On one approach to data fuzzification on the example of the Dow-Jones Index time series

Abstract

The nature of weakly structured systems is specified by using of expert estimates, the inherent uncertainty of which belongs to the fuzzy class. Unlike stochastic uncertainty, fuzziness complicates or even eliminates the use of statistical methods and models, but can be used to make subject-oriented decisions based on approximate reasoning of a person. The formalization of intellectual operations simulating fuzzy human statements about the state and behavior of weakly structured systems and/or complex phenomena today forms an independent direction of scientific and applied researches, one of which is fuzzy modeling of time (or dynamic) series. This direction includes a task complex, the methodology of which is based on the theory of fuzzy sets, fuzzy logic and fuzzy models (or fuzzy inference systems). The initial procedure for fuzzy modeling of time series is fuzzification of historical data obtained by observing on the basis of “soft measurements” of the behavior of a dynamic system for a certain period of time. The paper proposes a new rule of fuzzification of such data, which is tested on the indicators of the Dow Jones Industrial Average, established by the results of daily trading on the US stock exchange by the usual arithmetic averaging of component indicators. The fuzzification procedure proposed in the given paper is implemented through a fuzzy inference system, which ensures that the membership functions of the corresponding fuzzy subsets of the discrete universe are found, covering the entire set of indicators of the Dow Jones index for more than a year.