method usually applied to study flood susceptibility analysis. It was initially propounded by Duckstein and Opricovic in 1980 and was later postulated by Tzeng in 2004 (Khosravi et al. 2019;Sari 2021). It employs a multicriteria ranking index, which is the nearest to the ideal (Opricovic and Tzeng 2004), and evaluates each alternative for every criterion (17) based on weights by comparing the ideal closeness values to ideal alternatives (Opricovic and Tzeng 2007). The VIKOR method uses a set of alternatives, i.e., A (1) , A (2) , … .A (m) and criteria, i.e., C 1 , C 2 … .C n . x ij refers to the value of the A (i) alternatives and W j represents the weight under the C j criteria. m expresses the number of alternatives, and n denotes the number of criteria. This method considers two groups of criteria, especially for the larger and smaller value that manifest the alternatives' better performance (Eqs. 21 and 22).
The Sj , Rj, and Qj final values are computed using Eqs. 23, 24, and 25.
Like TOPSIS, VIKOR is also not a pixel-based method. The integration of VIKOR with GIS has been performed for computing the Sj , Rj, and Qj . Similarly, like TOPSIS, 15,000 random points have been produced and extracted in ArcGIS and all equations have been performed in an Excel sheet. Finally, values of the Sj (ideal best and ideal worst value), Rj (maximum of ideal best and ideal worst value), and Qj (performance score) were obtained for 15,000 points for flood susceptibility zonation.

EDAS
EDAS is another newly proposed MCDM technique extensively used for the ranking of the alternatives (Stanujkic et al. 2018). It was postulated by Ghorabaee et al. (2015), where evaluation is conducted depending on the positive and negative distance from average (Ghorabaee et al. 2017). The decision matrix of n alternatives and m criteria is illustrated as follows: where x ij represents the performance value of the i th alternatives on j th criterion (i = 1, 2, … , n and j = 1, 2, … , m) and weight of j th criterion by w j , where 0 < w j < 1 and ∑ m j=1 w j = 1. The following steps are considered to construct the method: Step I: Calculate the average solution ( V j ) using the Eq. 27 of each criterion.
Step II: Determination of the Pd ij and Nd ij as follows: where Pd ij stands for positive distance from the average, Nd ij stands for negative distance from the average, and BC and NC stand for the beneficial and non-beneficial criteria.
Step III: Ascertain the weighted summation of the Pd ij and Nd ij as described in Eqs. 30 and 31.
Step IV: Normalization of SP i and SNi as follows: Step V: Appraisal score ( A s i ) calculation of each alternative by Eq. 34.
Step VI: Finally, based on decreasing values of A s i , alternatives are ranked.
EDAS is based on an average solution (Ghorabaee et al. 2015). The integration of EDAS with GIS has been conducted in this study. As this method uses an average solution for appraising the alternatives, hence here applied 15,000 alternatives. A total of 15,000 random points were extracted from each layer, and the obtained values were used for further calculation in Excel. The decision matrix was firstly constructed in Excel using the random points value. The evaluation matrix and values of NSP i , NSNi , and A s i for 15,000 points were prepared for flood susceptibility assessment.

Role of GIS in the construction of the flood susceptibility maps
The ArcGIS software here is utilized for the final construction of the flood susceptibility maps. Firstly, in ArcGIS platform added the XY data, i.e., the calculation table for TOPSIS, VIKOR, and EDAS solution and positions of 15,000 sample points. The maps of criteria having a positive and negative impact for (a) S + (Positive TOPSIS) (b) S − (Negative TOPSIS), (c) Sj (Positive VIKOR), (d) Rj (Negative VIKOR), (e) NSPi (Positive EDAS), and (f) NSNi (Negative EDAS) were produced by using the "Interpolation" tool of "Spatial Analyst Tools" in ArcGIS. In the "Interpolation" (IDW) tool, frame the z value, output cell size, and environment setting for the generation of these maps. Finally, based on the obtaining values of C i of TOPSIS, Qj of VIKOR, and A s i of EDAS of 15,000 points, the "Interpolation" (IDW) technique is further applied for the construction of the zonation of the three flood susceptibility maps.

