This article delves into the process of fuzzifying time series, which entails converting a conventional time series into a time-indexed sequence of fuzzy numbers. The focus lies on the well-established practice of fuzzifying time series when a predefined degree of uncertainty is known, employing fuzzy numbers to quantify volatility or vagueness. To address practical challenges associated with volatility or vagueness quantification, we introduce the concept of informed time series. An algorithm is proposed to derive fuzzy time series, and findings include the examination of structural breaks within the realm of fuzzy time series. Additionally, this article underscores the significance of employing topological tools in the analysis of fuzzy time series, accentuating the role of these tools in extracting insights and unraveling intricate relationships within the data.
