Application of novel similarity measures in electric vehicle charging station site selection based on q-rung orthopair hesitant fuzzy rough sets under quantitative information

Why choosing the “best” option is so hard

Modern life is full of tricky choices: where to build electric vehicle charging stations, which city neighborhoods suffer most from air pollution, or even which medical diagnosis best matches a patient’s symptoms. In all of these cases, information is messy, uncertain, and sometimes even contradictory. This paper introduces new mathematical tools that help computers compare such fuzzy information more reliably, and then shows how those tools can guide real‑world choices about charging stations and air quality.

Comparing things that are not black and white

Many decisions hinge on how similar two situations are. A doctor might compare a patient’s symptoms with typical patterns of a disease, or a city planner might compare potential sites with an “ideal” location for a new charger. Classic similarity measures assume the data are neat and precise. In reality, experts often hesitate: a site may be “fair to good” on traffic access, or pollution data may be incomplete. Over the last decades, researchers in fuzzy logic have developed ways to represent this uncertainty, allowing something to be partly in and partly out of a category. This paper builds on one of the most flexible of these ideas, a framework that lets experts express not only how strongly something belongs to a group, but also how strongly it does not, and even how unsure they are.

A new way to measure likeness

The authors focus on a popular similarity tool called cosine similarity, which treats two sets of data as arrows and measures the angle between them. A small angle means the arrows point in almost the same direction, so the two cases are very similar. However, standard cosine similarity breaks down when the data include hesitation and multiple possible values for each criterion, as often happens in expert judgments. To fix this, the paper defines two improved measures—cosine and weighted cosine similarity—tailored to a rich fuzzy framework called q‑rung orthopair hesitant fuzzy rough sets. In simple terms, this framework allows each option to carry collections of possible “yes” and “no” degrees for every criterion, while still guaranteeing that the overall description remains logically consistent. The new formulas turn these complex descriptions into stable, meaningful similarity scores between 0 and 1.

Putting the method to work on charging stations

To show that the approach is not just abstract math, the researchers tackle a pressing planning problem: where to place electric vehicle charging stations. They consider three candidate sites and three key factors: how convenient the traffic access is, how much it would cost to build, and how well the station could serve drivers. Experts describe each site using hesitant, graded opinions under this fuzzy framework, and also specify what an ideal site would look like. The new cosine and weighted cosine measures then compare each real site with the ideal. Both versions of the method agree on the ranking: one site clearly emerges as closest to the target. This consistency is important—it suggests the method is robust, even when factors are given different weights.

Checking city air with fuzzy data

The second demonstration looks at air quality across different regions. Here, the input includes human activities such as traffic and smoking, as well as measured pollutants like sulfur dioxide, nitrogen oxides, carbon monoxide, and ozone. Because such data can be incomplete or inconsistent, each region’s air quality is again expressed using hesitant fuzzy values rather than a single crisp number. The new similarity measures compare each region to an ideal clean‑air profile, and the results sort the regions into better or worse air quality in a way that matches practical expectations. This shows that the same tools can handle environmental monitoring as well as infrastructure planning.

Testing against older methods

Beyond these two case studies, the authors pit their measures against many existing similarity formulas on benchmark problems, including medical diagnosis and pattern recognition. Several older methods either fail to distinguish between different patterns or behave oddly—for example, claiming perfect similarity when two patterns are clearly not identical. The new cosine‑based measures, by contrast, satisfy basic logical requirements, avoid numerical pitfalls, and correctly identify the closest match in these tests. This gives added confidence that the tools are not tuned to a single application but are generally reliable.

What it all means for real decisions

For non‑specialists, the technical jargon masks a simple message: when information is uncertain and experts disagree or hesitate, we still need to make choices. This paper offers a more careful way to compare such murky data, turning vague opinions and noisy measurements into consistent rankings of options. Whether the task is siting a new charging station, judging if a city’s air is safe, or supporting doctors with complex diagnoses, these improved similarity measures promise decisions that are more transparent and less prone to strange mathematical quirks. As computing tools based on this work are developed, planners and analysts may gain a new, sharper lens for looking at problems where the truth is not just yes or no, but somewhere in between.

Citation: Attaullah, Khan, A., Boulaaras, S. et al. Application of novel similarity measures in electric vehicle charging station site selection based on q-rung orthopair hesitant fuzzy rough sets under quantitative information. Sci Rep 16, 9504 (2026). https://doi.org/10.1038/s41598-025-34665-1

Keywords: electric vehicle charging, decision-making, fuzzy logic, air quality, similarity measures