Research On Test Cost Interval And Multi-Decision Based On Rough Sets

Rough sets can deal with various kinds of incomplete information and knowledge, the mainly difference between rough sets and other uncertainty theories is that rough sets do not need prior knowledge except for data sets. Rough set theory analyses data directly, finds potential knowledge and rules, and then makes reasonable decisions. F-rough set theory extends classic rough set theory from a single table to multi-table, which has important academic significance and application value for investigating the change and development of objects.The reduction of test-cost rough sets aims for the minimum test cost. Decision makers take it as a criterion to make a decision for the unilateral interests only. However, in many games, decision makers can be divided into two sides according to their inconsistent interests, one side is interested in the minimum test cost, but the opposite side pursues the maximum test cost. Test-cost rough sets have limitation to the unilateral interests only. In three-way decision, uncertain parameters can be obtained through data and algorithms, which shows the objectivity. Moreover, the idea of three-way decision is consistent with a single man’s thinking. But for multi-decision problems, different decision makers have different knowledge, and their decisions may be inconsistent. Classic three-way decision is not applicable to this kind of issue. This paper proposes a test-cost-interval and a model of three-way decision based on F-rough sets to solve the deficiencies mentioned above. The main researches are listed as follows:1.Test-cost-interval based on rough set. Classic test-cost rough set theory aiming for the reduct with the minimum test cost cannot solve opposite interest problems in a game. Combining game theory and rough set theory, we define a concept called test-cost-interval, propose evaluation criteria for a reasonable decision, and introduce algorithms for test-cost-intervals. The research has an important significance for excessive medical issues, and provides a new view for test cost sensitive researchers.2. Model of three-way decision based on F-rough sets. Classic three-way decision takes the cost of misclassification as a decision criterion, and its process of decision making is conducted in a single table, which means that decision makers have the same knowledge. But, in fact, different decision makers cannot have exactly the same knowledge, so their decisions may be inconsistent. Combining F-rough sets theory and three-way decision-theoretic rough set theory, we propose a model of three-way decision based on F-rough sets. The model may serve as a reference for multi-decision problems.The main innovation points are listed as follows:(1) Considering the opposite interests in a game, a test-cost-interval is defined, and an evaluation criterion for reasonable decisions based on test-cost-interval is proposed, as well as their algorithms are introduced.(2) Combining the F-rough sets theory and the model of three-way decision, a model of three-way decision based on F-rough sets is presented.