Real-world data is vague: a new method for analyzing time series with fuzzy numbers
A stock price isn’t just a point, it has volatility. We introduce a new method to convert standard time series into ‘fuzzy time series’ to better model and analyze this real-world uncertainty.
When we look at a stock chart or a temperature graph, we see a single, crisp line connecting precise points in time. But is the real world that precise?
A stock’s price isn’t just $100; it has volatility—it fluctuates. A weather forecast isn’t just 25°C; it has vagueness or uncertainty. Standard time series analysis often ignores this.
In our 2025 paper published in the International Journal of Approximate Reasoning, we introduce a formal method to “fuzzify” time series, converting them from simple lines into rich, fuzzy data that embraces uncertainty.
🧐 The problem: a line graph is a lie
Treating a day’s stock price as a single number (like the closing price) throws away vital information about the day’s volatility. We lose the “fuzziness” of the data.
While “fuzzy time series” isn’t a new idea, the practical challenges are significant. How do you decide how fuzzy to make each data point? How do you turn a series of sharp points into a series of “fuzzy numbers” (like “around 100”) in a principled, repeatable way?
💡 Our solution: “informed” fuzzification
Our paper provides a practical and theoretical framework for this “fuzzification” process.
Instead of applying a single, arbitrary level of fuzziness, we introduce the concept of an “informed time series”. This is a method where the “fuzziness” of each point is derived from the data itself, such as its local volatility or a known degree of vagueness.
We then propose an algorithm that automatically converts a conventional time series into this new, richer sequence of fuzzy numbers.
*
🚀 The results: a new way to analyze data
Once you have a fuzzy time series, you can ask new, more powerful questions. Our paper explores how to analyze these new data structures.
A key part of our work was examining “structural breaks” in the fuzzy time series. A structural break is a sudden change in a data’s pattern (like a market crash). We show how to detect these breaks even when the data is represented as a sequence of fuzzy numbers, a non-trivial task.
This proves that our new representation isn’t just a gimmick; it’s a new form of data that can be formally analyzed to find insights that the original crisp line might have hidden.
🔬 Why does this matter?
This work gives data scientists a tool to model uncertainty in a more honest and realistic way.
This is critical in fields like economics and finance. In these areas, volatility isn’t just “noise”—it’s a fundamental piece of information. By modeling time series as fuzzy numbers, analysts can build models that are more robust and better reflect the way markets actually behave.
It also opens the door to using powerful topological tools for analyzing time series, expanding the scope of what we can learn from our data.
📖 The full paper
For the complete methodology, the full algorithm, and the analysis of structural breaks in fuzzy time series, you can read the original journal article.
Fuzzy time series analysis: Expanding the scope with fuzzy numbers. Authors: Hugo J. Bello, Manuel Ojeda-Hernández, Domingo López-Rodríguez, Carlos Bejines. Journal: International Journal of Approximate Reasoning (vol. 180, 109387)