Biconic aggregation functions

We introduce a new method to construct aggregation functions. These aggregation functions are called biconic aggregation functions with a given diagonal (resp. opposite diagonal) section and their construction is based on linear interpolation on segments connecting the diagonal (resp. opposite diagonal) of the unit square to the points (0, 1) and (1, 0) (resp. (0, 0) and (1, 1)). Subclasses of biconic aggregation functions such as biconic semi-copulas, biconic quasi-copulas and biconic copulas are studied in detail.     

Ultramodular aggregation functions

Ultramodular aggregation functions are investigated and discussed, including a study of structural properties and the proposal of some construction methods.     

Characterizing quasi-metric aggregation functions

ABSTRACT

In this paper, we study those functions that allows us to combine a family of quasi-metrics, defined all of them on the same set, into a single one, which will be called quasi-metric aggregation functions. In particular, we characterize the quasi-metric aggregation functions and, in addition, we discuss a few of their properties. Moreover, a few methods to discard those functions that are useless as quasi-metric aggregation functions are introduced. Throughout the paper, different examples justify and illustrate the results presented. Finally, two possible fields where the developed theory can be useful are exposed.     

Approximation algorithms for facility location problems with a special class of subadditive cost functions

In this article we focus on approximation algorithms for facility location problems with subadditive costs. As examples of such problems, we present three facility location problems with stochastic demand and exponential servers, respectively inventory. We present a (1+ε,1)$(1+\epsilon ,1)$-reduction of the facility location problem with subadditive costs to the soft capacitated facility location problem, which implies the existence of a 2(1+ε)$2(1+\epsilon )$-approximation algorithm. For a special subclass of subadditive functions, we obtain a 2-approximation algorithm by reduction to the linear cost facility location problem.     

Set-based extended aggregation functions

Inspired by the Zadeh approach to fuzzy connectives in fuzzy set theory and by some applications, we introduce and study set-based extended functions, and in particular, set-based extended aggregation functions. These functions reflect neither reordering nor repetition of input values, and, linking different arities, they introduce serious constraints for extended functions. A complete characterization of set-based extended (aggregation) functions is given, and some constructions of such functions are also proposed, including several examples.     

On the constructions of constant-composition codes from perfect nonlinear functions

A new construction of constant-composition codes based on all known perfect nonlinear functions from F _q m to itself is presented, which provides a kind of unified constructions of constant-composition codes based on all known perfect nonlinear functions from F _q m to itself. It is proved that the new constant-composition codes are optimal with respect to the Luo-Fu-Vinck-Chen bound, when m is an odd positive integer greater than 1. Finally, we point out that two constructions of constant-composition codes, proposed by Ding Cunsheng et al. in 2005, are equivalent to two special types of the new constant-composition codes. Supported in part by the National Natural Science Foundation of China (Grant Nos. 60573028, 60803156), the Open Research Fund of the National Mobile Communications Research Laboratory of Southeast University (Grant No. W200805) and in part by Singapore Ministry of Education Academic Research Fund (Grant No. T206B2204)     

New constructions of balanced Boolean functions with high nonlinearity and optimal algebraic degree

In this paper, we propose a technique for constructing balanced Boolean functions on even numbers of variables. The main technique is to utilize a set of disjoint spectra functions and a special Boolean permutation to derive a balanced Boolean function with high nonlinearity and optimal algebraic degree. It is shown that the functions we construct are different from both Maiorana-McFarland's (M-M) super-class functions introduced by Carlet and modified M-M super-class functions presented by Zeng and Hu. Furthermore, we show that they have no nonzero linear structures.     

Piecewise linear aggregation functions based on triangulation

We introduce a method to construct piecewise linear binary aggregation functions on the unit interval, based on a triangulation of the unit square with one additional vertex. We derive conditions under which such piecewise linear aggregation functions possess additional interesting properties, such as idempotence, symmetry, Lipschitz continuity and 2-monotonicity. This construction method can also be used to approximate binary aggregation functions. In this way, copulas and quasi-copulas are approximated by singular copulas.     

Hierarchical aggregation functions generated from belief structures

We deal with the development of tools useful for the construction of multicriteria decision functions that allow for the modeling of the types of complexity that is the hallmark of human intelligence. We first discuss the fuzzy measure, describe its potential for characterizing relationships between multiple criteria, and introduce the class of ordered aggregation functions that can be based on a fuzzy measure. We then focus on the two fuzzy measures associated with the Dempster-Shafer belief structure, plausibility, and belief, and describe the types of ordered aggregation functions obtained using these measures. This leads us to introduce a new class of aggregation functions obtained by allowing a decision maker to provide his decision imperative in terms of components (concepts) that contribute to his overall satisfaction. Each component consists of a value, a subset of criteria and an agenda for combining the criteria in the component. Finally, it is shown how these components can be combined to allow for the representation of hierarchical decision functions     

Further constructions of control-Lyapunov functions and stabilizing feedbacks for systems satisfying the Jurdjevic-Quinn conditions

For a broad class of nonlinear systems, we construct smooth control-Lyapunov functions. We assume our systems satisfy appropriate generalizations of the Jurdjevic-Quinn conditions. We also design state feedbacks of arbitrarily small norm that render our systems integral-input-to-state stable to actuator errors.     