Spearman's rank test
The relationships between TOPSIS, VIKOR, and EDAS have been analyzed using Spearman's rank (r s ) non-parametric test. It has been computed using Eq. 35, as stated below (Gauthier 2001): where d i represents the difference between ranks for each data pair and n represents the number of data pairs.

ROC-AUC, MAE, MSE, and RMSE analyses
The ROC-AUC, MAE, MSE, and RMSE analyses have been applied to verify the final susceptibility maps (Arabameri et al. 2019;Ali et al. 2020;Nachappa et al. 2020;Afolayan et al. 2020), generated through the TOPSIS, VIKOR, and EDAS techniques. All the methods are applied using the flood and non-flood points of the flood inventory map of the district. ROC depicts the relationship involving specificity and sensitivity (Nguyen et al. 2022;(35) Farhangi et al. 2022;Ali et al. 2020). High sensitivity expresses true positives, representing the "y" axis of the ROC curve, and high 1-specificity manifests false positives in the "x" axis (Arabameri et al. 2019; Ali et al. 2020). The following Eq. 36 and Eq. 37 express them, where TN depicts true negative, FP depicts false positive, TP depicts true positive, and FN depicts false negative (Rasool et al. 2022;Pan et al. 2022;Swets 1988): AUC was applied to quantitatively measure the suitability of the TOPSIS, VIKOR, and EDAS techniques in the study area due to being widely used in this ground to judge the model's accuracy (Nguyen et al. 2021;Saha et al. 2021). The value of AUC ranges from 0 to 1, where 0.9 to 1 represents "excellent," 0.8 to 0.9 represents "very good," 0.7 to 0.8 represents "good," 0.6 to 0.7 represents "satisfactory," and 0.5 to 0.6 represents "unsatisfactory" relationship (Arabameri et al. 2019;Suppawimut 2021;Mitra and Roy 2022). Using the "ArcSDM" tool in the ArcGIS platform, the ROC-AUC has been prepared to evaluate the accuracy of three models. For this purpose, 313 flood points and 212 non-flood points have been used from the flood inventory vector layer.
In addition, MAE, MSE, and RMSE were used to determine prediction accuracy (Rasool et al. 2022;Pan et al. 2022). In all circumstances, a lower MAE, MSE, or RMSE number indicates higher model fitness (Pan et al. 2022;Fayaz et al. 2022). Equations 38, 39, and 40 were used for computing the MAE, MSE, and RMSE (Nguyen et al. 2022;Farhangi et al. 2022): where X i is the observed value, Y i is the predicted value, and n is the number of data points.

Selection of the flood conditioning indicators
In the present study, randomly 1000 points were considered for 21 parameters during multicollinearity checks.
The result shows a high correlation has persisted in the parameters MFI and long-term annual rainfall. The collinearity statistics stated that both parameters exhibit VIF, and the tolerance value is > 10 and < 0.1, respectively. The eigenvalue of respective dimensions exists close to 0, which indicates multicollinearity. The observed condition index for both dimensions is above 15 and has variance proportions > 0.90 in more than one predictor. Therefore, one strongly correlated parameter should be removed from two (i.e., MFI and long-term annual rainfall) to overcome this collinearity problem. Furthermore, using only MFI and the rest of the 19 parameters, multicollinearity was tested and observed that there is no existence of multicollinearity between the 20 flood triggering factors, as depicted in Table 3.

