Renkuan Guo

Predicting air pollution using fuzzy membership grade Kriging

Abstract A practical situation often facing us is that fuzzy spatial data are recorded as crisp real-valued numbers, e.g., a PM 10 record is 15.1, but we do know that it is an imprecise and vague observation. A new spatial analysis technique – fuzzy membership grade Kriging with semi-statistical membership, proposed by Guo has been developed to address fuzzy spatial data recorded as crisp numbers. In this paper, we will explain fuzzy membership grade Kriging, its root, its theory and its implementations. As an illustration, we will use PM 10 data of California, USA. Three sample membership functions are extracted from the data itself: linear, quadratic and hyperbolic tangent and applied to the PM 10 data. The predicted membership grades are also transformed back into PM 10 concentrations by using inverse functions in order to identify areas being dangerous to human health. Finally, we implement our new fuzzy membership grade Kriging in GIS.

The Coupling of Regression Model and Differential Equation Model in GM (1, 1) Modeling and Extended GM (1, 1) Models

The GM (1,1) model is a small-sample based coupled data-assimilation approach with the advantages of highly predictive power and easy computations. However, in the standard GM (1,1) model building exercises we often face a statistical-grey inconsistency problem. Therefore, in this paper we examine the GM(1,1) model from its component-level and try to reveal an interactive coupling nature of differential equation model and corresponding regression model constituting of a GM(1,1) model. Based our analysis, we state a coupling principle for establishing an extended GM(1,1) model and further explore certain families of extended GM(1,1) models with statistical-grey consistency.

Imprecise Uncertainty Modelling of Air Pollutant PM10

Particulate matter (PM) refers to solid particles and liquid droplets found in air. Many manmade and natural sources produce PM directly, or produce pollutants that react in the atmosphere to form PM. The resultant solid and liquid particles come in a wide range of sizes, and particles that are 10 micrometers or less in diameter (PM

Climate Change Impact on Quiver Trees in Arid Namibia and South Africa

The climate fluctuates and changes naturally, and adding the common problems of land transformation and deforestation, its impact can be very harsh on the natural environment, and cause a decline in the biodiversity of plants and animals. Aloe dichotoma, common name Quiver tree, is an important part of the arid regions, such as Namaqualand and Bushmanland in South Africa, and in arid parts of southern Namibia. This succulent tree species occurs in rocky areas, and it can grow quite rapidly under the right conditions. Succulents are able to survive long periods of drought conditions, due to the fact succulent plants has special water-storing tissue which makes part of the plant fleshy, and the Quiver tree has succulent leaf and stem (Van Wyk and Smith, 1996). The Quiver tree has a 200 year life span, and can grow up to 9 meters tall, and it occurs in summer and winter rainfall regions, and can live under a variety of climatic conditions (Fig. 1). The Quiver tree is important to the ecosystem due to the fact that it is as a source of moisture for a wide variety of mammals, birds, and insects. Foden’s detailed study of the demographic data of the Quiver trees show that negligible recruitment has occurred in certain populations for 50 years, and the effects of non-climatic variables, such as herbivory, competition, seed availability, fungal pathogens, plant collection... are very small (Foden, 2002). Today, the Quiver trees are threatened by agricultural expansion, overgrazing, and mining, as well as droughts and other climate changes (Foden, 2002). Climate changes is one of the major factors affecting the existence of Quiver trees, while the Quiver tree will unlikely to be affected by small climatic fluctuations, but will be affected larger or long term climatic changes. The Quiver tree can potentially provide a good indication of long term climate changes in the arid regions (Foden, 2002). Previous onsite observations show that Quiver trees are very sensitive to temperature changes, and does not do well under extreme hot and dry conditions. Observations has also shown that the Quiver trees might be responding to higher temperatures by shifting its distribution range towards higher and higher altitudes, showing a preference for slightly cooler regions (Midgley et al., 2009).

CREDIBILITY MEASURE-BASED FUZZY MEMBERSHIP GRADE KRIGING

A fundamental problem in fuzzy analysis is that the membership function is specified subjectively. In other words, the modelers specify the membership function form and assign the values of the parameters in membership function via their working experiences. Different from its probabilistic counterpart, fuzzy mathematical theory does not provide convenient parameter estimation approach. In this paper, we first review Lius non-classical credibility measure theory (i.e., (∨,·)-credibility measure theory) in Liu7, because the fuzzy theory initiated by Zadeh10 contains a critical weakness: non self-duality property for possibility measure. We establish a parameter estimation of the membership function in terms of maximum entropy principle on the ground of self-dual credibility measure theory. Furthermore, based on the data assimilated membership function, we can calculate membership grades on the fuzzy environmental index, using PM10 air pollution as an illustration. We treat the calculated membership grades as spatially distributed random quantity, and therefore perform the standard ordinary kriging approach for generating the predicted environmental index map, for PM10 prediction map.