Appropriate choice of aggregation operators in fuzzy decision support systems

Fuzzy logic provides a mathematical formalism for a unified treatment of vagueness and imprecision that are ever present in decision support and expert systems in many areas. The choice of aggregation operators is crucial to the behavior of the system that is intended to mimic human decision making. This paper discusses how aggregation operators can be selected and adjusted to fit empirical data—a series of test cases. Both parametric and nonparametric regression are considered and compared. A practical application of the proposed methods to electronic implementation of clinical guidelines is presented

Polycyclic aromatic hydrocarbon emission loads and profiles from the burning of locally grown wood species in Victoria, Australia - Some pilot project results

A testing facility for combustion of biomass and sampling of emissions has been established at Deakin University. In this pilot project using this facility, four kinds of locally grown wood species were burned and the particle emissions sampled and analysed for Polycyclic Aromatic Hydrocarbons (PAHs). The selected wood species covering pine, red gum, yellow box and sugar gum, are the most popular domestic fuel wood in Australia. Particulate matter emissions from burning of each load of wood were sampled from the flue using a standard stack emission sampling train. The particle-laden filters were extracted and the .extract analysed to determine PAH concentrations by Gas Chromatographyl Mass Spectrometer (Gc/MS). The sampling was conducted under two different burning conditions with the air inlet of the combustion chamber fully open and with it half open. A suite of 15 PAHs, ranging from naphthalene (C IOHB) to dibenzolahlanthracene (C12H14), were selected for analysis. PAH profiles for the four wood species, under the different burning regimes, have been generated. Some preliminary emission factors for the different wood species have been derived as microgram of summed PAHs (rPAHs) emittedlkilogram of wood burned. Total Particulate Matter (TPM) emission factors were also obtained from gravimetric measurement of the sample filter before and after the combustion. Based on these emission factors, pine displayed the highest level of rPAHs emitted from the combustion of the four wood species, with sugar gum showing the lowest level of rPAHs emission. Emission factors associated with the slow burning condition clearly showed higher l:PAH levels compared to the faster burning condition. During the faster burning condition, red gum and pine show a higher percentage of rPAH to TPM than sugar gum or yellow box. Under the slower burning. the l:PAHlTPM ratio in every case was greater.

Monotone approximation of aggregation operators using least squares splines

The need for monotone approximation of scattered data often arises in many problems of regression, when the monotonicity is semantically important. One such domain is fuzzy set theory, where membership functions and aggregation operators are order preserving. Least squares polynomial splines provide great flexbility when modeling non-linear functions, but may fail to be monotone. Linear restrictions on spline coefficients provide necessary and sufficient conditions for spline monotonicity. The basis for splines is selected in such a way that these restrictions take an especially simple form. The resulting non-negative least squares problem can be solved by a variety of standard proven techniques. Additional interpolation requirements can also be imposed in the same framework. The method is applied to fuzzy systems, where membership functions and aggregation operators are constructed from empirical data.

Thinking/acting locally/globally: western science and environmental education in a global knowledge economy

This paper critically appraises a number of approaches to 'thinking globally' in environmental education, with particular reference to popular assumptions about the universal applicability of Western science. Although the transnational character of many environmental issues demands that we 'think globally', I argue that the contribution of Western science to understanding and resolving environmental problems might be enhanced by seeing it as one among many local knowledge traditions. The production of a 'global knowledge economy' in/for environmental education can then be understood as creating transnational 'spaces' in which local knowledge traditions can be performed together, rather than as creating a 'common market' in which representations of local knowledge must be translated into (or exchanged for) the terms of a universal discourse.

How to build aggregation operators from data

This article discusses a range of regression techniques specifically tailored to building aggregation operators from empirical data. These techniques identify optimal parameters of aggregation operators from various classes (triangular norms, uninorms, copulas, ordered weighted aggregation (OWA), generalized means, and compensatory and general aggregation operators), while allowing one to preserve specific properties such as commutativity or associativity. © 2003 Wiley Periodicals, Inc.

Purely magnetic locally rotationally symmetric spacetimes

We consider all purely magnetic, locally rotationally symmetric (LRS) spacetimes. It is shown that such spacetimes belong to either LRS class I or III by the Ellis classification. For each class the most general solution is found exhibiting a disposable function and three parameters. A Segré classification of purely magnetic LRS spacetimes is given together with the compatibility requirements of two general energy–momentum tensors. Finally, implicit solutions are obtained, in each class, when the energy–momentum tensor is a perfect fluid.

Fitting generated aggregation operators to empirical data

This paper treats the problem of fitting general aggregation operators with unfixed number of arguments to empirical data. We discuss methods applicable to associative operators (t-norms, t-conorms, uninorms and nullnorms), means and Choquet integral based operators with respect to a universal fuzzy measure. Special attention is paid to k-order additive symmetric fuzzy measures.

Learning weights in the generalized OWA operators

This paper discusses identification of parameters of generalized ordered weighted averaging (GOWA) operators from empirical data. Similarly to ordinary OWA operators, GOWA are characterized by a vector of weights, as well as the power to which the arguments are raised. We develop optimization techniques which allow one to fit such operators to the observed data. We also generalize these methods for functional defined GOWA and generalized Choquet integral based aggregation operators.