Evaluation matrix
In this study, the generation of the final flood susceptibility maps of the TOPSIS, VIKOR, and EDAS methods was based on 20 criteria. The criteria selected for susceptibility analysis are physical environment oriented (Monte et al. 2021;Feldmeyer et al. 2021). All the considered MCDM techniques are not each pixel-based; hence, sample points were used in this analysis. The evaluation matrix was prepared separately in an Excel sheet for the TOPSIS, VIKOR, and EDAS by extracting the values of 15,000 sample points from each thematic layer (n = 20). The evaluation matrix of the three MCDM techniques is shown in Table 4, which contains 15,000 rows (sample points) and 20 columns (indicators). It was constructed on the basis of the category and weight of the conditioning parameters. The previous studies (Waqas et al. 2021;Ali et al. 2020;Talukdar et al. 2020;Rahmati et al. 2019;Weiss 2001;Ali et al. 2020;Vafakhah et al. 2020) and expert's opinions were taken into account for determining the category of the conditioning parameters. Among 20 criteria, 14 were performed as beneficial (B), while 6 criteria were as non-beneficial (NB) category. The assignments of weights for the flood conditioning criteria are an essential task in this regard. Therefore, based on expert judgments in several studies, weights were allocated for the three MCDM techniques. Table 5 demonstrates several works where weights (%) for each indicator in flood susceptibility mapping have been used. In this research, the highest weight was assigned for elevation (13%), followed by slope (11%), drainage density (10%), geomorphology (9%), rainfall deviation (9%), TWI (7%), mNDWI (6%), MFI (5%), lithology (4%), NDVI (4%), LULC (3%), soil (3%), curvature (2%), aspect (2%), lineament density (2%), STI (2%), roughness (2%), TRI (2%), and TPI (2%). A radar diagram in Fig. 6 depicts the assigned weights of these indicators.

TOPSIS, VIKOR, and EDAS solution and positions
Here, in TOPSIS, the positive ideal solution (S + ) varies between 0.007 and 0.018, while the negative ideal solution (S − ) varies from 0.011 to 0.020. Figure 7a and b depict the S + (positive TOPSIS) and S − (negative TOPSIS) maps of the region. The C i is computed to depict the final flood susceptibility map, where the maximum and the minimum value are 0.364 and 0.791, respectively. The VIKOR method represents the values of Sj , Rj , and Qj of the study area. Here, the Sj (positive VIKOR) value ranged from 0.280 to 0.713, while Rj (negative VIKOR) ranged from 0.043 to 0.122 ( Fig. 8a and b). The generated flood susceptibility map of the region in this method implies the value of Qj , which varies from 0.011 to 0.896. The EDAS described the normalization of SP i and SNi , i.e., the NSP i (positive EDAS) and NSNi (negative EDAS) displayed in Fig. 9a and b, where values range from 0.046 to 0.983 and 0.0006 to 0.6821, respectively. The appraisal score ( A s i ) of the susceptibility map in this model is found between 0.029 and 0.853. The computed flood susceptibility values ( C i , Qj , and A s i ) for the three respective methods are given in Table 6.

Produced susceptibility maps
The final flood susceptibility maps (Fig. 10a-c) in TOPSIS, VIKOR, and EDAS techniques were categorized into five distinct classes: "very low," "low," "medium," "high," and "very high" based on the principle of three MCDM technique. In the case of TOPSIS and EDAS, the higher value shows a very high flood susceptibility zone, while the lower value shows a very low susceptibility zone. But in VIKOR, inverse relationship has been observed, i.e., a lower value depicts a high flood susceptibility zone, and a higher value depicts a low susceptibility zone. Here, classification is conducted using the "quantile deviation" technique in ArcGIS software, as it is suitable to find out the best result in the concerned region (Tehrany et al. 2014;Shafapour Tehrany et al. 2019). Table 7 shows the distribution of flood susceptibility zones according to the "quantile deviation" technique. Additionally, a comparative graph (Fig. 11) is used to analyze these susceptibility class-wise distributions (in percentage). The spatial distribution of the "high" to "very high" flood-susceptible areas (about 40%) using the TOP-SIS, VIKOR, and EDAS is mainly observed in the riparian region. During the monsoonal season, floods mainly occur in the study area. The "high" susceptible regions were observed in the lower elevated active flood plain with higher TWI, drainage density, lineament density, rainfall deviation, MFI values, and vice versa. According to the susceptibility maps, the Tufanganj-I, Tufanganj-II, and Mathabhanga-I blocks of the district were very susceptible to floods. In these blocks, the "medium" to "very high" susceptible zones is observed maximum in their extent. The Haldibari, Sitalkuchi, and Sitai blocks were less susceptible to floods. Since the region received unusually severe torrential rains throughout the monsoon months, the water levels in almost all of the region's major rivers have been alarmingly high. As a result, the area has been devastated by floods. Physiographically, the dominance of the low-lying lands and numerous wetlands accelerate the development of waterlogged situations during monsoons throughout the region. These wetlands are locally known as "beel" or "bils." Hydrologically, there are large numbers of sinuous and braided major rivers and their lots of tributaries. In association, the region has a higher number of spill channels, ox-bow lakes, abandoned channels, meander cut-offs, and paleochannels, which along with channel migration and bank erosion of the rivers exaggerates flood susceptibility. According to the District Disaster Management Plan (2021-2022) of Koch Bihar, 48 villages in Tufanganj-I, Tufanganj-II, Dinhata-I, Sitalkuchi, Sitai, Koch Bihar-I, Koch Bihar-II, Mathabhanga-I, and Mathabhanga-II blocks were faced with prominent bank erosion problem. As an effect, human-congested riparian regions were flooded, numerous field crops were ruined, and people's livelihoods were impacted (Chakraborty and Mukhopadhyay 2019;      (Ghosh and Ghosal 2020). Some glimpses of the flood-susceptible areas during the rainy season in Koch Bihar district have been manifested in Fig. 12.

