Hesitant fuzzy entropy and cross‐entropy and their use in multiattribute decision‐making

We introduce the concepts of entropy and cross‐entropy for hesitant fuzzy information, and discuss their desirable properties. Several measure formulas are further developed, and the relationships among the proposed entropy, cross‐entropy, and similarity measures are analyzed, from which we can find that three measures are interchangeable under certain conditions. Then we develop two multiattribute decision‐making methods in which the attribute values are given in the form of hesitant fuzzy sets reflecting humans' hesitant thinking comprehensively. In one method, the weight vector is determined by the hesitant fuzzy entropy measure, and the optimal alternative is obtained by comparing the hesitant fuzzy cross‐entropies between the alternatives and the ideal solutions; in another method, the weight vector is derived from the maximizing deviation method and the optimal alternative is obtained by using the TOPSIS method. An actual example is provided to compare our methods with the existing ones. © 2012 Wiley Periodicals, Inc.     

Entropy and Cross‐entropy for Generalized Hesitant Fuzzy Information and Their Use in Multiple Attribute Decision Making

In this paper, we present the entropy, cross‐entropy, and similarity measure for generalized hesitant fuzzy information and discuss their desirable properties. Some measure formulas are developed, and the relationships among them are investigated. We show that the similarity measure and entropy for generalized hesitant fuzzy information can be transformed by each other based on their axiomatic definitions. Then we develop two approaches for solving multiple attribute decision making, in which the attribute values are given in the form of generalized hesitant fuzzy elements (GHFEs). In the first approach, the attribute weight vector is determined by the generalized hesitant fuzzy entropies, and the optimal alternative is obtained by comparing the generalized hesitant fuzzy cross‐entropies between alternatives and positive‐ideal or negative‐ideal solutions; in the second approach, the attribute weight vector is derived from the maximizing deviation method and optimal alternative is obtained by using the technique for order preference by similarly to ideal solution (TOPSIS) method. Finally, an example is provided to illustrate the practicality and effectiveness of the developed approaches.     

Exponential operation and aggregation operator for q‐rung orthopair fuzzy set and their decision‐making method with a new score function

q‐Rung orthopair fuzzy set (q‐ROFS) is a powerful tool that attracts the attention of many scholars in dealing with uncertainty and vagueness. The aim of paper is to present a new score function of q‐rung orthopair fuzzy number (q‐ROFN) for solving the failure problems when comparing two q‐ROFNs. Then a new exponential operational law about q‐ROFNs is defined, in which the bases are positive real numbers and the exponents are q‐ROFNs. Meanwhile, some properties of the operational law are investigated. Later, we apply them to derive the q‐rung orthopair fuzzy weighted exponential aggregation operator. Additionally, an approach for multicriteria decision‐making problems under the q‐rung orthopair fuzzy data is explored by applying proposed aggregation operator. Finally, an example is investigated to illustrate the feasibility and validity of the proposed approach. The salient features of the proposed method, compared to the existing q‐rung orthopair fuzzy decision‐making methods, are (1) it can obtain the optimal alternative without counterintuitive phenomena; (2) it has a great power in distinguishing the optimal alternative.     

Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets

Recently, a new model based on Pythagorean fuzzy set (PFS) has been presented to manage the uncertainty in real‐world decision‐making problems. PFS has much stronger ability than intuitionistic fuzzy set to model such uncertainty. In this paper, we define some novel operational laws of PFSs and discuss their desirable properties. For the multicriteria decision‐making problems with PFSs, we propose an extended technique for order preference by similarity to ideal solution method to deal effectively with them. In this approach, we first propose a score function based comparison method to identify the Pythagorean fuzzy positive ideal solution and the Pythagorean fuzzy negative ideal solution. Then, we define a distance measure to calculate the distances between each alternative and the Pythagorean fuzzy positive ideal solution as well as the Pythagorean fuzzy negative ideal solution, respectively. Afterward, a revised closeness is introduced to identify the optimal alternative. At length, a practical example is given to illustrate the developed method and to make a comparative analysis.     

Comparison between multiple-choice and analytic hierarchy process: measuring human perception

The objective of this study is to examine the effectiveness of the multiple‐choice method in measuring human perception. Specifically, the results of comparisons of the answers to two questions on the same issue are shown, each formatted in a different way: multiple‐choice (MC) and Analytic Hierarchy Process (AHP). AHP not only clearly identifies the most important alternative but also the preference for each alternative by each decision‐maker. Therefore, using AHP to analyze the decision‐making process results in a precise clarification of preference for alternatives. Based on public opinion research using AHP, two findings are shown: (1) MC and AHP yield different aggregated rankings of alternatives, and (2) AHP reveals that in modified MC format, which gives respondents the option of indicating their second‐best alternatives, the choice of a second‐best alternative is independent of the difference in the degree of importance between the best and the second best.     

