Water supply is strategic for the development of society. The water distribution in nature follows patterns linked to geographic and territorial issues. Climate fluctuations aggravate shortage problems in semi-arid regions. This study aims to develop a systematic review of research on water scarcity in semi-arid areas through bibliometric methods that allow the analysis of its structure, performance, evolution, and future trends. The methodology considers three phases: (i) literature review, (ii) data cleaning and processing, and (iii) analysis of the research field and future trends. The intellectual structure of water scarcity in semi-arid zones covers 2206 documents with the collaboration of sixty-one countries, distributed in studies carried out in 54 years (1967 to 2021). This field of research has been growing, especially since the 21st century (93.1% of the documents). The countries that study the issue the most are those with high population rates and large consumption patterns, such as the United States and China. There are two central areas of interest led by the terms "water scarcity" and "water stress" due to the intensive use of the resource for agriculture and the management of the water–energy–climate nexus. Thus, the most significant journals studied relate remote sensing to resource management, and the most cited are related to agriculture. This research made it possible to consider future topics such as the study of anthropogenic effects and climate change, the accuracy and applicability of models, and future trends in conventional and unconventional agriculture and resources.

Modeling an aquifer provides significant advantages when evaluating and estimating the water resource for its sustainable use. This study focuses on the rural parish Manglaralto, a semi-arid area with a shortage of water, and without supply service by the public network. Still, it has a great demand for supply by the local and floating population (tourism). This has caused the coastal aquifer, which supplies the area’s water, to show signs of overexploitation, and its natural balance is compromised. The aim is to establish a geometric model of the aquifer through geological and geophysical analysis to set sustainable water-use guidelines. The methodology includes: (i) the processing of the current technical and hydrogeological information to know the aquifer’s data; (ii) geometric modeling of the aquifer through the correlation of technical information, using the GeoModeller software; (iii) proposals for the sustainable use of water in the framework of the United Nations’ Agenda 2030. The geometric model results reveal that the aquifer’s thickness varies from 4 m at the head of the river to 30 m at the sea’s mouth. The volume of water is estimated at 13.6 Hm³. The sustainable-use proposals ensure that more than half of the population receives the community company’s service. More than 40% of the territory is a protected area, and 64% of the population has sewerage service. This geometric model is a visual contribution that allows us to know the aquifer’s shape and establishes guidelines that help strengthen the water supply’s development and sustainability over time.

We introduce fuzzy skew maps as a levelwise ($\alpha$-cut) extension of robustly chaotic skew transformations of S-unimodal maps to epistemically uncertain environments. Our central hypothesis is that the robust-chaos mechanism of the underlying skew family transfers to fuzzy parameter uncertainty in a set-based (not probabilistic) sense is as follows: for every $\alpha \in [0,1]$, the induced crisp family $\{F(·,q):q\in {\left[\tilde{q}\right]}_{\alpha }\}$ preserves the absence of periodic windows and maintains strictly positive Lyapunov exponents. This yields a precise notion of fuzzy robustness that is distinct from interval enclosures (pure bounds) and stochastic robustness (average-case guarantees). We also formalize fuzzy topological entropy via the extension principle and discuss its basic structural properties under mild continuity assumptions. For chaos-based image encryption, fuzzification provides an uncertainty-aware key representation and stabilizes cryptographic indicators across $\alpha$-cuts as follows: in our experiments, NPCR remains within $99.58$–$99.64\%$, UACI within $33.41$–$33.52\%$, and the cipher entropy is near 8 bits, while pixel correlation stays close to zero. These results support fuzzy skew maps as a robust primitive for secure information systems operating under parametric uncertainty.