Synthesis of fuzzy logic and Dempster–Shafer Theory for the simulation of the decision-making process in stock trading systems

Modern computerized stock trading systems (mechanical trading systems) are based on the simulation of the decision-making process and generate advice for traders to buy or sell stocks or other financial tools by taking into account the price history, technical analysis indicators, accepted rules of trading and so on. Two stock trading simulating systems based on trading rules defined using fuzzy logic are developed and compared. The first is based on the so-called “Logic-Motivated Fuzzy Logic Operators” (LMFL) approach and aims to avoid certain disadvantages of the classical Mamdani’s method, which has been developed for use in fuzzy logic controllers and not for solving the decision-making problems of stock trading. The LMFL approach is based on the modified mathematical representation of t-norm and Yager’s implication rule. The second trading system combines the tools of fuzzy logic and Dempster–Shafer Theory (DST) to represent the features of the decision-making process more transparently. The fuzzy representation of trading rules based on the theory of technical analysis is used in these expert systems. Since the theory of technical analysis is based on the indicators used by experts to predict stock price movements, the method maps these indicators into new inputs that can be used in a fuzzy logic system. The only required inputs to calculate these indicators are past sequences (history) of stock prices. The method relies on fuzzy logic to choose an appropriate decision when certain price movements or certain price formations occur. The optimization procedure based on historical (teaching) data is used as it significantly improves the performance of such expert systems. The efficiency of the developed expert systems is measured by comparing their outputs versus stock price movements. The results obtained using real NYSE data allow us to say that the developed expert system based on the synthesis of fuzzy logic and DST provides better results and is more reliable. Moreover, such a conjunction of fuzzy logic, DST and technical analysis, makes it possible to make a profit even when trading against a dominating trend.