Multi-hierarchical fuzzy judgment and nested dominance relation of rough set theory-based environmental risk evaluation for tailings reservoirs

Environmental risk assessment of tailings reservoir assessment system is complex and has many index factors.In order to accurately judge surrounding environmental risks of tailings reservoirs and determinate the corresponding prevention and control work,multi-hierarchical fuzzy judgment and nested dominance relation of rough set theory are implemented to evaluate them and find out the rules of this evaluation system with 14 representative cases.The methods of multi-hierarchical fuzzy evaluation can overall consider each influence factor of risk assessment system and their mutual impact,and the index weight based on the analytic hierarchy process is relatively reasonable.Rough set theory based on dominance relation reduces each index attribute from the top down,largely simplifies the complexity of the original evaluation system,and considers the preferential information in each index.Furthermore,grey correlation theory is applied to analysis of importance of each reducted condition attribute.The results demonstrate the feasibility of the proposed safety evaluation system and the application potential.

Rock burst laws in deep mines based on combined model of membership function and dominance-based rough set

Rock bursts are spontaneous, violent fracture of rock that can occur in deep mines, and the likelihood of rock bursts occurring increases as depth of the mine increases. Rock bursts are also affected by the compressive strength, tensile strength, tangential strength, elastic energy index, etc. of rock, and the relationship between these factors and rock bursts in deep mines is difficult to analyze from quantitative point. Typical rock burst instances as a sample set were collected, and membership function was introduced to process the discrete values of these factors with the discrete factors as condition attributes and rock burst situations as decision attributes. Dominance-based rough set theory was used to generate preference rules of rock burst, and eventually rock burst laws analysis in deep mines with preference relation was taken. The results show that this model for rock burst laws analysis in deep mines is more reasonable and feasible, and the prediction results are more scientific.

L^p-estimates on a ratio involving a Bessel process

Let Z=（ Zt）t≥0 be a Bessel process of dimension δ（ δ〉0） starting at zero and let K（t） be a differentiable function on [0,∞） with K（t）〉0 （A↓t≥0）. Then we establish the relationship between L^p-norm of log^1/2（1 ＋δJτ） and L^p-norm of sup Zt[t＋k（t）]^-1/2 （0≤t≤τ） for all stopping times τ and all 0〈p〈＋∞.As an interesting example, we show that ｜｜log^1/2（1＋δLm＋1（τ）｜｜p and ｜｜supZtП[1＋Lj（t]^1/2｜｜p （0≤j≤m,j∈Z;0≤t≤τ） are equivalent with 0〈p〈＋∞ for all stopping times rand all integer numbers m, where the function Lm（t） （t≥0） is inductively defined by Lm＋1（t）=log[ 1 ＋Lm（t）] with L0（t）= 1.

The robustness of sparse network under limited attack capacity

The paper studies the robustness of the network in terms of the network structure. We define a strongly dominated relation between nodes and then we use the relation to merge the network. Based on that, we design a dominated clustering algorithm aiming at finding the critical nodes in the network. Furthermore, this merging process is lossless which means the original structure of the network is kept. In order to realize the visulization of the network, we also apply the lossy consolidation to the network based on detection of the community structures. Simulation results show that compared with six existed centrality algorithms, our algorithm performs better when the attack capacity is limited. The simulations also illustrate our algorithm does better in assortative scale-free networks.

Assessment of Tree Diversity and Abundance in Rashad Natural Reserved Forest, South Kordofan, Sudan

This study aims to estimate the tree diversity status of Rashad Forest Reserves in the Rashad locality of the South Kordofan State of Sudan. For data collection, eight sample plots (20 × 20 m) were taken randomly, and parameters were determined: trees species diversity, composition, relative density, dominance, important value index, and species richness in the Rashad forest reserve. The results show that a total of 237 and 56 tree species, including 22 families, have been identified in the study area. Fabaceae family and species numbers have the highest number of 13 species in 8 genera, followed by Combretaceae with 8 species belonging to 3 different genera, Malvaceae with 5 species belonging to 4 different genera, Apocynaceae with 3 species belonging to 3 different genera. The Arecaceae, Burseraceae, Capparaceae, Euphorbiaceae, Meliaceae, and Rubiaceae families each had two species, and all the other 11 families had one species each. Among the 56 different tree species found within the reserve. The results also indicated that Tamarindus indica L. and Ziziphus spina-christi (L.) Desf. had the highest relative density and dominance of 4.64% and 11% respectively. Adansonia digitata L., Grewia villosa Willd, Vepris nobilis (Delile) Mziray had density and dominance of 4.80% and 9%. Followed by Anogeissus leiocarpa (DC.) Guill. & Perr, Adansonia digitata L., Catunaregam nilotica (Stapf) Tirveng. (Syn: Xeromphis nilotica (Stapf) Keay, Vangueria madagascariensis J. F. Gmel. with 3.38% and 8%, respectively. Eleven species recorded the least relative dominance of 0.42%. Shannon-Weiner diversity index (H’) value stood at 3.82. And as diversity indices varied with location depending on the species available within an ecological zone, Rashad forest reserve is blessed with a moderate diversity index.

Drought may be beneficial to the competitive advantage of Amaranthus spinosus

Drought can affect the growth and soil enzyme activities of invasive alien plants(IAPs).It is imperative to evaluate the competitive advantage of IAPs compared with that of the native species and the activities of soil enzymes under drought.This study aimed to evaluate the competitive advantage of the IAP Amaranthus spinosus that originated from tropical America compared with the native Chinese species A.tricolor and the activities of soil enzymes under drought.A competitive co-culture of A.spinosus and A.tricolor was established using a planting basin experiment.The two species were treated with different levels of drought,i.e.(i)the control;(ii)a light level of drought and(iii)a heavy level of drought.The functional traits,osmotic adjustment and the activities of antioxidant enzymes of the two species,as well as soil pH and electrical conductivity,contents of soil microbial biomass carbon and the activities of soil enzymes were determined.The relative competition intensity and relative dominance of A.spinosus were greater than those of A.tricolor under drought.Drought may provide an advantage to the competitive advantage of A.spinosus.Soil water-soluble salt content and sucrose hydrolytic power of A.spinosus were greater than those of A.tricolor under drought.The ability of A.spinosus to grow in soil with higher levels of water-soluble salt contents and sucrose hydrolytic power under drought may aid in its acquisition and utilization of nutrients.

Dominance-based fuzzy rough approach to an interval-valued decision system

Though the dominance-based rough set approach has been applied to interval-valued information systems for knowledge discovery, the traditional dominance relation cannot be used to describe the degree of dominance principle in terms of pairs of objects. In this paper, a ranking method of interval-valued data is used to describe the degree of dominance in the interval-valued information system. Therefore, the fuzzy rough technique is employed to construct the rough approximations of upward and downward unions of decision classes, from which one can induce at least and at most decision rules with certainty factors from the interval-valued decision system. Some numerical examples are employed to substantiate the conceptual arguments.