Abstract
Extensive research results of stock market time series using classical fuzzy sets (type-1) are available in the literature. However, type-1 fuzzy sets cannot fully capture the uncertainty associated with stock market developments due to their limited descriptiveness. This paper fills a scientific gap and focuses on type-2 fuzzy logic applied to stock markets. Type-2 fuzzy sets may include additional uncertainty resulting from unclear, uncertain, or inaccurate financial data through which model inputs are calculated. Here we propose four methods based on type-2 fuzzy logic, which differ in the level of uncertainty contained in fuzzy sets and compared with the type-1 fuzzy model. The case study aims to create a model to support investment decisions in Exchange-Traded Funds (ETFs) listed on international equity markets. The created models of type-2 fuzzy logic are compared with the classic type-1 fuzzy logic model. Based on the results of the comparison, it can be said that type-2 fuzzy logic with dual fuzzy sets is able to better describe data from financial time series and provides more accurate outputs. The results reflect the capability and effectiveness of the approach proposed in this document. However, the performance of type-2 fuzzy logic models decreases with the inclusion of increasing uncertainty in fuzzy sets. For further research, it would be appropriate to examine the different levels of uncertainty in the input parameters themselves and monitor the performance of such a modified model.
Highlights
Fuzzy logic is widely used in many areas because it can handle incomplete or uncertain data, and because its tools have been simplified using parameterized FS
E construction of the member function and the determination of its parameters are still a current problem, as stated by Yankova et al [6]. e choice of the shape and parameters of the membership functions plays an important role in the fuzzy model, as it can affect the performance of the whole system as a state of Wijayasekara and Manic [7]
Jankovaand Dostal [32] apply IT2FL on the Czech stock market and they are used when deciding on investing in shares of the PX index. e proposed type-2 fuzzy model uses the return and risk of investment instruments as input variables. e created system is able to generate aggregated models from a number of language rules, which allows the investor to understand the created financial model. e use of T2FLS can lead to more realistic and accurate results than T1FLS. Another hybrid approach to IT2FLS was provided by Hasan et al [33]. eir results correspond to similar outputs of other authors. us, it can be stated that type-2 fuzzy logic is able to improve the performance of existing models
Summary
Fuzzy logic is used in a wide range of decision-making problems such as risk management, finance, economics, and management, and in weather forecasting, physics, and many other areas. e usability of fuzzy logic is huge, mainly due to the fact that they allow you to work on the principle of human thinking, unlike neural networks or genetic algorithms. Since the introduction of fuzzy logic prediction models, this method is increasingly used in a number of studies to solve problems related to stock market forecasts or as a support to decision-making tool for investors, analysts, or the general investor public. Is approach, according to the authors, provides better prediction results. E above study demonstrated exclusively the use of type-1 fuzzy logic, which is represented by membership functions or fuzzy sets ranging from zero to one. Such membership functions represent a precise point or exact degree of membership. Liu et al [26] modified the classical hybrid neurofuzzy model and integrated a type-2 fuzzy set into it, which they used to predict the TAIEX index. Another hybrid approach to IT2FLS was provided by Hasan et al [33]. eir results correspond to similar outputs of other authors. us, it can be stated that type-2 fuzzy logic is able to improve the performance of existing models
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