NMGRS: Neighborhood-based multigranulation rough sets

AbstractRecently, a multigranulation rough set (MGRS) has become a new direction in rough set theory, which is based on multiple binary relations on the universe. However, it is worth noticing that the original MGRS can not be used to discover knowledge from information systems with various domains of attributes. In order to extend the theory of MGRS, the objective of this study is to develop a so-called neighborhood-based multigranulation rough set (NMGRS) in the framework of multigranulation rough sets. Furthermore, by using two different approximating strategies, i.e., seeking common reserving difference and seeking common rejecting difference, we first present optimistic and pessimistic 1-type neighborhood-based multigranulation rough sets and optimistic and pessimistic 2-type neighborhood-based multigranulation rough sets, respectively. Through analyzing several important properties of neighborhood-based multigranulation rough sets, we find that the new rough sets degenerate to the original MGRS when the size of neighborhood equals zero. To obtain covering reducts under neighborhood-based multigranulation rough sets, we then propose a new definition of covering reduct to describe the smallest attribute subset that preserves the consistency of the neighborhood decision system, which can be calculated by Chen’s discernibility matrix approach. These results show that the proposed NMGRS largely extends the theory and application of classical MGRS in the context of multiple granulations

Model granularity and related concepts

Models are integral to engineering design and basis for many decisions. Therefore, it is necessary to comprehend how a model’s properties might influence its behaviour. Model granularity is an important property but has so far only received limited attention. The terminology used to describe granularity and related phenomena varies and pertinent concepts are distributed across communities. This article positions granularity in the theoretical background of models, collects formal definitions for relevant terms from a range of communities and discusses the implications for engineering design

Searching for solar-like oscillations in the delta Scuti star rho Puppis

Despite the shallow convective envelopes of delta Scuti pulsators, solar-like oscillations are theoretically predicted to be excited in those stars as well. To search for such stochastic oscillations we organised a spectroscopic multi-site campaign for the bright, metal-rich delta Sct star rho Puppis. We obtained a total of 2763 high-resolution spectra using four telescopes. We discuss the reduction and analysis with the iodine cell technique, developed for searching for low-amplitude radial velocity variations, in the presence of high-amplitude variability. Furthermore, we have determined the angular diameter of rho Puppis to be 1.68 \pm 0.03 mas, translating into a radius of 3.52 \pm 0.07Rsun. Using this value, the frequency of maximum power of possible solar-like oscillations, is expected at ~43 \pm 2 c/d (498 \pm 23 muHz). The dominant delta Scuti-type pulsation mode of rho Puppis is known to be the radial fundamental mode which allows us to determine the mean density of the star, and therefore an expected large frequency separation of 2.73 c/d (31.6 muHz). We conclude that 1) the radial velocity amplitudes of the delta Scuti pulsations are different for different spectral lines; 2) we can exclude solar-like oscillations to be present in rho Puppis with an amplitude per radial mode larger than 0.5 m/s.Comment: 14 pages, 12 figure, accepted for MNRA