Correlation studies of the models
The correlation studies between the three techniques were performed using 15,000 sample points. It reflects the degree of linear association among the variables. As in this study, the distribution of data is not regularly spaced; hence, Spearman's rank r s is more appropriate to statistically judge the relationship between the three MCDM techniques (Gauthier 2001). For assigning rank, the lower value gets the highest rank in the VIKOR model, whereas in TOPSIS and EDAS, a higher value is assigned a higher rank. The correlation graphics are illustrated in Fig. 13. It is examined that, based on r s statistical measures, high correlation (0.714) persisted among the TOPSIS and EDAS techniques. In contrast, VIKOR-EDAS and TOPSIS-VIKOR revealed a moderate correlation, i.e., 0.651 and 0.639, respectively. Hence, the normalization and aggregation outcomes of the TOPSIS and EDAS have been substantially equivalent to each other. The r s correlation studies between the TOPSIS-EDAS, VIKOR-EDAS, and TOPSIS-VIKOR among 15,000 sample points are found significant at the 0.01 level (two-tailed), as displayed in Table 8.

Models' validation evaluation
The validation of the final flood susceptibility maps with the flood inventory map of the district has been assessed by performing the ROC-AUC, MAE, MSE, and RMSE analysis. Figure 14a-c displayed the ROC curves and AUC with speedometer diagrams for the three respective techniques. The AUC exhibits the accuracy rate of every flood susceptibility prediction model. It estimates the probability that the value of an appropriately identified pixel will outperform that of an improperly identified pixel. The analysis manifests that the highest accuracy is observed in the VIKOR technique (0.953), followed by TOPSIS (0.773) and EDAS (0.735). The VIKOR performs as "excellent," while the TOPSIS and EDAS are "very good" based on the satisfaction scale. The statistical output of the MAE, MSE, and RMSE represents outstanding performance (i.e., < 0.300 of error) of the three MCDM models. The computed value of MAE, MSE, and RMSE shows very good accuracy in the TOPSIS model compared to VIKOR and EDAS. The TOPSIS model manifests just only 12% (MAE), 2% (MSE), and 16% (RMSE) errors for the generated susceptibility map. Table 9 represents different performance matrices with their obtained values for flood modelling.

