Abstract
In this chapter, we present a fuzzy approach to portfolio selection based on interpolative Boolean algebra. Interpolative Boolean algebra is a real-valued generalization of Boolean algebra. After an extensive overview of the theoretical framework, we present two interpolative Boolean-based methods: logical clustering and logical DuPont. Both methods are extended to address portfolio selection problems. Logical clustering method for portfolio selection employs interpolative Boolean algebra dissimilarity within a hierarchical clustering algorithm to group companies according to investment ratios. Further, this method uses expert logic-based rules for investment decision making. Logical DuPont method for portfolio selection is applied to give insight into the structure of companyis earnings and further identify profit drivers to recommend investment actions. The presented methods are validated on S&P 500 stock market data. Logical clustering and logical DuPont methods have proven to be valuable fuzzy tools for an automated stock selection.
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