**5. Conclusions**

The primary purpose of this research was to explore the process of built-up expansion and model the future built-up probability zones based on the datasets from 2001 to 2021. Our findings showed that the study area observed a sharp rise in built-up areas, accompanied by a decrease in agricultural and vegetation cover. The built-up fragmentation model

identified the process of built-up expansion in the form of permanent, isolated, and newly formed built-up areas. Then, using the frequency approach model, the process of built-up expansion over time was created on a single map, showing it during three separate periods. Then, the dominance, diversity, and connection models were employed as parameters for the built-up probability model. Finally, we used the fuzzy logic-based built-up stability and built-up probability model to predict future built-up growths and trends. The results showed that the built-up area in the study area increased in tandem with the substantial economic expansion. In the previous 20 years (2001–2021), the built-up area has grown by nearly 2.5 times what it was, with a 36 km<sup>2</sup> net increase. Between 2001 and 2021, the LULC was altered, demonstrating a rise in a built-up area (almost by 6%) but a decrease in vegetation cover (by 4.54%) and agricultural land (by 3.78%). Moreover, from 2001 to 2021, barren land was also converted into agricultural land, built-up, and vegetation cover because of the increasing population, the necessity for food, and mango farming, a dominant orchard in Malda District. The expansion and growth of the built-up regions and the elimination of agriculture and vegetation across the English Bazar increased its population and subsequent economic development. According to this study, the English Bazar municipality has established itself as a permanent and stable location for built-up areas that span time and geography (beyond its administrative boundary). The study has some limitations, although we developed a model for the urban growth process and the likelihood of future urban expansion, which can minimise urban sprawling and foster compact green towns. We employed a satellite image with a moderate resolution, which has certain limitations in recognising built-up areas and traditional machine learning methods like SVM. High-resolution satellite imagery and deep learning algorithms can solve these problems. We can finely detect the expansion of urbanisation with minor errors using high-resolution satellite images such as Sentinel, LISS-IV, Worldview, QuickBird, and others. After tackling the drawbacks, these approaches can be implemented in small and medium-sized cities for proper management. The MODIS and night-time images can be used in future research with the proposed models for exploring the urbanisation process and the probability of large and megacities. The U-Net model (deep learning model) can be used in future research to analyse and predict urbanisation expansion, providing pixel-level information with grea<sup>t</sup> accuracy.

**Author Contributions:** Conceptualisation, T.D., A.R.M.T.I., A.M. and A.R.; software, T.D., S.T. and S.; validation, M.W.N., A.P., M.S.A. and S.P.; formal analysis, T.D., S.T. and A.M.; investigation, M.W.N., S.T. and A.R.M.T.I.; resources, A.R., M.S.A. and A.M.; data curation, T.D., S.T. and S.; writing—original draft preparation, T.D., A.P., S.T., and S.; writing—review and editing, A.R. and S.P.; visualisation, S.T. and A.M.; supervision, A.R., A.M. and S.P.; project administration, A.R. and A.M.; and funding acquisition, A.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** All the authors are thankful to the USGS for making the Landsat data freely available.

**Conflicts of Interest:** The authors declare no conflict of interest.
