A Study Of The Attribute Reduction In The Real Valued Decision Table Based On Rough Set Theory

Rough set theory is a new tool of dealing with the uncertain information. The main idea of this theory is attribute reduction without changing the ability of partition in domain, and gets the decision rules from the database. This paper focuses on the real valued decision table and studies the attribute reduction skill. However, the classical rough set theory focuses on the data with symbol values, as for the real valued data, it needs them to be discrete. Unfortunately, the discrete processes always lose information. In order to make sure that the loss of information can be as little as possible; this paper introduces a new discrete method with fuzzy clustering based on the equivalence relationship. With series discrete parameters it gets a series partition of the domain. This method is called fuzzy cluster discerning. And then, uses the knowledge of classical rough set theory, this paper presents the notions based on the discrete parameters, such as approximate operators and so on, and proves that the approximate operators change when the discrete parameter does. Besides, in order to guarantee the consistence of the discrete decision table, it also defines the feasible domain of the discrete parameter. In the feasible domain, it is proved that the reduction does not increase when the parameter does, so the minimum in the domain is the optimal discrete parameter. The reduction based on the optimal discrete parameter can avoid over discrete and over reduction, and make this be the attribute reduction in real valued decision table. Next, this paper builds the variable precision rough set model to increase the robustness of the proposed attribute reduction, and gets the optimal discrete parameter, too. In this situation, the optimal parameter is the minimum one, too. Because the properties aboat the parameter and the reduction are similar to them in the classical model. Further, this paper gets the covering of the domain with the discrete parameter by replacing the fuzzy equivalent relationship to fuzzy similar one. Using the covering rough set theory, there are optimal discrete parameters both in covering model and its variable model. What’s more, this paper discusses the difference between the optimal discrete parameters from different models and presents the attribute reduction based on the optimal discrete parameter. At the end of this paper, it sets up four reduction models based on the four attribute reductions, and then performs them by several real valued decision tables. It turns out that the methods proposed in this paper are effective.