**1. Introduction**

The urban population of the world is rapidly growing, and according to a projection by the United Nations, approximately 9.8 billion people by 2050 and 11.2 billion by 2100 will be living in urban areas [1]. Due to this rapid growth in population, cities around the world are facing very fast transformation of their land use land cover (LULC) pattern [2–4]. This is creating serious problems, such as urban sprawl, unplanned expansion of impervious surfaces (built-up land), and decline in urban green spaces, as well as deterioration of the

**Citation:** Das, T.; Shahfahad; Naikoo, M.W.; Talukdar, S.; Parvez, A.; Rahman, A.; Pal, S.; Asgher, M.S.; Islam, A.R.M.T.; Mosavi, A. Analysing Process and Probability of Built-Up Expansion Using Machine Learning and Fuzzy Logic in English Bazar, West Bengal. *Remote Sens.* **2022**, *14*, 2349. https://doi.org/ 10.3390/rs14102349

Academic Editor: Gwanggil Jeon

Received: 30 March 2022 Accepted: 10 May 2022 Published: 12 May 2022

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urban environmental quality [5–7]. The rate of unplanned expansion due to population growth and economic development is very high in developing countries of South and East Asia such as India, China, Bangladesh, etc. [8–10]. In India, small and mediumsized towns have experienced the very fast expansion of built-up surfaces in the last few decades [11–14], which has resulted in the unplanned expansion of these towns, as well as urban sprawling [15,16]. The rapid lateral expansion of India's small and medium-sized cities is considered a serious urban problem [17]. As of 2011, India had 3894 small and medium-sized towns [18], which are growing at a greater rate in terms of population and spatial distribution than large and metro cities [19]. Most of the studies on the urbanisation and LULC changes in medium-sized Indian cities have addressed some aspects of urban expansion and its consequences [14,20–22]. India's urban population has increased from 79 million in 1961 to 388 million in 2011, whereas its rural population doubled from 360 million to 860 million [23]. The primary cause for this continuous population rise was the development of infrastructural activities such as transport networks, internet connection, health sector development, new institutional sector establishment, etc. [7,17]. As a city's population grows, the city and countryside expand laterally to accommodate the increasing population, resulting in a lateral extension of cities beyond their formal city authority boundaries, a phenomenon known as "urban sprawl" [24]. The phenomenon of built-up expansion in the process of urban sprawl is one of the most noticed and studied phenomenon among urban researchers [12,25,26].

The expansion of built-up land leads to several negative and harmful effects on the urban environment and ecology [5,27–29]. Thus, measuring and modelling different forms of built-up land expansion might assist planners in better understanding and addressing the challenges related to the expansion of built-up areas [30–32]. Researchers have tried to analyse and quantify the urbanisation-induced built-up land expansion around the world [12,33–36]. For instance, Salem et al. [34] analysed the pattern of built-up land expansion and urban sprawl in the peri-urban area of Cairo City in the post-revolution era using remote sensing techniques coupled with logistic regression. Similarly, Talukdar et al. [37] used the transferable build-up area extraction (TBUAE) technique for assessing urban growth using high-resolution satellite datasets. Further, Fawad et al. [38] combined multispectral satellite data with synthetic aperture radar (SAR) datasets for extracting urban impervious surfaces. Xu [39] and Shahfahad et al. [12] applied an index-based built-up index (IBI) technique for urban area expansion that was based on the multiple spectral indices derived from satellite data.

Studies have been done in developing countries like South Africa [40], Pakistan [41], Nigeria [42], and India [43] for mapping and monitoring urban LULC changes and built-up area expansion using remote sensing. However, most of these studies in India have been done on large metropolitan cities like Delhi, Kolkata, Mumbai, Chennai, etc. [44–48]. On the other hand, only a few studies have been done on small and medium-sized cities in India [14,16,49]. Despite the considerable growth in the literature on urban expansion and sprawling in major cities, studies on built-up expansion in small/medium-sized blocks/districts have received little attention from scholars and urban planners in India. Therefore, to fill this literature gap, this study aims to analyse the built-up growth and LULC change in the English Bazar block, which is a small town of West Bengal. The English Bazar Municipal Corporation, which is located in the centre of the English Bazar block has witnessed very fast population growth and landscape transformation in the last few decades [49]. In this context, an analysis of the built-up growth and LULC change is a matter of concern for medium-sized towns like English Bazar. Therefore, in this work, we identified the land use features using SVM for 2001, 2011, and 2021, including built-up areas, as an essential input for further research. We introduced a model to study the process of built-up expansion using fragmentation indices and the frequency approach. Additionally, we developed a built-up probability model using fuzzy logic for exploring the future built-up expansion probable areas, which have not been studied so far.
