Multiple attribute decision making method based on trapezoid fuzzy linguistic variables

The problem of multiple attribute decision making under fuzzy linguistic environments, in which decision makers can only provide their preferences （attribute values）in the form of trapezoid fuzzy linguistic variables（TFLV）, is studied. The formula of the degree of possibility between two TFLVs is defined, and some of its characteristics are studied. Based on the degree of possibility of fuzzy linguistic variables, an approach to ranking the decision alternatives in multiple attribute decision making with TFLV is developed. The trapezoid fuzzy linguistic weighted averaging （TFLWA） operator method is utilized to aggregate the decision information, and then all the alternatives are ranked by comparing the degree of possibility of TFLV. The method can carry out linguistic computation processes easily without loss of linguistic information, and thus makes the decision results reasonable and effective. Finally, the implementation process of the proposed method is illustrated and analyzed by a practical example.

Reliability analysis for aeroengine turbine disc fatigue life with multiple random variables based on distributed collaborative response surface method

The fatigue life of aeroengine turbine disc presents great dispersion due to the randomness of the basic variables,such as applied load,working temperature,geometrical dimensions and material properties.In order to ameliorate reliability analysis efficiency without loss of reliability,the distributed collaborative response surface method(DCRSM) was proposed,and its basic theories were established in this work.Considering the failure dependency among the failure modes,the distributed response surface was constructed to establish the relationship between the failure mode and the relevant random variables.Then,the failure modes were considered as the random variables of system response to obtain the distributed collaborative response surface model based on structure failure criterion.Finally,the given turbine disc structure was employed to illustrate the feasibility and validity of the presented method.Through the comparison of DCRSM,Monte Carlo method(MCM) and the traditional response surface method(RSM),the results show that the computational precision for DCRSM is more consistent with MCM than RSM,while DCRSM needs far less computing time than MCM and RSM under the same simulation conditions.Thus,DCRSM is demonstrated to be a feasible and valid approach for improving the computational efficiency of reliability analysis for aeroengine turbine disc fatigue life with multiple random variables,and has great potential value for the complicated mechanical structure with multi-component and multi-failure mode.

THE ACTIVATION METHOD FOR DISCRETIZED CONSERVATIVE NONLINEAR STABILITY PROBLEMS WITH MULTIPLE PARAMETER AND STATE VARIABLES

For nonlinear stability problems of discretized conservative systems with multiple parameter variables and multiple state variables, the activation method is put forward, by which activated potential functions and activated equilibrium equations are derived. The activation method is the improvement and enhancement of Liapunov-Schmidt method in elastic stability theory. It is more generalized and more normalized than conventional perturbation methods. The activated potential functions may be transformed into normalized catastrophe potential functions. The activated equilibrium equations may be treated as bifurcation equations. The researches in this paper will motivate the combination of elastic stability theory with catastrophe theory and bifurcation theory

Breakdown voltage model and structure realization of a thin silicon layer with linear variable doping on a silicon on insulator high voltage device with multiple step field plates

Based on the theoretical and experimental investigation of a thin silicon layer（TSL） with linear variable doping（LVD） and further research on the TSL LVD with a multiple step field plate（MSFP）,a breakdown voltage（BV） model is proposed and experimentally verified in this paper.With the two-dimensional Poisson equation of the silicon on insulator（SOI） device,the lateral electric field in drift region of the thin silicon layer is assumed to be constant.For the SOI device with LVD in the thin silicon layer,the dependence of the BV on impurity concentration under the drain is investigated by an enhanced dielectric layer field（ENDIF）,from which the reduced surface field（RESURF） condition is deduced.The drain in the centre of the device has a good self-isolation effect,but the problem of the high voltage interconnection（HVI） line will become serious.The two step field plates including the source field plate and gate field plate can be adopted to shield the HVI adverse effect on the device.Based on this model,the TSL LVD SOI n-channel lateral double-diffused MOSFET（nLDMOS） with MSFP is realized.The experimental breakdown voltage（BV） and specific on-resistance（R on,sp） of the TSL LVD SOI device are 694 V and 21.3 ·mm 2 with a drift region length of 60 μm,buried oxide layer of 3 μm,and silicon layer of 0.15 μm,respectively.

Combined model based on optimized multi-variable grey model and multiple linear regression

The construction method of background value is improved in the original multi-variable grey model （MGM（1,m）） from its source of construction errors. The MGM（1,m） with optimized background value is used to eliminate the random fluctuations or errors of the observational data of all variables, and the combined prediction model together with the multiple linear regression is established in order to improve the simulation and prediction accuracy of the combined model. Finally, a combined model of the MGM（1,2） with optimized background value and the binary linear regression is constructed by an example. The results show that the model has good effects for simulation and prediction.

