A novel computation for predicting time series using fuzzy logical distance connectivity function and visibility graph theory

: pp.14–21
Received: June 18, 2019
Revised: November 26, 2019
Accepted: November 26, 2019

Mathematical Modeling and Computing, Vol. 7, No. 1, pp. 14–21 (2020)

Krishna Engineering College
GL Bajaj Institute of Technology and Management

The visibility graph is a set of locations that lie in a line that can be interpreted as a graph-theoretical representation of a time series, while the fuzzy graph speaks about the connection between the lines by accurately demonstrating the level of the connection between the objects of a given set.  Many graphs do not show proper previous values.  Even knowing the previous values of times series,  prediction of the future values will not be accurate.  Therefore, to find the real values exactly, this paper introduces the Visibility graph by time series values $(x_{t},y_{t}),(x_{u},y_{u})$ along with the Fuzzy node values $f_{1},f_{2},\ldots,f_{n}$.  Considering the past nodes by Fuzzy logic, similarity does not give a more accurate prediction because the nodes similarity contains the past node values only.  The fundamental target of this paper is to propose a calculation to predict a more exact strategy to measure information by finding the similarities of all fuzzy nodes $f_{1},f_{2},\ldots,f_{n}$ with their distance function $f_{d}(\alpha)$ and the connectivity function $\alpha$.  The results of the computational outcome $Y_{(x+1)}$ will demonstrate more accurate values of time series.

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