12805492
PFB-Integrals and PFA-Integrals with Respect to Monotone Set Functions
A pair of new integrals, a PFB-integral and a PFA-integral, are introduced. Given a measurable space, these integrals are defined for nonnegative functions with respect to monotone set functions, and they are generalizations of both the Lebesgue integral and the fuzzy integral. Some primary properties of the PFB-integral and PFA-integral are discussed and an inequality between them is established in this paper.
1885677
Learning nonlinear multiregression networks based on evolutionary computation
This paper describes a novel knowledge discovery and data mining framework dealing with nonlinear interactions among domain attributes. Our network-based model provides an effective and efficient reasoning procedure to perform prediction and decision making. Unlike many existing paradigms based on linear models, the attribute relationship in our framework is represented by nonlinear nonnegative multiregressions based on the Choquet integral. This kind of multiregression is able to model a rich set of nonlinear interactions directly. Our framework involves two layers. The outer layer is a network structure consisting of network elements as its components, while the inner layer is concerned with a particular network element modeled by Choquet integrals. We develop a fast double optimization algorithm (FDOA) for learning the multiregression coefficients of a single network element. Using this local learning component and multiregression-residual-cost evolutionary programming (MRCEP), we propose a global learning algorithm, called MRCEP-FDOA, for discovering the network structures and their elements from databases. We have conducted a series of experiments to assess the effectiveness of our algorithm and investigate the performance under different parameter combinations, as well as sizes of the training data sets. The empirical results demonstrate that our framework can successfully discover the target network structure and the regression coefficients.
26197775
Using Neural Networks to Determine Sugeno Measures by Statistics
Abstract To replace the traditional weighted average method, Choquet integrals or Sugeno integrals with respect to fuzzy measures are used to obtain a synthetic evaluation of a given object (or its quality, function, etc. respectively) with multi-attribute. Generally, it is not easy to determine fuzzy measures in real problems due to the subjectivity of human thinking. It is even much more difficult than determining weights in the weighted average method, because of the nonadditivity of fuzzy measures. This paper uses a neural network algorithm to optimize the inverse problem of synthetic evaluation, and thus to determine Sugeno measures by the Choquet integral and statistics of given data. Since the Choquet integral is a generalization of the weighted average method, this technology has a broad applicability in areas of multivariate analysis, decision making, pattern recognition, image and speech processing and expert systems. Copyright © 1996 Elsevier Science Ltd.
8746593
Modal logic interpretation of Dempster-Shafer theory: An infinite case
Abstract A modal logic interpretation of belief and plausibility measures defined on infinite sets is established. As a special case, a modal logic interpretation of necessity and possibility measures defined on infinite sets is also established. It is proven in both cases that the interpretation is complete. These results establish, in effect, modal logic interpretations of the Dempster-Shafer theory and possibility theory.
2059324
Choquet integrals and natural extensions of lower probabilities
Abstract Both the Choquet integral with respect to monotone set functions and the natural extensions of lower probabilities are generalizations of the Lebesgue integral with respect to σ-additive measures. The relation between these generalizations is investigated. We show that the Choquet integral with respect to a belief measure is always greater than or equal to the corresponding natural extension. Also, we compare some concepts introduced in the theory of imprecise probabilities with concepts established in fuzzy measure theory, capacity theory, and Dempster-Shafer theory.
29035045
Genetic algorithms for determining fuzzy measures from data
A synthetic evaluation of a given object in terms of multiple factors that contribute to some feature of the object (quality, performance, etc.) may be regarded as a system with multiple inputs and one output. Traditionally, the output is expressed as the weighted average of the inputs. Unfortunately, this method is severely limited as it cannot capture any inherent relation among the factors involved. This limitation can be overcome by using the Choquet integral or the fuzzy integral with respect to a fuzzy measure that captures the relation among the factors. The crux of this method is to determine the right fuzzy measure. In this paper, we describe an efficient genetic algorithm for constructing a suitable fuzzy measure from relevant input-output data. This algorithm has a broad applicability in various problem areas, such as decision making, cluster analysis, pattern recognition, image and speech processing, and expert systems.
1087779
A note on the robust stability of uncertain stochastic fuzzy systems with time-delays
Takagi-Sugeno (T-S) fuzzy models are now often used to describe complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear submodels. In this note, the T-S fuzzy model approach is exploited to establish stability criteria for a class of nonlinear stochastic systems with time delay. Sufficient conditions are derived in the format of linear matrix inequalities (LMIs), such that for all admissible parameter uncertainties, the overall fuzzy system is stochastically exponentially stable in the mean square, independent of the time delay. Therefore, with the numerically attractive Matlab LMI toolbox, the robust stability of the uncertain stochastic fuzzy systems with time delays can be easily checked.
6164572
Video quality assessment using structural distortion measurement
Objective image/video quality measures play important roles in various image/video processing applications, such as compression, communication, printing, analysis, registration, restoration and enhancement. Most proposed quality assessment approaches in the literature are error sensitivity-based methods. We follow a new philosophy in designing image/video quality metrics, which uses structural distortion as an estimation of perceived visual distortion. We develop a new approach for video quality assessment. Experiments on the video quality experts group (VQEG) test data set shows that the new quality measure has higher correlation with subjective quality measurement than the proposed methods in VQEG's Phase I tests for full-reference video quality assessment.
11332367
Quality-of-Service Routing for Supporting Multimedia Applications
Several new architectures have been developed for supporting multimedia applications such as digital video and audio. However, quality-of-service (QoS) routing is an important element that is still missing from these architectures. In this paper, we consider a number of issues in QoS routing. We first examine the basic problem of QoS routing, namely, finding a path that satisfies multiple constraints, and its implications on routing metric selection, and then present three path computation algorithms for source routing and for hop-by-hop routing.
47404061
Diversity and Multiplexing Tradeoff in General Fading Channels
The optimal tradeoff between diversity gain and multiplexing gain for multiple-inputmultiple-output (MIMO) channels has been studied recently under the independent and identically distributed (i.i.d.) Rayleigh-fading assumption. In this correspondence, this result is extended and the optimal tradeoff performance is derived for generalized fading channel conditions, including different fading types, nonidentical fading distributions, spatial correlation, and nonzero channel means. Our results include many known models as special cases and shed light on the effects of different channel parameters on the optimal tradeoff performance
17971442
Exogenous connectors for software components
In existing component models, control originates in components, and connectors are channels for passing on the control to other components. This provides a mechanism for message passing, which allows components to invoke one another's operations by method calls (or remote procedure calls) either directly or indirectly via a channel such as a bus. Thus components in these models mix computation with control, since in performing their computation they also initiate method calls and manage their returns, via connectors. Consequently, in terms of control, components are not loosely coupled. In this paper, we propose exogenous connectors, and demonstrate their use in a small example. In contrast to connectors in existing component models, exogenous connectors initiate calls and manage their returns, and are used to encapsulate control in a component model we are working on. In the example, we demonstrate the feasibility of exogenous connectors, and compare them with connectors in closely related architecture description languages.