Subsethood Measures of Spatial Granules

Subsethood, which is to measure the degree of set inclusion relation, is predominant in fuzzy set theory. This paper introduces some basic concepts of spatial granules, coarse-fine relation, and operations like meet, join, quotient meet and quotient join. All the atomic granules can be hierarchized by set-inclusion relation and all the granules can be hierarchized by coarse-fine relation. Viewing an information system from the micro and the macro perspectives, we can get a micro knowledge space and a micro knowledge space, from which a rough set model and a spatial rough granule model are respectively obtained. The classical rough set model is the special case of the rough set model induced from the micro knowledge space, while the spatial rough granule model will be play a pivotal role in the problem-solving of structures. We discuss twelve axioms of monotone increasing subsethood and twelve corresponding axioms of monotone decreasing supsethood, and generalize subsethood and supsethood to conditional granularity and conditional fineness respectively. We develop five conditional granularity measures and five conditional fineness measures and prove that each conditional granularity or fineness measure satisfies its corresponding twelve axioms although its subsethood or supsethood measure only hold one of the two boundary conditions. We further define five conditional granularity entropies and five conditional fineness entropies respectively, and each entropy only satisfies part of the boundary conditions but all the ten monotone conditions

Economic geology of the Avoca mineralized belt S.E. Ireland and Parys Mountain, Anglesey

Imperial Users onl

Proceedings of the Sixth Annual Precise Time and Time Interval (PTTI) Planning Meeting

Time and frequency measurements are described for navigation and reference systems. Time measuring instruments and experiments performed are discussed

A close-up of the sun

NASA's long-range plan for the study of solar-terrestrial relations includes a Solar Probe Mission in which a spacecraft is put into an eccentric orbit with perihelion near 4 solar radii (0.02 AU). The scientific experiments which might be done with such a mission are discussed. Topics include the distribution of mass within the Sun, solar angular momentum, the fine structure of the solar surface and corona, the acceleration of the solar wind and energetic particles, and the evolution of interplanetary dust. The mission could also contribute to high-accuracy tests of general relativity and the search for cosmic gravitational radiation