2.3.2. Validation of LULC Map

The most significant and last stage in the image classification process is the accuracy assessment estimation. Validation is a crucial component of robust and accurate LULC mapping, because it assists planners and administrative departments in understanding the significance, impact, and accuracy between ground reality and research work in the studied region [55,56]. Post-classification validation of the LULC maps also helps planners and administrative divisions in launching their strategies. The standard kappa coefficient, overall accuracy, producer accuracy, and user accuracy were among the accuracy measurement methodologies used in the present study. The following formula was used to determine the kappa coefficient [58]:

Kappa coefficient

$$\frac{N\sum\_{i}^{r}\boldsymbol{\chi}\_{ii} - \sum\_{i}^{r}(\boldsymbol{\chi}\_{i+})(\boldsymbol{\chi}\_{i})}{N^{2} - \sum\_{i}^{r}(\boldsymbol{\chi}\_{i+})(\boldsymbol{\chi}\_{i})} \tag{1}$$

where *r* represents the number of rows, *x* represents the number of observations in the rows and columns (diagonal elements), and *N* represents the number of total observations:

Overall accuracy

$$\text{OA} = \left(\frac{1}{N}\right) \sum\_{i=1}^{r} n\_{ii} \tag{2}$$

Producer's accuracy

$$\text{PA} = \left(\frac{n\_{ii}}{n\_{icol}}\right) \tag{3}$$

User's accuracy

$$\text{UA} = \left(\frac{n\_{\bar{i}\bar{i}}}{n\_{iron}}\right) \tag{4}$$

where the number of correctly classified pixels is *–ii*, the total number of pixels is *N*, the number of rows is *r*, and the column and row totals are *nicol* and *nirow*., respectively.

The total accuracy estimator determines how many pixels in the image have been correctly identified. For this work, we used the kappa coefficient to validate the LULC maps based on the testing samples. In the present study, we randomly chose 20% of the field data as the testing sample. Fifty-six samples were calculated as the testing sample, which comprised 2641 total pixels. Out of total pixels, we collected 286 pixels from water bodies, 780 from built-up, 690 from vegetation, 655 from agricultural land, and 230 from barren land.

### 2.3.3. Method for the LULC Change Detection

Using the GIS environment and a post-classification change detection approach, the changes in LULC during 2001–2011, 2011–2021, and 2001–2021 were examined (Figure 2). Post-classification change detection is one of the most common methods for analysing the details of changes in LULC patterns in a region during a time period [52]. This approach may evaluate the temporal variations in the LULC types and the level of LULC conversion

caused by urbanisation. We calculated the change statistics for two time periods of LULC maps using Equation (5):

$$\text{Change } (\%) = \frac{\beta^1 - \beta^2}{\beta^1} \tag{5}$$

where *β*1 = present year (2021) and *β*2 = initial year (2001).

**Figure 2.** Hierarchical structure of the methodological framework of the entire study.

2.3.4. Methods for the Modelling of Built-Up Expansion Process

In this study, the built-up growth was represented using a frequency technique. We first categorised the LULC map, then divided the entire map into two groups, built-up and non-built up, for distinction when using the reclassification tool in GIS. The built-up area was denoted by 1 and the non-built-up area by 0. Then, we used the spatial analyst tool with the less than frequency and the reclassified raster layer as the input. This approach calculates the number of times a collection of the raster is smaller than another raster on a cell-by-cell basis. The number of instances (frequency) in which a raster in the input list has a lower value is counted for each cell position in the input value raster. Finally, a frequency map is produced. The value reflects the number of times the associated cells in the list of the raster are less than the value raster for each cell in the output raster. The final map is overlaid by a built-up area of different (three) times.

We employed landscape fragmentation tools to analyse the growth rate trend to categorise the built-up area. The LULC map was divided into two categories: built-up and non-built-up, with built-up denoted by 2 and non-built-up denoted by 1. As an input raster, we utilised this reclassified map. We followed two steps to perform this model that reclassified LULC data and analysed the fragmentation. The final map was divided into four categories: patch, edge, perforated, and core. Based on the size of the core tract, the core category is further classified into large, medium, and small cores. The primary categories are determined by a parameter called edge width. Many studies have established the deterioration of forests or grasslands along disturbance edges, but we used it in our study to demonstrate the extension of newly formed built-up areas via the edge effect.

### 2.3.5. Built-Up Expansion Probability Model Using Fuzzy Logic

A suitability analysis, often known as site selection, is an advanced remote sensingbased study used to discover the optimal location for anything. To generate a built-up expansion probability model, first, we created a dominance, diversity, and connectivity model in SAGA GIS, and then, we used fuzzy tools in GIS and determined three different fuzzified models with the help of suitable fuzzy membership types. We used six membership functions (linear, small, large, MS Small, MS Large, and near) for the model. The fuzzy membership tool reclassifies or converts the input data into a 0 to 1 scale, depending on the probability of being a member of a certain set [59]. We mainly used the 'large' membership function, because it has a positive relationship with built-up expansion, and 'large' indicates a high fuzzy membership value. Fuzzy membership assigns values ranging from 0 to 1, with 0 indicating that something is unlikely or inappropriate and 1 indicating that something is most probable or appropriate [60]

After that, we created a built-up stability model using fuzzy overlay methods (In a multicriteria overlay analysis, the fuzzy overlay tool may estimate the probability of a phenomena belonging to various sets. Fuzzy overlay not only determines which sets the occurrence could belong to, but it also examines the connections between the sets' membership [59]. Since the multiple classes' surfaces are compared, this phase is analogous to weighted site selection (a site selection type that allows users to rank raster cells and provide a critical relative value to each layer). Then, we utilised the fuzzy operator (And, Or, Sum, Product, and Gamma) 'And', which gave us the best results, because this operator is grea<sup>t</sup> for identifying places that fulfil all requirements. Finally, we created a built-up probability model using Euclidean distance from spatial analyst tools in GIS. From the centre of the source cell to the centre of each surrounding cell, the Euclidean distance was determined. Each of the distance tools calculated the actual Euclidean distance. If the shortest distance to a source is less than the maximum distance given, the value is allocated to the cell location on the output raster. Therefore, we used the built-up stability map as a raster layer to generate the final output map, signified through 0 and 1, and quickly predicted the built-up expansion probability zone in the English Bazar block. The methodology of this study is summarised in Figure 2.