Convolutional Sparse Coding for High Dynamic Range Imaging

Current HDR acquisition techniques are based on either (i) fusing multibracketed, low dynamic range (LDR) images, (ii) modifying existing hardware and capturing different exposures simultaneously with multiple sensors, or (iii) reconstructing a single image with spatially‐varying pixel exposures. In this paper, we propose a novel algorithm to recover high‐quality HDRI images from a single, coded exposure. The proposed reconstruction method builds on recently‐introduced ideas of convolutional sparse coding (CSC); this paper demonstrates how to make CSC practical for HDR imaging. We demonstrate that the proposed algorithm achieves higher‐quality reconstructions than alternative methods, we evaluate optical coding schemes, analyze algorithmic parameters, and build a prototype coded HDR camera that demonstrates the utility of convolutional sparse HDRI coding with a custom hardware platform.     

Composite Flow Maps

Flow maps are widely used to provide an overview of geospatial transportation data. Existing solutions lack the support for the interactive exploration of multiple flow components at once. Flow components are given by different materials being transported, different flow directions, or by the need for comparing alternative scenarios. In this paper, we combine flows as individual ribbons in one composite flow map. The presented approach can handle an arbitrary number of sources and sinks. To avoid visual clutter, we simplify our flow maps based on a force‐driven algorithm, accounting for restrictions with respect to application semantics. The goal is to preserve important characteristics of the geospatial context. This feature also enables us to highlight relevant spatial information on top of the flow map such as traffic conditions or accessibility. The flow map is computed on the basis of flows between zones. We describe a method for auto‐deriving zones from geospatial data according to application requirements. We demonstrate the method in real‐world applications, including transportation logistics, evacuation procedures, and water simulation. Our results are evaluated with experts from corresponding fields.     

Implementation and optimization of GPU‐based parallel one‐step leapfrog ADI‐FDTD for far‐field scattering problems

The one‐step leapfrog alternative‐direction‐implicit finite‐difference time‐domain (ADI‐FDTD), free from the Courant‐Friedrichs‐Lewy (CFL) stability condition and sub‐step computations, is efficient when dealing with fine grid problems. However, solution of the numerous tridiagonal systems still imposes a great computational burden and makes the method hard to execute in parallel. In this paper, we proposed an efficient graphic processing unit (GPU)‐based parallel implementation of the one‐step leapfrog ADI‐FDTD for the far‐field EM scattering simulation of objects, in which we present and analyze the manners of calculation area division and thread allocation and a data layout transformation of z components is proposed to achieve better memory access mode, which is a key factor affecting GPU execution efficiency. The simulation experiment is carried out to verify the accuracy and efficiency of the GPU‐based implementation. The simulation results show that there is a good agreement between the proposed one‐step leapfrog ADI‐FDTD method and Yee's FDTD in solving the far‐field scattering problem and huge benefits in performance were encountered when the method was accelerated using GPU technology.     

Self‐similarity Analysis for Motion Capture Cleaning

Motion capture sequences may contain erroneous data, especially when the motion is complex or performers are interacting closely and occlusions are frequent. Common practice is to have specialists visually detect the abnormalities and fix them manually. In this paper, we present a method to automatically analyze and fix motion capture sequences by using self‐similarity analysis. The premise of this work is that human motion data has a high‐degree of self‐similarity. Therefore, given enough motion data, erroneous motions are distinct when compared to other motions. We utilize motion‐words that consist of short sequences of transformations of groups of joints around a given motion frame. We search for the K‐nearest neighbors (KNN) set of each word using dynamic time warping and use it to detect and fix erroneous motions automatically. We demonstrate the effectiveness of our method in various examples, and evaluate by comparing to alternative methods and to manual cleaning.     

On‐Site Example‐Based Material Appearance Acquisition

We present a novel example‐based material appearance modeling method suitable for rapid digital content creation. Our method only requires a single HDR photograph of a homogeneous isotropic dielectric exemplar object under known natural illumination. While conventional methods for appearance modeling require prior knowledge on the object shape, our method does not, nor does it recover the shape explicitly, greatly simplifying on‐site appearance acquisition to a lightweight photography process suited for non‐expert users. As our central contribution, we propose a shape‐agnostic BRDF estimation procedure based on binary RGB profile matching. We also model the appearance of materials exhibiting a regular or stationary texture‐like appearance, by synthesizing appropriate mesostructure from the same input HDR photograph and a mesostructure exemplar with (roughly) similar features. We believe our lightweight method for on‐site shape‐agnostic appearance acquisition presents a suitable alternative for a variety of applications that require plausible “rapid‐appearance‐modeling”.     

