A generalization of the Bonferroni mean based on partitions

The mean defined by Bonferroni in 1950 (known by the same name) averages all non-identical product pairs of the inputs. Its generalizations to date have been able to capture unique behavior that may be desired in some decision-making contexts such as the ability to model mandatory requirements. In this paper, we propose a composition that averages conjunctions between the respective means of a designated subset-size partition. We investigate the behavior of such a function and note the relationship within a given family as the subset size is changed. We found that the proposed function is able to more intuitively handle multiple mandatory requirements or mandatory input sets.

On some properties of weighted averaging with variable weights

Density-based means have been recently proposed as a method for dealing with outliers in the stream processing of data. Derived from a weighted arithmetic mean with variable weights that depend on the location of all data samples, these functions are not monotonic and hence cannot be classified as aggregation functions. In this article we establish the weak monotonicity of this class of averaging functions and use this to establish robust generalisations of these means. Specifically, we find that as proposed, the density based means are only robust to isolated outliers. However, by using penalty based formalisms of averaging functions and applying more sophisticated and robust density estimators, we are able to define a broader family of density based means that are more effective at filtering both isolated and clustered outliers. © 2014 Elsevier Inc. All rights reserved.

Can indices of ecological evenness be used to measure consensus?

In the context of group decision making with fuzzy preferences, consensus measures are employed to provide feedback and help guide automatic or semi-automatic decision reaching processes. These measures attempt to capture the intuitive notion of how much inputs, individuals or groups agree with one another. Meanwhile, in ecological studies there has been an ongoing research effort to define measures of community evenness based on how evenly the proportional abundances of species are distributed. The question hence arises as to whether there can be any cross-fertilization from developments in these fields given their intuitive similarity. Here we investigate some of the models used in ecology toward their potential use in measuring consensus. We found that although many consensus characteristics are exhibited by evenness indices, lack of reciprocity and a tendency towards a minimum when a single input is non-zero would make them undesirable for inputs expressed on an interval scale. On the other hand, we note that some of the general frameworks could still be useful for other types of inputs like ranking profiles and that in the opposite direction consensus measures have the potential to provide new insights in ecology.

Characterizing compactness of geometrical clusters using fuzzy measures

Certain tasks in image processing require the preservation of fine image details, while applying a broad operation to the image, such as image reduction, filtering, or smoothing. In such cases, the objects of interest are typically represented by small, spatially cohesive clusters of pixels which are to be preserved or removed, depending on the requirements. When images are corrupted by the noise or contain intensity variations generated by imaging sensors, identification of these clusters within the intensity space is problematic as they are corrupted by outliers. This paper presents a novel approach to accounting for spatial organization of the pixels and to measuring the compactness of pixel clusters based on the construction of fuzzy measures with specific properties: monotonicity with respect to the cluster size; invariance with respect to translation, reflection, and rotation; and discrimination between pixel sets of fixed cardinality with different spatial arrangements. We present construction methods based on Sugeno-type fuzzy measures, minimum spanning trees, and fuzzy measure decomposition. We demonstrate their application to generating fuzzy measures on real and artificial images.

Extension of bivariate means to weighted means of several arguments by using binary trees

ABSTRACTAveraging aggregation functions are valuable in building decision making and fuzzy logic systems and in handling uncertainty. Some interesting classes of averages are bivariate and not easily extended to the multivariate case. We propose a generic method for extending bivariate symmetric means to n-variate weighted means by recursively applying the specified bivariate mean in a binary tree construction. We prove that the resulting extension inherits many desirable properties of the base mean and design an efficient numerical algorithm by pruning the binary tree. We show that the proposed method is numerically competitive to the explicit analytical formulas and hence can be used in various computational intelligence systems which rely on aggregation functions.

Improving tenants' trust in SaaS applications using dynamic security monitors

It is almost impossible to prove that a given software system achieves an absolute security level. This becomes more complicated when addressing multi-tenant cloud-based SaaS applications. Developing practical security properties and metrics to monitor, verify, and assess the behavior of such software systems is a feasible alternative to such problem. However, existing efforts focus either on verifying security properties or security metrics but not both. Moreover, they are either hard to adopt, in terms of usability, or require design-time preparation to support monitoring of such security metrics and properties which is not feasible for SaaS applications. In this paper, we introduce, to the best of our knowledge, the first unified monitoring platform that enables SaaS application tenants to specify, at run-time, security metrics and properties without design-time preparation and hence increases tenants’ trust of their cloud-assets security. The platform automatically converts security metrics and properties specifications into security probes and integrates them with the target SaaS application at run-time. Probes-generated measurements are fed into an analysis component that verifies the specified properties and calculates security metrics’ values using aggregation functions. This is then reported to SaaS tenants and cloud platform security engineers. We evaluated our platform expressiveness and usability, soundness, and performance overhead.