Variable precision rough set for multiple decision attribute analysis

A variable precision rough set (VPRS) model is used to solve the multi-attribute decision analysis (MADA) problem with multiple conflicting decision attributes and multiple condition attributes. By introducing confidence measures and a β-reduct, the VPRS model can rationally solve the conflicting decision analysis problem with multiple decision attributes and multiple condition attributes. For illustration, a medical diagnosis example is utilized to show the feasibility of the VPRS model in solving the MADA problem with multiple decision attributes and multiple condition attributes. Empirical results show that the decision rule with the highest confidence measures will be used as the final decision rules in the MADA problem with multiple conflicting decision attributes and multiple condition attributes if there are some conflicts among decision rules resulting from multiple decision attributes. The confidence-measure-based VPRS model can effectively solve the conflicts of decision rules from multiple decision attributes and thus a class of MADA problem with multiple conflicting decision attributes and multiple condition attributes are solved.

THE METHOD OF MULTIPLE SCALES APPLIED TO THE NONLINEAR STABILITY PROBLEM OF A TRUNCATED SHALLOW SPHERICAL SHELL OF VARIABLE THICKNESS WITH THE LARGE GEOMETRICAL PARAMETER

Using the modified method of multiple scales, the nonlinear stability of a truncated shallow spherical shell of variable thickness with a nondeformable rigid body at the center under compound loads is investigated. When the geometrical parameter k is larger, the uniformly valid asymptotic solutions of this problem are obtained and the remainder terms are estimated.

Establishment and Comparison of Pulsed-field Gel Electrophoresis,Multiple-locus Variable Number Tandem Repeat Analysis and Automated Ribotyping Methods for Subtyping of Citrobacter Strains

Objective To establish and compare the pulsed-field gel electrophoresis （PFGE）, multiple-locus variable number tandem repeat analysis （MLVA） and automated ribotyping for subtyping of Citrobacter strains. Methods PFGE protocol was optimized in terms of plug preparation procedure, restriction enzymes and configuration of electrophoretic parameters. MLVA method was evaluated by finding variable number tandem repeats in two genomes of Citrobacter strains. The ribotyping was performed by using the automated RiboPrinter system. Results We optimized the plug preparation procedure, focused on the cell suspension concentration （turbidity of 2.5 to 3.5）, SDS addition （no SDS needed） and lysis time （1 h）, and selected the appropriate restriction enzyme （Xbal） and the electrophoretic parameters （1.0 s-20.0 s for 19 h） of PFGE. There was nearly no discriminatory power of MLVA between Citrobacter strains. For 51 Citrobacter strains, automated ribotyping gave a D-value of 0.9945, while PFGE gave a D-value of 0.9969. Both PFGE and automated ribotyping clustered strains from the same sources （with the same species from the same place at the same time identified as the same source） and divided strains from different sources （from different years, places and hosts） into different subtypes. Conclusion PFGE protocol established in this paper and automated ribotyping are suitable for application in Citrobacter subtyping.

An Efficient Multiple-Dimensional Finite Element Solution for Water Flow in Variably Saturated Soils

Multiple-dimensional water flow in variably saturated soils plays an important role in ecological systems such as irrigation and water uptake by plant roots; its quantitative description is usually based on the Richards＇ equation. Because of the nonlinearity of the Richards＇ equation and the complexity of natural soils, most practical simulations rely on numerical solutions with the nonlinearity solved by iterations. The commonly used iterations for solving the nonlinearity are Picard and Newton methods with the former converging at first-order rate and the later at second-order rate. A recent theoretical analysis by the authors, however, revealed that for solving the diffusive flow, the classical Picard method is actually a chord-Newton method, converging at a rate faster than first order; its linear convergence rate is due to the treatment of the gravity term. To improve computational efficiency, a similar chord-Newton method as for solving the diffusive term was proposed to solve the gravity term. Testing examples for one-dimensional flow showed significant improvement. The core of this method is to produce a diagonally dominant matrix in the linear system so as to improve the iteration-toiteration stability and hence the convergence. In this paper, we develop a similar method for multiple-dimensional flow and compare its performance with the classical Picard and Newton methods for water flow in soils characterised by a wide range of van Genuchten parameters.

Multiple attribute decision making based on different types of linguistic information

Distance measures between exact linguistic variables and between uncertain linguistic variables are introduced respectively. Based on exact linguistic variables and uncertain linguistic variables, the concepts of positive linguistic ideal solution and negative linguistic ideal solution of attribute values are defined. To rank and select alternatives, based on the distance measures of two types of linguistic variables and the linguistic ideal solutions, a method for multiple attribute decision making with different types of linguistic information is proposed, by which all alternatives can be ranked. The method can carry out linguistic computation processes easily without loss of linguistic information, and thus makes the decision result reasonable and effective. Finally, the implementation process of the proposed method is illustrated and analyzed by a numerical example.

