Abstract
In recent years, the theory of decision-theoretic rough set and its applications have been studied, including the attribute reduction problem. However, most researchers only focus on decision cost instead of test cost. In this paper, we study the attribute reduction problem with both types of costs in decision-theoretic rough set models. A new definition of attribute reduct is given, and the attribute reduction is formulated as an optimization problem, which aims to minimize the total cost of classification. Then both backtracking and heuristic algorithms to the new problem are proposed. The algorithms are tested on four UCI (University of California, Irvine) datasets. Experimental results manifest the efficiency and the effectiveness of both algorithms. This study provides a new insight into the attribute reduction problem in decision-theoretic rough set models.
Highlights
We are involved in decision making all the time
This study provides a new insight into the attribute reduction problem in decision-theoretic rough set models
Minimizing the total cost is equal to minimizing the average total cost (ATC), so we study the minimal average-total-cost reduct problem
Summary
We are involved in decision making all the time. Most of the decisions are based on a group of criteria. According to the data models constructed in [21], the issues of test-cost-sensitive attribute reduction have been studied based on classical rough sets [22, 23], neighborhood rough sets [24], covering rough sets [25, 26], and so forth In these works, both backtracking and heuristic algorithms have been implemented through an open source software Coser [27]. We study the cost-sensitive attribute reduction problem for DTRS through considering the tradeoff between test costs and decision costs, which is remarkably related to decision making and game theory.
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