Discussion
Floods are the most frequent hydrological hazard in the Indian sub-continent. It is a relatively high flow that overwhelms the natural runoff (Chow 1956) and disrupts people's normal lifestyle (Mitra and Kumar Mandal 2022; Chakraborty and Mukhopadhyay 2019). There has been significant investigation on determining flooding susceptibility since flooding is a serious   (Mirza 2011). This region is probable to encounter intermittent flooding due to the anticipated increase in  a, b, c, d), school at Tufanganj-II block was fully waterlogged (e), houses, fields, and roads inundated at Koch Bihar-II block (f), culvert was destructed and displaced due to flood at Koch Bihar-I block (g), houses and roads were waterlogged, and people shifted in rescue shelters at Mathabhanga-I block (h, i, j, k) temperature and precipitation in the monsoon months (Lal 2003;Pal and Al-Tabbaa 2010). Furthermore, a significant increase in severe rainfall occurrences throughout central India is found to be related to a spike in sea surface temperature (SST) across the Indian Ocean (Camberlin et al. 2001;Dash et al. 2007). Floods, according to published reports, will never be controlled (Huang et al. 2008). The geospatial models allow for identifying areas of high risk of flooding and help to construct a strategic plan for recovery (El-Haddad et al. 2021). Flood  susceptibility estimation and flood control are critical topics for evaluating flood-prone areas and mitigating flood damage through appropriate actions. Susceptibility mapping studies have also been very interested in MCDM techniques since they are useful in understanding the interactive correlations between environmental components. It has recently been noted that researchers have employed MCDM methods to determine flood susceptibility. MCDM methods have been utilized to improve the precision of environmental hazard prediction. The integration of GIS techniques with the TOPSIS, VIKOR, and EDAS model is involved in the present research to recognize and comparative assessment of flood susceptibility zones. These methods were selected relying on the literatures on flood susceptibility that was currently available. The techniques globally applied for ranking the alternatives based on their performance (Sari 2021). Several scholars work on the flood susceptibility assessment in West Bengal using different MCDM and machine learning techniques, viz., Sinha et al. (2008), Ghosh and Kar (2018), Samanta et al. (2018), Chakraborty and Mukhopadhyay (2019), Roy et al. (2021), and Chakrabortty et al. (2021). Previous work to determine flood risk zones of Koch Bihar district has been conducted by Chakraborty and Mukhopadhyay (2019) and Choudhury et al. (2022). In this present study, more diversified and potential flood conditioning parameters have been taken into account. To solve the collinearity issue, VIF, tolerance value, eigenvalue, and condition index were considered and significantly interrelated variable was eliminated. The weightage of the conditioning parameters has been determined based on expert's opinions in several studies. Seventy percent weights were assigned for the seven conditioning parameters, i.e., elevation (13%), slope (11%), drainage density (10%), geomorphology (9%), rainfall deviation (9%), TWI (7%), mNDWI (6%), and MFI (5%). However, elevation is the major important parameter in determining the spatial distribution of floods. In some other studies, the assigned weightage for the elevation parameter was 36% (Msabi and Makonyo 2021), 26% (Nachappa et al. 2020), 15% , and 22.5% (Souissi et al. 2020). The study also identified the beneficial and non-beneficial parameters for flooding based on previous   Sari 2021). In the VIKOR method, lower value indicates the better performance of the model, while in TOPSIS and EDAS, higher value shows better performance. The fundamental tenet of TOPSIS is that the selected alternative should be closest to the ideal solution and furthest from the negative ideal solution. The TOPSIS approach employs vector normalizing, while the VIKOR approach makes use of linear normalization (Opricovic and Tzeng 2004). When there are contradicting criteria, the EDAS approach is highly helpful since it allows us to choose the optimum option by calculating the distance between the ideal and nadir responses (Rashid et al. 2021). The study shows that, in terms of achieving the goals of this research, the TOPSIS and EDAS were highly correlated. As per the ROC-AUC assessment, the VIKOR method accurately identified the areas with flood havoc. Therefore, it is one of the best suitable methods for mapping the flood susceptibility zones of the concerned region, among others (Nachappa et al. 2020). On the other hand, based on MAE, MSE, and RMSE matrices, TOPSIS shows very less error in the produced susceptibility map. Considering the existing literature on flood susceptibility of this Sub-Himalayan region, three comparably novel and advanced GIS-based MCDM techniques were used in the Koch Bihar district.
In the present context, the importance of the study relies on several aspects which have been depicted as a new dimension for flood susceptibility studies: (a) In this research, integration of GIS with MCDM techniques has been conducted. The role of GIS in the construction of the flood susceptibility map has been presented in a very lucid manner. (b) The database and methodological section is very scientifically presented throughout the study. (c) The research incorporated the correlation study between all MCDM methods. (d) Weights for conditioning factors is assigned based on previous flood susceptibility study and expert opinion for the construction of the MCDM models. (e) The study also included very new MCDM technique with GIS, i.e., the EDAS technique which was postulated in 2015 by Ghorabaee et al.. (f) The study also identified the flood susceptibility zones of the Sub-Himalayan region depending on only physical environment-related aspects. Thus, the study can improve the existing literatures on flood susceptibility assessment. The data and methods utilized in the current investigation, meanwhile, have certain constraints. The limitations of the study are basically due to the flood triggering parameters, which were acquired from different spatial resolutions. Furthermore, it is widely recognized that no model can completely capture reality. This also applies to the models used in the current study, despite the fact that the validation process showed that the techniques were extremely reliable.

