# Fuzzy-Based Time Series Forecasting and Modelling: A Bibliometric Analysis
###### Abstract  
The purpose of this paper is to present the results of a systematic literature review regarding the development of fuzzy-based models for time series forecasting in the period 2017-2021. The study was conducted using a well-established review protocol and a couple of powerful tools for bibliometric analysis to know and analyse the main approaches adopted in the research field of interest. We analysed 118 articles published in peer-reviewed journals indexed in the 2020 Journal Citation Reports of the Web of Science. This allowed us to present an in-depth performance analysis and a science mapping regarding the current situation of fuzzy time series forecasting and modelling. The outputs of this study provide a practical base for further investigations that address this topic from both a methodological point of view and in terms of applicability. time series; forecasting; prediction; modelling; fuzzy model; bibliometric analysis +
Footnote †: journal: Medical Informatics  
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of the historical time series data set; (iv) establishing the fuzzy logical relationship (FLRs) between the fuzzified time series values, and creation of the FLR groups; and (v) defuzzification. These steps can be organized into two main stages: the data partitioning phase (steps i-iii) and the forecasting or prediction phase (steps iv-v). From these general steps, partitioning the UoD, identification of FLRs and defuzzification are considered critical in the performance of the forecasting model. An alternative, also based on Fuzzy Set Theory and Fuzzy Logic, is fuzzy inference systems (FIS) [8], which are rule-based mechanisms that establish a relationship between a series of input and output sets. There are two basic types of FIS, namely the Mamdani model [9] and the Takagi-Sugeno-Kang (TSK) model [10]; while fuzzification of input variables and application of operators in IF-THEN rules are the same in both types of FIS, they mainly differ in terms of translating the fuzzy outputs inferred from the fuzzy rules into crisp values (i.e., the defuzzification process). The Mamdani type has a better interpretation ability, whereas the TSK-type has a better approximation accuracy. Two well-developed approaches to FIS are the adaptive network-based fuzzy inference system (ANFIS) [11] and the type-1 fuzzy FIS [12]. ANFIS employs TSK-type FIS in a five-layered network structure, but it is computationally expensive and generates complex models for even relatively simple problems. It has been argued that the main problem with the fuzzy-based time series forecasting models comes from the difficulty constructing and deconstructing the fuzzy sets, and also from the complexity of the FLRs [13]. A competitive strategy to tackle these difficulties consists of using some type of hybridization together with the fuzzy components. Among others, artificial neural networks, evolutionary algorithms, fuzzy clustering, ant colony and particle swarm optimization and rough set rule induction have successfully been applied to different steps of FTS forecasting, especially for partitioning the UoD, fuzzification and defining FLRs [14; 15; 16; 17]. Given the proliferation of forecasting models, elaborating any up-to-date systematic review and/or bibliometric analysis offers a comprehensive understanding of the current status of the topic and allows the identification of several gaps for the development of new research. Accordingly, the purpose of this study is to provide a thorough review of articles published in peer-reviewed journals between January 2017 and December 2021 to highlight the most relevant and influential research areas, articles, authors, geographical regions and developments in the framework of time series forecasting with fuzzy-based models.