Aggregation and Definition of an Algebraic Framework for Fuzzy Time Series: An Application in the Supply-Demand Domain

Luis Rodriguez-Benitez, Juan Moreno-Garcia, Ester del Castillo-Herrera, J. Liu, Luis Jimenez-Linares

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This paper proposes a method for aggregating the information contained in
sets of Time Series (TS) into a Fuzzy Time Series (FTS). First, an aggregation
technique is defined, which is based on the algorithm known as Kernel Density
Estimation (KDE) which reconstructs the probabilistic density function of a set
of points, in this case a TS. Second, to operate with FTS, an algebraic framework
is created based on Zadeh’s extension principle and as a result of operating
with FTS, a new FTS is obtained, which allows obtaining richer information
and operating under conditions of uncertainty. Finally, the operations needed
to compute the membership function of any TS in the aggregated FTS are
introduced too. As a use case, it is proposed to work with sets of TS in the supply
and demand domain, in such a way that information regarding the satisfaction
of demand over time can be extracted. The specific application domain chosen
will be that of the electricity market, analysing the consumption of buildings
and their self-generation of energy to obtain information about the dependence
on the electricity grid
Original languageEnglish
Pages (from-to)104-115
Number of pages12
JournalInternational Journal of Approximate Reasoning
Early online date29 Jul 2022
Publication statusPublished (in print/issue) - 1 Oct 2022

Bibliographical note

Funding Information:
We are grateful for support by Grants PID2020-112967GB-C32 and PID2020-112967GB-C33 funded by MCIN/AEI/10.13039/501100011033 and by ERDF A way of making Europe .

Publisher Copyright:
© 2022 Elsevier Inc.


  • Fuzzy time series
  • Time series aggregation
  • Zadeh's extension principle
  • Supply-demand time series
  • Kernel density estimation


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