On representations of 2-increasing binary aggregation functions

In this paper, we provide two different representations of 2-increasing binary aggregation functions by means of their lower and upper margins and a suitable copula.     

A class of aggregation functions encompassing two-dimensional OWA operators

In this paper we prove that, under suitable conditions, Atanassov’s K_α operators, which act on intervals, provide the same numerical results as OWA operators of dimension two. On one hand, this allows us to recover OWA operators from K_α operators. On the other hand, by analyzing the properties of Atanassov’s operators, we can generalize them. In this way, we introduce a class of aggregation functions - the generalized Atanassov operators - that, in particular, include two-dimensional OWA operators. We investigate under which conditions these generalized Atanassov operators satisfy some properties usually required for aggregation functions, such as bisymmetry, strictness, monotonicity, etc. We also show that if we apply these aggregation functions to interval-valued fuzzy sets, we obtain an ordered family of fuzzy sets.     

局部几何结构驱动的图像插值放大及超分辨率复原

众所周知,图像插值是根据一幅低分辨率噪声图像重建相应高分辨率清晰图像的数字图像处理技术。虽然已有一些文献报道了多种图像插值算法,然而现有算法在插值视觉效果和计算复杂度两者间往往难以实现均衡,为此,提出了一种局部几何结构驱动的偏微分方程(PDE)图像插值算法。该算法通过耦合边缘、纹理和角形3种不同几何结构的扩散机制来进行插值,插值结果表明,该算法不仅具有抗噪声性能,而且能够同时增强边缘、纹理以及角形结构。考虑到图像的超分辨率复原与插值放大在数学本质上的一致性,特将上述PDE应用推广到图像的超分辨率复原,并且针对高强度噪声情形下,超分辨率图像中出现的伪纹理结构,提出了一种耦合全变差模型的改进的PDE。实验结果表明,不论是插值放大图像,还是超分辨率复原图像都具有较高的视觉质量和峰值信噪比。     

Multi-criteria decision making approach based on SVTrN Dombi aggregation functions

Artificial Intelligence Review - The neutrosophic set is constructed for modelling of situations specifically with incomplete, indeterminate and inconsistent information. In the study, Dombi...     

压缩视频超分辨率重构的一种新算法

针对传统重构算法不能很好地解决压缩视频的超分辨率图像重构的问题,文中提出了一种基于凸集投影(POCS)理论的压缩视频超分辨率重构算法.整个算法是在严格数学推理基础上形成的,具有较强的逻辑性和严密性.实验结果也表明,该算法不仅在峰值信噪比(PSNR)值和重构效果对压缩视频有较大提高和明显改善,而且易于扩展,具有广泛的应用范围.     

Parallel computations and committee constructions

The paper reviewed the results bearing out the deep-seated relation between the parallel computations and learning procedures for the laminated neural networks one of whose formalizations is represented by the theory of committee constructions. Additionally, consideration was given to two combinatorial problems concerned with learning pattern recognition in the class of affine committees—the problem of verifying existence of a three-element affine separating committee and that of element-minimal affine separating committee. The first problem was shown to be N P-complete, whereas the second problem is N P-hard and does not belong to the Apx class.     

压缩视频超分辨率重构的一种新算法

针对传统重构算法不能很好地解决压缩视频的超分辨率图像重构的问题，文中提出了一种基于凸集投影（POCS）理论的压缩视频超分辨率重构算法。整个算法是在严格数学推理基础上形成的，具有较强的逻辑性和严密性。实验结果也表明，该算法不仅在峰值信噪比（PSNR）值和重构效果对压缩视频有较大提高和明显改善，而且易于扩展，具有广泛的应用范围。     

The uncertain OWA aggregation with weighting functions having a constant level of orness

Since the ordered weighted averaging (OWA) operator was introduced by Yager [IEEE Trans Syst Man Cybern 1988;18:183–190], numerous aggregation operators have been presented in academic journals. Apart from a setting where exact numerical assessments on weights and input arguments can be obtained, the issue of generalizing the OWA to take into account uncertainties in weights and/or input arguments has been considered. Recently, Xu and Da [Int J Intell Syst 2002;17:569–575] proposed an uncertain OWA operator in which input arguments are given in the form of interval numbers. The interval numbers within the interval sometimes do not have the same meaning for the decision maker as is implied by the use of interval ranges. Thus, we present a way of prioritizing interval numbers, taking into account the strength of preference based on the probabilistic measure. Further, rank‐based weighting functions having constant values of orness irrespective of the number of objectives aggregated are presented and a final rank ordering of courses of action is performed by the use of those weighing functions. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 469–483, 2006.     

Relaxation of reachable sets and extension constructions

Regularization of the reachability set is performed by relaxing the constraints on the system. We use compactification constructions in the solution space from the class of finitely additive measures and derive conditions of asymptotic robustness to various disturbances.Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 78–87, July–August, 1992.