Construction of aggregation operators for automated decision making via optimal interpolation and global optimization

This paper examines methods of point wise construction of aggregation operators via optimal interpolation. It is shown that several types of application-specific requirements lead to interpolatory type constraints on the aggregation function. These constraints are translated into global optimization problems, which are the focus of this paper. We present several methods of reduction of the number of variables, and formulate suitable numerical algorithms based on Lipschitz optimization.

Absorbent tuples of aggregation operators

We generalize the notion of an absorbent element of aggregation operators. Our construction involves tuples of values that decide the result of aggregation. Absorbent tuples are useful to model situations in which certain decision makers may decide the outcome irrespective of the opinion of the others. We examine the most important classes of aggregation operators in respect to their absorbent tuples, and also construct new aggregation operators with predefined sets of absorbent tuples.

Construction of aggregation operators with noble reinforcement

This paper examines disjunctive aggregation operators used in various recommender systems. A specific requirement in these systems is the property of noble reinforcement: allowing a collection of high-valued arguments to reinforce each other while avoiding reinforcement of low-valued arguments. We present a new construction of Lipschitz-continuous aggregation operators with noble reinforcement property and its refinements.

Fitting ST-OWA operators to empirical data

The OWA operators gained interest among researchers as they provide a continuum of aggregation operators able to cover the whole range of compensation between the minimum and the maximum. In some circumstances, it is useful to consider a wider range of values, extending below the minimum and over the maximum. ST-OWA are able to surpass the boundaries of variation of ordinary compensatory operators. Their application requires identification of the weighting vector, the t-norm, and the t-conorm. This task can be accomplished by considering both the desired analytical properties and empirical data.

Constructions of aggregation operators that preserve ordering of the data

We address the issue of identifying various classes of aggregation operators from empirical data, which also preserves the ordering of the outputs. It is argued that the ordering of the outputs is more important than the numerical values, however the usual data fitting methods are only concerned with fitting the values. We will formulate preservation of the ordering problem as a standard mathematical programming problem, solved by standard numerical methods.

Motorcycle ownership and injury in China

Background. China has made tremendous progress in its economic development in the past two decades. Accompanying this economic development has been an evident shift in the modes of transport, from walking and cycling to the use of motorcycles and, increasingly, four-wheel vehicles. Such changes are likely to have also produced changes in the patterns and numbers of road traffic injuries, including increases in motorcycle injuries. However, such changes have not been well documented. The work described in this paper sought, therefore, to document the changes in motorcycle ownership, motorcyclist mortality and injury rates in China since 1987.
Methods. National traffic ownership and injury data from 1987 to 2001 were obtained from the National Bureau for Traffic Administration. Additionally, traffic ownership and injury records from 1997 to 2001 were collected from local police offices from 20 counties in Guangxi Region. Population data were obtained from the national and county statistics bureaus. Motorcycle ownership, fatality and injury trends over time were calculated.
Results. Nationally, motorcycles accounted for 23.4% of all registered motor vehicles in 1987, increasing to 63.2% in 2001. Motorcyclist fatalities and injuries increased 5.5-fold and 9.3-fold, respectively, between 1987 and 2001. In 1987, 7.5% of all traffic fatalities and 8.8% of all traffic injuries were sustained by motorcyclists, with the corresponding proportions increasing to 18.9% and 22.8%, respectively, in 2001. The changing proportions of both traffic fatalities and injuries sustained by motorcyclists were positively correlated with the change in the proportion of motorcycles among all motor vehicles. In the 20 counties in Guangxi, motorcyclist fatality and injury rates also increased between 1997 and 2001. Moreover, these rates were considerably higher than the national rates.
Conclusions. Motorcyclist injury in China is a serious public health problem. Motorcyclist fatalities and injuries are likely to continue to increase unless appropriate intervention programmes are implemented.

Helmets for preventing injury in motorcycle riders

Background: Motorcycle crash victims form a high proportion of those killed or injured in road traffic accidents. Injuries to the head, following motorcycle crashes, are a common cause of severe morbidity and mortality. It seems intuitive that helmets should protect against head injuries but it has been argued that motorcycle helmet use decreases rider vision and increases neck injuries. This review will collate the 'current available evidence on helmets and their impact on mortality, and head, face and neck injuries following motorcycle crashes.

Objectives: To quantify the effectiveness of wearing a motorcycle helmet in reducing mortality and head and neck injury following motorcycle crashes.

Search strategy: Databases including the Cochrane Injuries Group Specialised Register, Cochrane Central Register of Controlled Trials (The Cochrane Library issue 1,2003), MEDLINE (January 1966 to February 2003), EMBASE (January 1985 to February 2003), CINAHL (January 1982 to February 2003), IRRD (International Road Research Documentation), TRANSDOC, TRIS (Transport Research Information Service), ATRI (Australian Transport Index) (1976 to Feb 2003), Science Citation Index were searched for relevant articles. Web sites of traffic and road accident research bodies including government agencies were also searched. Reference lists from topic reviews, identified studies and bibliographies were examined for relevant articles.

