An Automated System for Stock Market Trading Based on Logical Clustering

In this paper a novel clustering-based system for automated stock market trading is introduced. It relies on interpolative Boolean algebra as underlying mathematical framework used to construct logical clustering method which is the central component of the system. The system uses fundamental analysis ratios, more precisely market valuation ratios, as clustering variables to differentiate between undervaluated and overvaluated stocks. To structure investment portfolio, the proposed system uses special weighting formulas which automatically diversify investment funds. Finally, a simple trading simulation engine is developed to test our system on real market data. The proposed system was tested on Belgrade Stock Exchange historical data and was able to achieve a high rate of return and to outperform the BelexLine market index as a benchmark variable. The paper has also provided in-depth analysis of the system’s investment decision making process which reveals some exciting insights

Formalization of Human Categorization Process Using Interpolative Boolean Algebra

Since the ancient times, it has been assumed that categorization has the basic form of classical sets. This implies that the categorization process rests on the Boolean laws. In the second half of the twentieth century, the classical theory has been challenged in cognitive science. According to the prototype theory, objects belong to categories with intensities, while humans categorize objects by comparing them to prototypes of relevant categories. Such categorization process is governed by the principles of perceived world structure and cognitive economy. Approaching the prototype theory by using truth-functional fuzzy logic has been harshly criticized due to not satisfying the complementation laws. In this paper, the prototype theory is approached by using structure-functional fuzzy logic, the interpolative Boolean algebra. The proposed formalism is within the Boolean frame. Categories are represented as fuzzy sets of objects, while comparisons between objects and prototypes are formalized by using Boolean consistent fuzzy relations. Such relations are directly constructed from a Boolean consistent fuzzy partial order relation, which is treated by Boolean implication. The introduced formalism secures the principles of categorization showing that Boolean laws are fundamental in the categorization process. For illustration purposes, the artificial cognitive system which mimics human categorization activity is proposed