A complete ranking of trapezoidal fuzzy numbers and its applications to multi-criteria decision making

The problem (or scenario) involving qualitative or imprecise information is not solvable by classical set theory. To overcome the shortcoming of classical set theory, Zadeh (Inf Control 8(3):338–356, 26) introduced the concept of fuzzy sets that generalizes the concept of classical sets. Fuzzy set theory allows modelling and handling of imprecise information in an effective way. As a special class of fuzzy sets, fuzzy numbers (FN) which are very much important in decision making was introduced by Dubois and Prade (Int J Syst Sci 9:631–626, 12). The available methods for solving multi-criteria decision making problems (MCDM) are problem dependent in nature due to the partial ordering on the class of FN. Total ordering on the class of FN by countable number of real-valued parameters was achieved by Wang and Wang (Fuzzy Sets Syst 243:131–141, 21). A complete ranking on the class of trapezoidal fuzzy numbers (TrFNs) using finite number of score functions is achieved in this paper. In this paper, a new ranking procedure (complete) on the class of TrFNs using the concepts of mid-point, radius, left and right fuzziness of TrFN is proposed and further we introduce a method for solving fuzzy multi-criteria decision making (Fuzzy MCDM) problem. Finally, comparisons of our proposed method with familiar existing methods are listed.

     

矩阵方程AX-EXF=BY的通解及其应用

给出矩阵方程AX—EXY=BY的一个完全解析的、具有显式表达式和完全自由度的参数解(X,Y)．这里假设矩阵束(E,A B)为R-能控的,F为任意的方阵．相比于现有结论,求解算法不要求矩阵A和F具有特殊的形式,且对它们的特征值没有任何的限制,此外,本文给出的通解还具有结构简洁的特点,作为一个应用,给出了广义系统正常Luenberger函数观测器的一种参数化的设计方法,算例证明了方法的有效性．     

A new analytical solution for the load-deflection of squaremembranes

Accurate models are essential for the determination of the elastic properties of thin films from load-deflection experiments. Although finite element method (FEM) models have the potential to be very accurate, analytical models are desirable because of their simplicity. In this paper we present a new analytical solution for the load-deflection of membranes. Our solution yields the same relationship between the load and the deflection as the known analytical solution. However, the values of two constants are up to 35% higher and correspond well with the results from FEM analysis. In addition, the new solution yields analytical forms of the bending lines, which agree well with experimental measurements carried out with silicon nitride membranes     

A complete characterization of statistical query learning with applications to evolvability

Statistical query (SQ) learning model of Kearns is a natural restriction of the PAC learning model in which a learning algorithm is allowed to obtain estimates of statistical properties of the examples but cannot see the examples themselves (Kearns, 1998 [29]). We describe a new and simple characterization of the query complexity of learning in the SQ learning model. Unlike the previously known bounds on SQ learning (Blum, et al., 1994; Bshouty and Feldman, 2002; Yang, 2005; Balcázar, et al., 2007; Simon, 2007 [9], [11], [42], [3], [37]) our characterization preserves the accuracy and the efficiency of learning. The preservation of accuracy implies that our characterization gives the first characterization of SQ learning in the agnostic learning framework of Haussler (1992) [23] and Kearns, Schapire and Sellie (1994) [31]. The preservation of efficiency is achieved using a new boosting technique and allows us to derive a new approach to the design of evolution algorithms in Valiant?s model of evolvability (Valiant, 2009 [40]). We use this approach to demonstrate the existence of a large class of monotone evolution algorithms based on square loss performance estimation. These results differ significantly from the few known evolution algorithms and give evidence that evolvability in Valiant?s model is a more versatile phenomenon than there had been previous reason to suspect.     

TiO2 nanoparticles-enhanced luminol chemiluminescence and its analytical applications in organophosphate pesticide imprinting

This paper reports a surface molecular self-assembly strategy for chlorpyrifos (CPF) imprinting of polymer membranes at the surface of TiO₂ nanoparticles for flow injection chemiluminescence (CL) detection of pesticide CPF which using the character of TiO₂ enhance the chemiluminescence of the luminol–H₂O₂ system. The CL signals produced by the reaction between luminol and H₂O₂, were increased in the presence of CPF imprinting of polymer membranes at the surface of TiO₂ which were eluted from the column through luminol and H₂O₂ injection. The CL enhancement by TiO₂ nanoparticles of the luminol–H₂O₂ system was supposed to originate from the catalysis of TiO₂ nanoparticles and CPF. The CL intensity was linear over the logarithm of concentration of chlorpyrifos ranging from 1.0 × 10⁻¹⁰ to 5.0 × 10⁻⁷ mol/L (r² = 0.996), and the limit of detection was 1.0 × 10⁻¹¹ mol/L (3σ). The detection limit for CPF is lower than other methods. An excellent CL selectivity for CPF over other pesticides was also achieved. The combination of surface molecular self-assembly with polymer molecular imprinting on larger surface area of TiO₂ nanoparticles produce a high ratio of imprinted sites and, thus, provide an ultrasensitive CL detection of CPF.     

