Rough Vague Research Articles

Approximation operators based on vague relations and roughness measures of vague sets

Rough set theory and vague set theory are powerful tools for managing uncertain, incomplete and imprecise information. This paper extends the rough vague set model based on equivalence relations and the rough fuzzy set model based on fuzzy relations to vague sets. We mainly focus on the lower and upper approximation operators of vague sets based on vague relations, and investigate the basic properties of approximation operators on vague sets. Specially, we give some essential characterizations of the lower and upper approximation operators generated by reflexive, symmetric, and transitive vague relations. Finally, we structure a parameterized roughness measure of vague sets and similarity measure methods between two rough vague sets, and obtain some properties of the roughness measure and similarity measures. We also give some valuable counterexamples and point out some false properties of the roughness measure in the paper of Wang et al.

Knowledge acquisition in vague objective information systems based on rough sets

: The growing volume of vague information poses interesting challenges and calls for new theories, techniques and tools for analysis of vague data sets. In this paper, we study how to extract knowledge from vague objective information systems (VOISs) based on rough sets theory. We first introduce the basic notion termed rough vague sets by combining rough sets theory and vague sets theory. By using the rough vague lower approximation distribution in the VOIS, the concept of attribute reduction is introduced. Then, we develop an algorithm based on a discernibility matrix to compute all the attribute reductions. Finally, a viable approach for extracting decision rules from the VOIS is proposed. An example is also presented to illustrate the application of the proposed theories and approaches in handling medical diagnosis problems.