Learning stable weights for data of varying dimension

In this paper we develop a data-driven weight learning method for weighted quasi-arithmetic means where the observed data may vary in dimension.

Predicting protein functions from PPI networks using functional aggregation

Predicting protein functions computationally from massive protein–protein interaction (PPI) data generated by high-throughput technology is one of the challenges and fundamental problems in the post-genomic era. Although there have been many approaches developed for computationally predicting protein functions, the mutual correlations among proteins in terms of protein functions have not been thoroughly investigated and incorporated into existing prediction methods, especially in voting based prediction methods. In this paper, we propose an innovative method to predict protein functions from PPI data by aggregating the functional correlations among relevant proteins using the Choquet-Integral in fuzzy theory. This functional aggregation measures the real impact of each relevant protein function on the final prediction results, and reduces the impact of repeated functional information on the prediction. Accordingly, a new protein similarity and a new iterative prediction algorithm are proposed in this paper. The experimental evaluations on real PPI datasets demonstrate the effectiveness of our method.

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.

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.

Strong fuzzy subsethood measures and strong equalities via implication functions

In this work we present the definition of strong fuzzy subsethood measure as a unifiying concept for the different notions of fuzzy subsethood that can be found in the literature. We analyze the relations of our new concept with the definitions by Kitainik ( [20]), Young ( [26]) and Sinha and Dougherty ( [23]) and we prove that the most relevant properties of the latter are preserved. We show also several construction methods. © 2014 Old City Publishing, Inc.

On the weak monotonicity of Gini means and other mixture functions

Weak monotonicity was recently proposed as a relaxation of the monotonicity condition for averaging aggregation, and weakly monotone functions were shown to have desirable properties when averaging data corrupted with outliers or noise. We extended the study of weakly monotone averages by analyzing their ϕ-transforms, and we established weak monotonicity of several classes of averaging functions, in particular Gini means and mixture operators. Mixture operators with Gaussian weighting functions were shown to be weakly monotone for a broad range of their parameters. This study assists in identifying averaging functions suitable for data analysis and image processing tasks in the presence of outliers.

Two functions of Aristotle's common advantage

This paper identifies two distinct functions of the common advantage in Aristotle’s political thought and argues that distinguishing these functions allows for a reconciliation of the individualist and holist aspects of the Aristotelian account of the polis. I demonstrate that the Aristotelian common advantage functions both as (i) a motivating reason for individuals to enter the polis and (ii) a normative reason — the political good of justice — that provides a criterion for an assessment of the correctness of constitutions (politeiai). The two functions of the common advantage are, I suggest, reconcilable insofar as the Aristotelian polis is best understood as a unity of order rather than a mere aggregation of individual citizens or an organic whole.

PPM-HDA: privacy-preserving and multifunctional health data aggregation with fault tolerance

Wireless body area networks (WBANs), as a promising health-care system, can provide tremendous benefits for timely and continuous patient care and remote health monitoring. Owing to the restriction of communication, computation and power in WBANs, cloud-assisted WBANs, which offer more reliable, intelligent, and timely health-care services for mobile users and patients, are receiving increasing attention. However, how to aggregate the health data multifunctionally and efficiently is still an open issue to the cloud server (CS). In this paper, we propose a privacy-preserving and multifunctional health data aggregation (PPM-HDA) mechanism with fault tolerance for cloud-assisted WBANs. With PPM-HDA, the CS can compute multiple statistical functions of users' health data in a privacy-preserving way to offer various services. In particular, we first propose a multifunctional health data additive aggregation scheme (MHDA⁺) to support additive aggregate functions, such as average and variance. Then, we put forward MHDA^⊕ as an extension of MHDA⁺ to support nonadditive aggregations, such as min/max, median, percentile, and histogram. The PPM-HDA can resist differential attacks, which most existing data aggregation schemes suffer from. The security analysis shows that the PPM-HDA can protect users' privacy against many threats. Performance evaluations illustrate that the computational overhead of MHDA⁺ is significantly reduced with the assistance of CSs. Our MHDA^⊕ scheme is more efficient than previously reported min/max aggregation schemes in terms of communication overhead when the applications require large plaintext space and highly accurate data.