Conclusions
The present research manifested the integration of MCDM approaches with the GIS software for flood susceptibility modelling of the Sub-Himalayan foothills district of West Bengal. It is a widely used technique in contemporary periods and is applied as an essential resource for flood management studies and the execution of any developmental plans. It is the preliminary process to recover assets and life from future flooding events. The novelty of the study implies the statistical analysis of the performance of the GIS-based models and the application of the new MCDM model (i.e., EDAS) in the field of hazards, vulnerability, and risk assessment study, which along with the outcome of the research can be applied to flood management and mitigation studies in the future for better development of the district. The VIKOR and TOPSIS techniques produced excellent outcomes compared to EDAS. Due to excellent performance, VIKOR and TOPSIS were highly recommended for similar physical characterized regions. Overall, research finds that all the MCDM methods acquired high performance (i.e., > 70% in ROC-AUC and < 30% in MAE, MSE, and RMSE). The study highlights that the TOPSIS and EDAS were highly correlated in respect of fulfilling the goal of the study. The indices elevation, slope, drainage density, geomorphology, and rainfall deviation have greatly influenced the susceptibility mapping of the district. In contrast, curvature, roughness, STI, TRI, and TPI have been slightly affected in the delineation of the susceptibility zones. The multi-dimensional parameters of flood susceptibility here are recognized, which all are related to the natural environment. More diversified factors were considered as they can accurately identify the hazard-prone zones with the selected MCDM models. However, there are no bounds in the selection of the number of parameters in the case of TOPSIS, VIKOR, and EDAS. The respective three models revealed the higher susceptible areas (about 40%) are primarily associated with the riverine "chars" (islands) and riparian areas throughout the district. They are also characterized by lower elevation, gentle slope, loamy soil, and maximum drainage density. The Tufanganj-I, Tufanganj-II, and Mathabhanga-I blocks were depicted in the high-risk zone. Decision makers, regional government agencies, environmentalists, and engineers can all take advantage of the proposed models for microlevel (block-level) flood management, which can also be applied to numerous flood-prone regions throughout the world.
The flood susceptibility mapping of the study area in general merely indicates potential flood zones without addressing the depth and velocity of the flood. Therefore, it is advised that in future work, the current type of research be integrated with several hydraulic modelling, viz., River Analysis System (HEC-RAS 5 and newer versions) of the Hydrologic Engineering Center (CEIWR-HEC), that offer additional 2D layouts, including both depth and velocity. In third-world countries, geospatial data are limited; perhaps the drawback, the MCDM approaches are widely helpful in analyzing the susceptibility, vulnerability, and risk at a regional scale. By utilizing machine learning approaches, the study can also improve its decisions in order to better identify flood susceptibility. The study prioritizes flood hazard zones for appropriate preservation and management strategies. The findings of this study are likely to make a substantial contribution to the research in flood hazard analysis throughout the world.