Abstract
This article deals with the determination and comparison of different types of functions of the type-2 interval of fuzzy logic, using a case study on the international financial market. The model is demonstrated on the time series of the leading stock index DJIA of the US market. Type-2 Fuzzy Logic membership features are able to include additional uncertainty resulting from unclear, uncertain or inaccurate financial data that are selected as inputs to the model. Data on the financial situation of companies are prone to inaccuracies or incomplete information, which is why the type-2 fuzzy logic application is most suitable for this type of financial analysis. This paper is primarily focused on comparing and evaluating the performance of different types of type-2 fuzzy membership functions with integrated additional uncertainty. For this purpose, several model situations differing in shape and level or degree of uncertainty of membership functions are constructed. The results of this research show that type-2 fuzzy sets with dual membership functions is a suitable expert system for highly chaotic and unstable international stock markets and achieves higher accuracy with the integration of a certain level of uncertainty compared to type-1 fuzzy logic.
Highlights
Fuzzy set theory was first introduced by Lotfi Zadeh in the 1960s as a way to capture the uncertainty and ambiguity often overlooked in complex systems
Fuzzy logic has a number of advantages, in particular being able to work with vague terms, chaotic and dynamic environments and nonlinear behaviors that are typical of everyday use in stock market analysis
A total of nine models were created for each MF, which differ in the magnitude of the uncertainty contained in the duplicate membership functions
Summary
Fuzzy set theory was first introduced by Lotfi Zadeh in the 1960s as a way to capture the uncertainty and ambiguity often overlooked in complex systems. The expression of membership functions depends on both the subject (how deep the researcher’s experience is) and the context (where the problem is) For this reason, the present research focuses on the use of membership functions with varying degrees of uncertainty, which is gradually increasing. The paper is organized as follows: Section 1 introduction the subject matter, including the identification of the urgency of the problem and the definition of the aim of the work; Section 2 provides the theoretical background and examines already published works; Section 3 is focused on the theory of fuzzy mathematical background of fuzzy system type-1 and type-2; Section 4 is devoted to the methodology and experiments on the data of the international stock market; Section 5 discusses obtained results and evaluation of the created model; Section 6 summarizes outputs of the paper, recognized limits and suggestions for the subsequent research
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