Searching for the Complex Decision Reducts - The case study of the survival analysis

Generalization of the fundamental rough set discernibility tools aiming at searching for relevant patterns for complex decisions is discussed. As an example of application, there is considered the postsurgery survival analysis problem for the head and neck cancer cases

Naive Bayesian rough sets

Abstract. A naive Bayesian classifier is a probabilistic classifier based on Bayesian decision theory with naive independence assumptions, which is often used for ranking or constructing a binary classifier. The theory of rough sets provides a ternary classification method by approximating a set into positive, negative and boundary regions based on an equivalence relation on the universe. In this paper, we propose a naive Bayesian decision-theoretic rough set model, or simply a naive Bayesian rough set (NBRS) model, to integrate these two classification techniques. The conditional probability is estimated based on the Bayes ’ theorem and the naive probabilistic independence assumption. A discriminant function is defined as a monotonically increasing function of the conditional probability, which leads to analytical and computational simplifications