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.

Presence of fish on the shallow flooded margins of a small intermittently open estuary in South Eastern Australia under variable flooding regimes

Shallow water habitats within estuarine systems are believed to be important areas for small fish. While a wide variety of shallow habitats have been studied, the land that becomes inundated by the damming effect after the closure of intermittently open mouths has previously been overlooked. Fish were sampled monthly from both the main channel and flood zone of an intermittently open estuary between July 2004 and June 2005 using minifyke nets during the day and at night. A total of 7,787 fish were collected during the study representing 13 species and 11 families. Philypnodon grandiceps was the most abundant species and, together with Atherinosoma microstoma, Pseudogobius olorum, and Galaxias maculatus, made up 94% of the total catch. Inundation of the flood zone occurred in two discrete forms associated with mouth condition, which consisted of sporadic flooding while the mouth was open, to long-term flooding for 6 months after its closure. Large numbers of fish were captured on the flood zone, which included nine species; however, A. microstoma dominated the catch. A distinct shift in the flood zone fish assemblage occurred between the two mouth conditions, which is likely associated with changes in hydro-period and food availability of the flood zone and physico-chemical parameters in the main channel. There was no longitudinal variation in the fish assemblage in both the main channel and flood zone; similarly, the diel period was found to have little effect on the fish assemblage. The total catch per unit effort did not vary across seasons and suggests that fish abundance within the estuary is stable throughout the year. Unlike other estuarine systems where shallow water fish assemblages may be structured by variations in tide and elevation within the Surrey, freshwater inflow and, more importantly, mouth condition appear to have the greatest influence in composition of the shallow water flood zone fish assemblage of intermittently open estuaries.

Texture recognition by using GLCM and various aggregation functions

We discuss the problem of texture recognition based on the grey level co-occurrence matrix (GLCM). We performed a number of numerical experiments to establish whether the accuracy of classification is optimal when GLCM entries are aggregated into standard metrics like contrast, dissimilarity, homogeneity, entropy, etc., and compared these metrics to several alternative aggregation methods.We conclude that k nearest neighbors classification based on raw GLCM entries typically works better than classification based on the standard metrics for noiseless data, that metrics based on principal component analysis inprove classification, and that a simple change from the arithmetic to quadratic mean in calculating the standard metrics also improves classification.

Inhibition of platelet aggregation by omega-3 polyunsaturated fatty acids is gender specific — redefining platelet response to fish oils

Existence of gender differences in cardiovascular disease (CVD) following long-chain omega-3 polyunsaturated fatty acid (LCn-3 PUFA) supplementation have suggested that sex hormones play a role in cardio-protection. The objective of this study was to determine gender specific responses in the efficacy of LCn-3 PUFA to inhibit platelet aggregation in vitro. Blood was analyzed for collagen-induced platelet aggregation following pre-incubation with LCn-3 PUFA in healthy adults (n=42). Eicosapentaenoic acid (EPA) was significantly more effective in reducing platelet aggregation compared with docosapentaenoic acid (DPA) and docosahexaenoic acid (DHA). When grouped by gender, this differential pattern was followed in males only. In females, DHA, DPA and EPA were all equally effective. Between group analyses (LCn-3 PUFA vs. gender) showed that both DHA and DPA were significantly less effective in males compared with females. EPA was equally effective in reducing platelet aggregation in both groups. These findings show that significant gender differences exist in platelet aggregation in response to various LCn-3 PUFA treatments.

Variable step-size LMS algorithm with a quotient form

An improved robust variable step-size least mean square (LMS) algorithm is developed in this paper. Unlike many existing approaches, we adjust the variable step-size using a quotient form of filtered versions of the quadratic error. The filtered estimates of the error are based on exponential windows, applying different decaying factors for the estimations in the numerator and denominator. The new algorithm, called more robust variable step-size (MRVSS), is able to reduce the sensitivity to the power of the measurement noise, and improve the steady-state performance for comparable transient behavior, with negligible increase in the computational cost. The mean convergence, the steady-state performance and the mean step-size behavior of the MRVSS algorithm are studied under a slow time-varying system model, which can be served as guidelines for the design of MRVSS algorithm in practical applications. Simulation results are demonstrated to corroborate the analytic results, and to compare MRVSS with the existing representative approaches. Superior properties of the MRVSS algorithm are indicated.

A class of modified variable step-size NLMS algorithms for system identification

This paper proposes a class of modified variable step-size normalized least mean square (VS NLMS) algorithms. The class of schemes are obtained from estimating the optimum step-size of NLMS that minimizes the mean square deviation (MSD). During the estimation, we consider the properties of the additive noise and the input excitation together. The developed class of VS NLMS algorithms have simple forms and give improved tradeoff of fast convergence rate and low misadjustment in system identification.

An illustration of variable precision rough set theory : The gender classification of the European barn swallow (Hirundo rustica)

This paper introduces a new technique in the investigation of object classification and illustrates the potential use of this technique for the analysis of a range of biological data, using avian morphometric data as an example. The nascent variable precision rough sets (VPRS) model is introduced and compared with the decision tree method ID3 (through a ‘leave n out’ approach), using the same dataset of morphometric measures of European barn swallows (Hirundo rustica) and assessing the accuracy of gender classification based on these measures. The results demonstrate that the VPRS model, allied with the use of a modern method of discretization of data, is comparable with the more traditional non-parametric ID3 decision tree method. We show that, particularly in small samples, the VPRS model can improve classification and to a lesser extent prediction aspects over ID3. Furthermore, through the ‘leave n out’ approach, some indication can be produced of the relative importance of the different morphometric measures used in this problem. In this case we suggest that VPRS has advantages over ID3, as it intelligently uses more of the morphometric data available for the data classification, whilst placing less emphasis on variables with low reliability. In biological terms, the results suggest that the gender of swallows can be determined with reasonable accuracy from morphometric data and highlight the most important variables in this process. We suggest that both analysis techniques are potentially useful for the analysis of a range of different types of biological datasets, and that VPRS in particular has potential for application to a range of biological circumstances.

The spatial pattern of natural selection when selection depends upon experience

Apostatic (frequency‐ or density‐dependent) selection, aposematic signals, and mate choice behavior generally require that the mean prey or potential mate density m value be high enough (above a threshold T) to result in sufficient encounter rates for the searcher to learn or retain the association between conspicuous signals and prey unprofitability, to forage apostatically, or to choose among mates. This assumes that all searchers experience , which implicitly assumes an even dispersion of targets among searcher territories. Uneven dispersion generates new phenomena. If , then only territories with local density x values that are greater than T favor experience‐based behavior, leading to spatially variable frequency‐ or density‐dependent selection intensity. As aggregation increases, the increase in percentage of targets in favorable territories ( ) is greater than the increase in the percentage of territories that are favorable. The relationship is reversed when . In both cases, because as few as 10% of the territories can contain 80% of the targets, only a few territory holders may account for most of the selection on most of the target population; accidents of experience in only a few searchers can have unexpectedly large effects on the target population. This also provides an explanation for high searcher behavior variation (personalities) : individuals from favorable territories will behave differently in behavioral experiments than those from unfavorable territories, at least with respect to similar kinds of targets. These effects will generate spatial heterogeneity in natural and sexual selection in what are otherwise uniform environments.