Extension of Rough Set Based on Positive Transitive Relation

The application of rough set theory in incomplete information systems is a key problem in practice since missing values almost always occur in knowledge acquisition due to the error of data measuring, the limitation of data collection, or the limitation of data comprehension, etc. An incomplete information system is mainly processed by compressing the indiscernibility relation. The existing rough set extension models based on tolerance or symmetric similarity relations typically discard one relation among the reflexive, symmetric and transitive relations, especially the transitive relation. In order to overcome the limitations of the current rough set extension models, we define a new relation called the positive transitive relation and then propose a novel rough set extension model built upon which. The new model holds the merit of the existing rough set extension models while avoids their limitations of discarding transitivity or symmetry. In comparison to the existing extension models, the proposed model has a better performance in processing the incomplete information systems while substantially reducing the computational complexity, taking into account the relation of tolerance and similarity of positive transitivity, and supplementing the related theories in accordance to the intuitive classification of incomplete information. In summary, the positive transitive relation can improve current theoretical analysis of incomplete information systems and the newly proposed extension model is more suitable for processing incomplete information systems and has a broad application prospect.Comment: 9 page

Decision-theoretic rough sets based on time-dependent loss function

A fundamental notion of decision-theoretic rough sets is the concept of loss functions, which provides a powerful tool of calculating a pair of thresholds for making a decision with a minimum cost. In this paper, time-dependent loss functions which are variations of the time are of interest because such functions are frequently encountered in practical situations, we present the relationship between the pair of thresholds and loss functions satisfying time-dependent uniform distributions and normal processes in light of bayesian decision procedure. Subsequently, with the aid of bayesian decision procedure, we provide the relationship between the pair of thresholds and loss functions which are time-dependent interval sets and fuzzy numbers. Finally, we employ several examples to illustrate that how to calculate the thresholds for making a decision by using time-dependent loss functions-based decision-theoretic rough sets