28890
Extension of Lower Probabilities and Coherence of Belief Measures
Coherence is an important concept which is introduced and discussed in a new mathematics branch, Imprecise Probability Theory. By using the Choquet integral, belief measures can be extended to be coherent lower previsions on the linear space consisting of all bounded functions. As a special case, we establish that all belief measures are coherent imprecise probabilities.
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.
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.
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.
2505136
Indeterminate integrals with respect to nonadditive measures
Recently, nonadditive set functions have been used in information fusion and data mining to describe the interaction among the predictive attributes. In this case, replacing the traditional weighted average or, more generally, the linear mapping from a higher dimensional space to a one-dimensional space, relevant nonlinear integrals should be used as the aggregation tool to express how the objective attribute depends on predictive attributes. Several different types of nonlinear integral, such as the Choquet integral and the Wang integral, have been discussed in literature. In these models, the objective attribute is the integral, while the predictive attributes are the integrand. In this paper, a new concept of indeterminate integral is introduced when the universe of discourse is finite. It is a family of integrals including nonlinear integrals mentioned above and, therefore, possesses a large adaptability as a new aggregation tool. Each specified type of indeterminate integral can be obtained from the family of indeterminate integrals by specifying a decomposition of the integrand. Such a new aggregation tool can be used in information fusion and data mining as well as in expert systems.
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.
12482658
On circulant chromatic number and circulant chromatic function
Abstract A new concept of circulant chromatic function of a graph is introduced to generalize the concept of chromatic polynomial of a graph. This is similar to the generalization from the concept of chromatic number to the concept of circulant chromatic number. We provide circulant chromatic functions for a few classes of graphs. We consider circulant chromatic functions on the graphs obtained by elementary operations on given graphs, and the relationship between the circulant chromatic number of a graph and that of its complement. We also investigate some sufficient conditions for the circulant chromatic number and the chromatic number of a graph to be equal to each other.
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.
14221801
An opto-VLSI based tunable fiber ring laser
We demonstrate a novel Opto-VLSI tunable fiber ring laser structure in which an Opto-VLSI processor driven by steering phase holograms dynamically selects the lasing wavelengths. A proof-of-concept tunable fiber ring laser which has a wavelength tuning range of more than 4 nm around 1530 nm and a side-mode suppression ratio more than 25 dB is demonstrated at room temperature. The output power of the lasing wavelengths can be controlled within 0.5 dB uniformity by reconfiguring the phase hologram of the Opto-VLSI processor. Dual-wavelength laser tuning is also experimentally demonstrated.
14687819
On finite precision implementation of low density parity check codes decoder
In this paper, we analyze the finite precision effects on the decoding performance of Gallager's low density parity check (LDPC) codes and develop optimal finite word lengths of variables as far as the tradeoffs between the performance and hardware complexity are concerned. We have found that 4 bits and 6 bits are adequate for representing the received data and extrinsic information, respectively. Simulation results indicate that the quantization scheme we have developed for the LDPC decoder is effective in approximating the infinite precision implementation.
33403859
Area-power-time efficient pipeline-interleaved architectures for wave digital filters
Various forms of pipelining are explored for low power implementation of lattice wave digital filters realized with 3-port adaptors. In these filters, the time performance of pipelining is constrained by recursion. Using the fastest, block pipelined architecture as a reference point, it is shown that additional levels of pipelining can be applied to reduce the power consumption, at the expense of slightly changing the maximum sample rate. In one case power is reduced by 65% with only a modest speed penalty. Area increases due to additional pipeline registers can be more than offset if the consequent interleaving capability is utilized.