Selection criteria: We considered for inclusion studies that investigated a population of motorcycle riders who had crashed, examining helmet use as an intervention and with outcomes that included one or more of the following: death, head, neck or facial injury. Studies included any that compared an intervention and control group and, therefore, included any randomised controlled trials, non-randomised controlled trials, cohort, case-control and cross-sectional studies. Ecological and case series studies were excluded.

Data collection and analysis: Two reviewers independently screened reference lists for eligible articles. Two reviewers independently assessed articles for inclusion criteria. Data were abstracted by two independent reviewers using a standard abstraction form.

Main results: Fifty-three observational studies were identified of varying quality. Despite methodological differences there was a remarkable consistency in results, particularly for mortality and head injury outcomes. Motorcycle helmets appear to reduce the risk of mortality although, due to heterogeneity in study design, an overall estimate of effect was not calculated. There was some evidence that the effect of helmets on mortality is modified by speed. Motorcycle helmets were found to reduce the risk of head injury and from five well-conducted studies the risk reduction is estimated to be 72% (OR 0.28, 95%CI 0.23,0.35). Insufficient evidence was found to estimate the effect of motorcycle helmets compared with no helmet on facial or neck injuries. However, studies of poorer quality suggest that helmets have no effect on the risk of neck injuries and are protective for facial injury. There was insufficient evidence to demonstrate whether differences in helmet type confer more or less advantage in injury reduction.

Conclusions: Motorcycle helmets reduce the risk of mortality and head injury in motorcycle riders who crash, although the former effect may be modified by other crash factors such as speed. Further well-conducted research is required to determine the effects of helmets and different helmet types on mortalIty, head, neck and facial injuries. However, the findings suggest that global efforts to reduce road traffic injuries may be facilitated by increasing helmet use by motorcyclists.

Guest editorial: foreword to the special issue on aggregation operators

The fourteen papers in this special section are devoted to aggregation operators with respect to knowledge based systems.

Fitting aggregation operators to data

Theoretical advances in modelling aggregation of information produced a wide range of aggregation operators, applicable to almost every practical problem. The most important classes of aggregation operators include triangular norms, uninorms, generalised means and OWA operators.
With such a variety, an important practical problem has emerged: how to fit the parameters/ weights of these families of aggregation operators to observed data? How to estimate quantitatively whether a given class of operators is suitable as a model in a given practical setting? Aggregation operators are rather special classes of functions, and thus they require specialised regression techniques, which would enforce important theoretical properties, like commutativity or associativity. My presentation will address this issue in detail, and will discuss various regression methods applicable specifically to t-norms, uninorms and generalised means. I will also demonstrate software implementing these regression techniques, which would allow practitioners to paste their data and obtain optimal parameters of the chosen family of operators.

Pointwise construction of Lippschitz aggregation operators with specific properties

This paper describes an approach to pointwise construction of general aggregation operators, based on monotone Lipschitz approximation. The aggregation operators are constructed from a set of desired values at certain points, or from empirically collected data. It establishes tight upper and lower bounds on Lipschitz aggregation operators with a number of different properties, as well as the optimal aggregation operator, consistent with the given values. We consider conjunctive, disjunctive and idempotent n-ary aggregation operators; p-stable aggregation operators; various choices of the neutral element and annihilator; diagonal, opposite diagonal and marginal sections; bipolar and double aggregation operators. In all cases we provide either explicit formulas or deterministic numerical procedures to determine the bounds. The findings of this paper are useful for construction of aggregation operators with specified properties, especially using interpolation schemata.

Interpolatory type construction of general aggregation operators

In this chapter we examine a number of methods to construct aggregation operators of interpolatory type for specific applications. The construction is based on the desired values of the aggregation operator at certain prototypical points, and on other desired properties, such as, conjuctive, disjunctive or averaging behaviour, symmetry and marginals.

Identification of weights in aggregation operators

This chapter provides a review of various techniques for identification of weights in generalized mean and ordered weighted averaging aggregation operators, as well as identification of fuzzy measures in Choquet integral based operators. Our main focus is on using empirical data to compute the weights. We present a number of practical algorithms to identify the best aggregation operator that fits the data.

OWA operators in linear regression and detection of outliers

We consider the use of Ordered Weighted Averaging (OWA) in linear regression. Our goal is to replace the traditional least squares, least absolute deviation, and maximum likelihood criteria with an OWA function of the residuals. We obtain several high breakdown robust regression methods as special cases (least median, least trimmed squares, trimmed likelihood methods). We also present new formulations of regression problem. OWA-based regression is particularly useful in the presence of outliers.