A closed-form solution to tensor voting: theory and applications

We prove a closed-form solution to tensor voting (CFTV): Given a point set in any dimensions, our closed-form solution provides an exact, continuous, and efficient algorithm for computing a structure-aware tensor that simultaneously achieves salient structure detection and outlier attenuation. Using CFTV, we prove the convergence of tensor voting on a Markov random field (MRF), thus termed as MRFTV, where the structure-aware tensor at each input site reaches a stationary state upon convergence in structure propagation. We then embed structure-aware tensor into expectation maximization (EM) for optimizing a single linear structure to achieve efficient and robust parameter estimation. Specifically, our EMTV algorithm optimizes both the tensor and fitting parameters and does not require random sampling consensus typically used in existing robust statistical techniques. We performed quantitative evaluation on its accuracy and robustness, showing that EMTV performs better than the original TV and other state-of-the-art techniques in fundamental matrix estimation for multiview stereo matching. The extensions of CFTV and EMTV for extracting multiple and nonlinear structures are underway.     

An analytical solution to fuzzy TOPSIS and its application in personnel selection for knowledge-intensive enterprise

Personnel selection is a critical enterprise strategic problem in knowledge-intensive enterprise. Fuzzy number which can be described as triangular (trapezoid) fuzzy number is an adequate way to assess the evaluation and weights for the alternatives. In that case, fuzzy TOPSIS, as a classic fuzzy multiple criteria decision making (MCDM) methods, has been applied in personnel selection problems. Currently, all the researches on this topic either apply crisp relative closeness but causing information loss, or employ fuzzy relative closeness estimate but with complicated computation to rank the alternatives. In this paper, based on Karnik–Mendel (KM) algorithm, we propose an analytical solution to fuzzy TOPSIS method. Some properties are discussed, and the computation procedure for the proposed analytical solution is given as well. Compared with the existing TOPSIS method for personnel selection problem, it obtains accurate fuzzy relative closeness instead of the crisp point or approximate fuzzy relative closeness estimate. It can both avoid information loss and keep computational efficiency in some extent. Moreover, the global picture of fuzzy relative closeness provides a way to further discuss the inner properties of fuzzy TOPSIS method. Detailed comparisons with approximate fuzzy relative closeness method are provided in personnel selection application.     

矩阵方程AX-EXF=BY的通解及其应用

给出矩阵方程 AX-EXY=BY的一个完全解析的、具有显式表达式和完全自由度的参数解 (X,Y) .这里假设矩阵束 (E,A,B) 为R-能控的, F为任意的方阵.相比于现有结论,求解算法不要求矩阵A和F具有特殊的形式,且对它们的特征值没有任何的限制.此外,本文给出的通解还具有结构简洁的特点.作为一个应用,给出了广义系统正常Luenberger函数观测器的一种参数化的设计方法.算例证明了方法的有效性.     

A new analytical solution to mobile robot trajectory generation in the presence of moving obstacles

The problem of determining a collision-free path for a mobile robot moving in a dynamically changing environment is addressed in this paper. By explicitly considering a kinematic model of the robot, the family of feasible trajectories and their corresponding steering controls are derived in a closed form and are expressed in terms of one adjustable parameter for the purpose of collision avoidance. Then, a new collision-avoidance condition is developed for the dynamically changing environment, which consists of a time criterion and a geometrical criterion, and it has explicit physical meanings in both the transformed space and the original working space. By imposing the avoidance condition, one can determine one (or a class of) collision-free path(s) in a closed form. Such a path meets all boundary conditions, is twice differentiable, and can be updated in real time once a change in the environment is detected. The solvability condition of the problem is explicitly found, and simulations show that the proposed method is effective.     

A PC data-base with analytical applications for evoked potentials

Visual Evoked Potentials (VEPs) are gaining ground in the research for diagnosis of neurological disorders and visual defects, as a non-invasive diagnostic tool. Yet, the methods used towards these goals are not universal and far from able to provide a common ground among researchers in collecting, analyzing and comparing their results. This paper is an attempt to close the gap. We have developed a PC data-base and a set of analysis programs with graphic capabilities, frequency analysis, as well as an objective way of describing the signals obtained during VEP experiments.     

A simple dual control problem with an analytical solution

A stochastic control problem for which the optimal dual control law can be calculated analytically is given. The system is a four state Markov chain with transition probabilities that depend on the control variable. The performance of the optimal dual control law and of some suboptimal control laws are calculated and compared.     

