Aggregation and definition of an algebraic framework for fuzzy time series: An application in the supply-demand domain

Abstract

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.