Fisheries and cage culture of three reservoirs in west Java, Indonesia; a case study of ambitious development and resulting interactions

The interactions between cage culture and wild fishery activities in three Indonesian reservoirs, Saguling, Cirata and Jatiluhur, of the greater Ciratum watershed, West Java, were evaluated using historical data and interviews with cage culture operators. In all three reservoirs, cage culture of common carp, Cyprinus carpio L., and later of common carp and Nile tilapia, Oreochromis niloticus (L.), were encouraged as an alternative livelihood for persons displaced by the impoundment. Currently, a two-net culture system, locally known as 'lapis dua', in which in the inner cage (7 × 7 × 3 m) is used for common carp culture and the outer cage (7 × 7 × 5/7 m) is stocked with Nile tilapia, is practised. On average each cage is stocked with  approximately 100 kg fingerlings each of common carp and Nile tilapia. The numbers of cages and production of cultured fish has increased in the reservoirs, but total and per cage production began to decline from about 1995 in Saguling from 2200 kg cage−1 in 1989 to <500 kg cage−1 in 2002, and in Cirata from a peak of approximately 2300 kg cage−1 in 1995 to approximately 400 kg cage−1 in 2002. In Jatiluhur, which has a considerably lower cage density, total fish production and production per cage has increased since 2000, and currently is approximately 4000 kg cage−1, close to production in the early years of cage culture activities. The cage culture operations also resulted in substantial nutrient loading, estimated at 3.2, 15.2 and 3.1 t of nitrogen and 134, 636 and 128 kg of phosphorous per year in the maximum years of production for Saguling, Cirata and Jatiluhur reservoirs, respectively. In later years, when cage culture production was high, fish kills occurred in the cages, and in Jatiluhur reservoir coincided with a dramatic decline in wild fishery catches. An attempt is made to determine the maximum number of cages for each of the reservoirs that will bring long-term sustainability of cage culture operations and the wild fisheries in the three reservoirs.

Large-scale mathematics assessment : looking globally to act locally

In this paper, I will argue that it is possible to use data from large-scale international and national mathematics assessment programmes, whose attention is on summative achievement, to provide formative information that informs teachers about the effects of their classroom practice. However, to have impact on, and be useful for, classroom practitioners, these achievement data need to be reworked and re-presented in ways that are plausible, provide a basis for inferences about practice, and be appropriate for the intended audience. This paper examines achievement-focused assessment programmes in terms of their aims and approaches, and develops the argument that formative assessment possibilities are present, within these programmes, although usually hidden. Examples are drawn from several sources to support this argument, and demonstrate a variety of approaches that have been taken in the past. Suggestions for further action are made.

Body mass index and parent-reported self-estem in elementary school children: evidence for a causal relationship.

OBJECTIVE: To clarify relationships between body mass index (BMI) and self-esteem in young children at a population level. To assess whether low self-esteem precedes or follows development of overweight/obesity in children. DESIGN: Prospective cohort study in elementary schools throughout Victoria, Australia. Child BMI and self-esteem were measured in 1997 and 2000. SUBJECTS: Random sample of 1,157 children who were in the first 4 y of elementary school (aged 5-10 y) at baseline. MEASURES: BMI was calculated from measured height and weight, then transformed to z-scores. Children were classified as nonoverweight, overweight or obese based on international cut-points. Low child self-esteem was defined as a score below the 15th percentile on the self-esteem subscale of the parent-reported Child Health Questionnaire. RESULTS: Overweight/obese children had lower median self-esteem scores than nonoverweight children at both timepoints, especially at follow-up. After accounting for baseline self-esteem, higher baseline BMI z-score predicted poorer self-esteem at follow-up (P=0.008). After accounting for baseline BMI z-score, poorer baseline self-esteem did not predict higher BMI z-score at follow-up. While nonoverweight children with low baseline self-esteem were more likely to develop overweight/obesity (OR=2.1, 95% CI=1.2, 3.6), this accounted for only a small proportion of the incidence of overweight. CONCLUSIONS: Our data show an increasingly strong association between lower self-esteem and higher body mass across the elementary school years. Overweight/obesity precedes low self-esteem in many children, suggesting a causal relationship. This indicates that prevention and management strategies for childhood overweight/obesity need to begin early to minimise the impact on self-esteem.

Methods of construction of OWA operators from data

This paper investigates the problem of obtaining the weights of the ordered weighted aggregation (OWA) operators from observations. The problem is formulated as a restricted least squares and uniform approximation problems. We take full advantage of the linearity of the problem. In the former case, a well known technique of non-negative least squares is used. In a case of uniform approximation, we employ a recently developed cutting angle method of global optimisation. Both presented methods give results superior to earlier approaches, and do not require complicated nonlinear constructions. Additional restrictions, such as degree of orness of the operator, can be easily introduced

Identification of general and double aggregation operators using monotone smoothing

Aggregation operators model various operations on fuzzy sets, such as conjunction, disjunction and averaging. Recently double aggregation operators have been introduced; they model multistep aggregation process. The choice of aggregation operators depends on the particular problem, and can be done by fitting the operator to empirical data. We examine fitting general aggregation operators by using a new method of monotone Lipschitz smoothing. We study various boundary conditions and constraints which determine specific types of aggregation.