On the analytical derivation of the Pareto-optimal set with applications to structural design

The Fritz John conditions for Pareto-optimality have been set in matrix form and used for introducing a procedure for the analytical derivation of the Pareto-optimal set in the design variables domain. Subsequently, the derivation of the Pareto-optimal set in the objective functions domain can be obtained, if possible, by a proper analytical derivation. Both the objective and constraint functions are assumed to be available in analytical form and twice differentiable and convex (or pseudo-convex). The proposed procedure to find the Pareto-optimal set is relatively simple. The computation of the determinant of a matrix is required. A symbolic manipulator can be exploited. If there are two design variables and two objective functions, the Pareto-optimal set can be easily computed by applying a simple formula derived in the paper. If the number of design variables equals the number of objective functions, the Pareto-optimal set in the design variables domain can be found by computing the product of the constraint functions times the determinant of the Jacobian of the objective functions. A number of case studies have been proposed to test the effectiveness of the proposed procedure. The optimal structural design of, respectively, a pair of compressed spheres, a cantilever with rectangular cross section have been faced and solved. Additionally the test problem proposed by Fonseca and Fleming has been addressed and solved analytically. Optimization problems with low dimensionality (2 or 3 design variables and 2 objective functions, 2 or more constraints) have been easily solved. The proposed procedure can be useful in the actual engineering practice at the earliest design stage. In this case the designer can be made aware on the proper design variables setting to obtain the desired tradeoff among conflicting objective functions.     

Correlated inhibitory and excitatory inputs to the coincidence detector: analytical solution

We present a solution for the steady-state output rate of an ideal coincidence detector receiving an arbitrary number of excitatory and inhibitory input spike trains. All excitatory spike trains have identical binomial count distributions (which includes Poisson statistics as a special case) and arbitrary pairwise cross correlations between them. The same applies to the inhibitory inputs, and the rates and correlation functions of excitatory and inhibitory populations may be the same or different from each other. Thus, for each population independently, the correlation may range from complete independence to perfect correlation (identical processes). We find that inhibition, if made sufficiently strong, will result in an inverted U-shaped curve for the output rate of a coincidence detector as a function of input rates for the case of identical inhibitory and excitory input rates. This leads to the prediction that higher presynaptic (input) rates may lead to lower postsynaptic (output) rates where the output rate may fall faster than the inverse of the input rate, and shows some qualitative similarities to the case of purely excitatory inputs with synaptic depression. In general, we find that including inhibition invariably and significantly increases the behavioral repertoire of the coincidence detector over the case of pure excitatory input.     

Voltammetric studies of the interaction of rutin with DNA and its analytical applications on the MWNTs-COOH/Fe3O4 modified electrode

Multi-walled carbon nanotubes functionalized with a carboxylic acid group (MWNTs-COOH)/iron oxide (Fe₃O₄) modified glassy carbon electrode (MWNTs-COOH/Fe₃O₄/GCE) and DNA/MWNTs-COOH/Fe₃O₄/GCE were prepared. The electrochemical behaviors of rutin (RU) were investigated on MWNTs-COOH/Fe₃O₄/GCE by cyclic voltammetry (CV) and differential pulse voltammetry (DPV) in britton-robinson buffer solution (B-R). The interaction of RU with DNA was also explored. Dramatic decrease of peak current without obvious peak potential shift were observed in both cases of DNA in the solution and immobilized on the electrode surface. In addition, the electron transfer coefficient (α) and the rate constant (k_s) kept unchanged in the absence and presence of DNA. So interaction of DNA with RU formed a non-electroactive complex. The binding constant and binding ratio was obtained in the process. The interaction was also confirmed by UV-visible spectroscopy. The reduction peak current was linear with the concentration of RU in the range of 2.50 × 10⁻⁸ to 1.37 × 10⁻⁶ M, with a detection limit of 7.5 nM. The MWNTs-COOH/Fe₃O₄/GCE showed comparatively low detection limit, rapid response, simplicity for the determination of RU.     

A simple solution to the l optimization problem

It is pointed out in this brief paper that the l¹ optimization problem min_{Q ε lqp¹} | H − U * Q * V |₁, H ε l_mn¹, U ε l_mq¹, V ε l_pn¹ can be solved in one step rather than two. The solution of the dual problem is obviated by the direct solution of the primal problem via linear programming. The method here is applicable to finite-dimensional problems or approximating finite-dimensional problems, in the general case.     

A schmidt type process for the solution of Ax=b

An orthogonalization type algorithm is presented for the triangularization of the coefficient matrix of a system of linear algebraic equations. A backward error analysis is performed on the algorithm. Some numerical examples are presented. The algorithm is extended in order to perform the complete forward reduction.