189,918 research outputs found
Research on Rough Set Model Based on Golden Ratio
AbstractHow to make decision with pre-defined preference-ordered criteria also depends on the environment of the problem. Dominance rough set model is suitable for preference analysis and probabilistic rough set introduces probabilistic approaches to rough sets. In this paper, new dominance rough set rough set models are given by taking golden ratio into account. Also, we present steps to make decision using new dominance rough set models
Rough Sets Determined by Quasiorders
In this paper, the ordered set of rough sets determined by a quasiorder
relation is investigated. We prove that this ordered set is a complete,
completely distributive lattice. We show that on this lattice can be defined
three different kinds of complementation operations, and we describe its
completely join-irreducible elements. We also characterize the case in which
this lattice is a Stone lattice. Our results generalize some results of J.
Pomykala and J. A. Pomykala (1988) and M. Gehrke and E. Walker (1992) in case
is an equivalence.Comment: 18 pages, major revisio
Generation of Exhaustive Set of Rules within Dominance-based Rough Set Approach
AbstractThe rough sets theory has proved to be a useful mathematical tool for the analysis of a vague description of objects. One of extensions of the classic theory is the Dominance-based Set Approach (DRSA) that allows analysing preference-ordered data. The analysis ends with a set of decision rules induced from rough approximations of decision classes. The role of the decision rules is to explain the analysed phenomena, but they may also be applied in classifying new, unseen objects. There are several strategies of decision rule induction. One of them consists in generating the exhaustive set of minimal rules. In this paper we present an algorithm based on Boolean reasoning techniques that follows this strategy with in DRSA
Uncertainty Measures in Ordered Information System Based on Approximation Operators
This paper focuses on constructing uncertainty measures by the pure rough set approach in ordered information system. Four types of definitions of lower and upper approximations and corresponding uncertainty measurement concepts including accuracy, roughness, approximation quality, approximation accuracy, dependency degree, and importance degree are investigated. Theoretical analysis indicates that all the four types can be used to evaluate the uncertainty in ordered information system, especially that we find that the essence of the first type and the third type is the same. To interpret and help understand the approach, experiments about real-life data sets have been conducted to test the four types of uncertainty measures. From the results obtained, it can be shown that these uncertainty measures can surely measure the uncertainty in ordered information system
- …