Rough sets in hybrid methods for pattern recognition

The article shows how rough sets can be applied to improve the classification ability of a hybrid pattern recognition system. The system presented here consists of a feature extractor based on a computer‐generated hologram (CGH) playing the role of a ring‐wedge detector. Features extracted by it are shift, rotation, and scale invariant. Although they can be optimized, no method has been proposed in the literature. This article presents an original method of optimizing the feature extraction abilities of a CGH. The method uses rough set theory (RST) to measure the amount of essential information contained in the feature vector. This measure is used to define an objective function in the optimization process. Since RST‐based factors are not differentiable, we use a nongradient approach for a search in the space of possible solutions. Finally, RST is used to determine decision rules for the classification of feature vectors. The alternative method of classification based on neural networks is also discussed. The whole method is illustrated by a system recognizing the class of speckle pattern images indicating the class of distortion of optical fibers. © 2001 John Wiley & Sons, Inc.     

A polynomial approach for optimal control of switched nonlinear systems

Optimal control problems for switched nonlinear systems are investigated. We propose an alternative approach for solving the optimal control problem for a nonlinear switched system based on the theory of moments. The essence of this method is the transformation of a nonlinear, nonconvex optimal control problem, that is, the switched system, into an equivalent optimal control problem with linear and convex structure, which allows us to obtain an equivalent convex formulation more appropriate to be solved by high‐performance numerical computing. Consequently, we propose to convexify the control variables by means of the method of moments obtaining semidefinite programs. Copyright © 2013 John Wiley & Sons, Ltd.     

Some Hesitant Fuzzy Information Aggregation Operators Based on Einstein Operational Laws

The performance and development review (PADR) evaluation in a company is a complex group decision‐making problem that is influenced by multiple and conflicting objectives. The complexity of the PADR evaluation problem is often due to the difficulties in determining the degrees of an alternative that satisfies the criteria. In this paper, we present a hesitant fuzzy multiple criteria group decision‐making methods for PADR evaluation. We first develop some operations based on Einstein operations. Then, we proposed some aggregation operators to aggregate hesitant fuzzy elements and the relationship between our proposed operators and the existing ones are discussed in detail. Furthermore, the procedure of multicriteria group decision making based on the proposed operators is given under hesitant fuzzy environment. Finally, a practical example about PADR evaluation in a company is provided to illustrate the developed method.     

Perceptually‐motivated Stereoscopic Film Grain

Independent management of film grain in each view of a stereoscopic video can lead to visual discomfort. The existing alternative is to project the grain onto the scene geometry. Such grain, however, looks unnatural, changes object perception, and emphasizes inaccuracies in depth arising during 2D‐to‐3D conversion. We propose an advanced method of grain positioning that scatters the grain in the scene space. In a series of perceptual experiments, we estimate the optimal parameter values for the proposed method, analyze the user preference distribution among the proposed and the two existing methods, and show influence of the method on the object perception.     

Effect of experimental methodology on the JND of the black level for natural images

Abstract— The effect of experimental methodology on the Just Noticeable Difference (JND) of the black level (BL) is assessed using a set of representative natural images. Two methodologies, known in psychophysics to determine JNDs, are mutually compared: an adapted method of adjustment with a same‐difference task and a one‐up‐two‐down staircase method with a two‐alternative forced‐choice task. Thus far, the literature has shown contradictory results for which of the two methods yields the lower difference thresholds. Experimental results show that the second method yields lower JNDs, but is slightly less efficient. Based on this second method, it was found that the JND of the BL for natural images ranges from 0.2 to 1.0 cd/m², varying with image content significantly.     

The effect of uncontrolled concurrency on model checking

Correctness of concurrent software is usually checked by techniques such as peer code reviews or code walkthroughs and testing. These techniques, however, are subject to human error, and thus do not achieve an in‐depth verification of correctness. Model‐checking techniques, which can systematically identify and verify every state that a system can enter, are a powerful alternative method for verifying concurrent systems. However, the usefulness of model checking is limited because the number of states for concurrent models grows exponentially with the number of processes in the system. This is often referred to as the ‘state explosion problem.’ Some processes are a central part of the software operation and must be included in the model. However, we have found that some exponential complexity results due to uncontrolled concurrency introduced by the programmer rather than due to the intrinsic characteristics of the software being modeled. We have performed tests on multimedia synchronization to show the effect of abstraction as well as uncontrolled concurrency using the Promela/SPIN model checker. We begin with a sequential model not expected to have exponential complexity but that results in exponential complexity. In this paper, we provide alternative designs and explain how uncontrolled concurrency can be removed from the code. Copyright © 2007 John Wiley & Sons, Ltd.