Multiple subtraction method based on a non-causal matching filter

The filter operator used in normal multichannel matching filter is physically realizable. This filter operator only delays seismic data in the filtering process. A non- causal multichannel matching filter based on a least squares criterion is proposed to resolve the problem in which predicted multiple model data is later than real data. The differences between causal and non-causal multichannel matching filters are compared using a synthetic shot gather, which demonstrates the validity of the non-causal matching filter. In addition, a variable length sliding window which changes with offset and layer velocity is proposed to solve the count of events increasing with increasing offset in a fixed length sliding window. This variable length sliding window is also introduced into the modified and expanded multichannel matching filter. This method is applied to the Pluto1.5 synthetic data set. The benefits of the non-causal filter operator and variable length sliding window are demonstrated by the good multiple attenuation result.

An Algorithm of the Adaptive Grid and Fuzzy Interacting Multiple Model

This paper studies the algorithm of the adaptive grid and fuzzy interacting multiple model （AGFIMM） for maneuvering target tracking, while focusing on the problems of the fixed structure multiple model （FSMM） algorithm＇s cost-efficiency ratio being not high and the Markov transition probability of the interacting multiple model （IMM） algorithm being difficult to determine exactly. This algorithm realizes the adaptive model set by adaptive grid adjustment, and obtains each model matching degree in the model set by fuzzy logic inference. The simulation results show that the AGFIMM algorithm can effectively improve the accuracy and cost-efficiency ratio of the multiple model algorithm, and as a result is suitable for enineering apolications.

Switching variability index based multiple strategy CFAR detector

A switching variability index （SVl） constant false alarm rate （CFAR） detector is proposed for improving the detection performance of VI-CFAR detectors in multiple targets backgrounds. When the presence of non-homogeneity in CFAR reference windows is indicated by a VI-CFAR detector, a switching- CFAR detector is introduced to optimize the performance of the VI-CFAR detector in homogeneous, multiple targets and clutter edge backgrounds. The structure and parameters selection method of the SVI-CFAR detector is presented. Comparisons with classic CFAR detectors and recently proposed detectors are also given. Theoretical analysis and simulation results show that SVICFAR detector maintains the good performance of the VI-CFAR detector in homogeneous and clutter edge backgrounds, while greatly improving the capacity of anti-multi targets.

New Refinement Relations of Z Specifications for Multiple Viewpoints Oriented Requirements Method

In this paper we develop several new refinement relations of Z for multiple viewpoints oriented requirements method (MVORM). The original motivation is that we found the standard Z refinement relation is not adequate or correct when considering specifications that have temporal relationships of operations. The concept of temporal state variables is introduced into Z. Then new implementation relations are defined and new refinement relations are deduced, mainly for temporal state variables to process temporal relationships of operations. We use state transition systems to abstract the temporal state transitions. A simple example is used to show the procedures of MVORM. Finally some directions of further work are forwarded.

Coupling of high order multiplication perturbation method and reduction method for variable coefcient singular perturbation problems

Based on the precise integration method （PIM）, a coupling technique of the high order multiplication perturbation method （HOMPM） and the reduction method is proposed to solve variable coefficient singularly perturbed two-point boundary value prob lems （TPBVPs） with one boundary layer. First, the inhomogeneous ordinary differential equations （ODEs） are transformed into the homogeneous ODEs by variable coefficient dimensional expansion. Then, the whole interval is divided evenly, and the transfer ma trix in each sub-interval is worked out through the HOMPM. Finally, a group of algebraic equations are given based on the relationship between the neighboring sub-intervals, which are solved by the reduction method. Numerical results show that the present method is highly efficient.

Mixture Regression Estimators Using Multi-Auxiliary Variables and Attributes in Two-Phase Sampling

In this paper, we have developed estimators of finite population mean using Mixture Regression estimators using multi-auxiliary variables and attributes in two-phase sampling and investigated its finite sample properties in full, partial and no information cases. An empirical study using natural data is given to compare the performance of the proposed estimators with the existing estimators that utilizes either auxiliary variables or attributes or both for finite population mean. The Mixture Regression estimators in full information case using multiple auxiliary variables and attributes are more efficient than mean per unit, Regression estimator using one auxiliary variable or attribute, Regression estimator using multiple auxiliary variable or attributes and Mixture Regression estimators in both partial and no information case in two-phase sampling. A Mixture Regression estimator in partial information case is more efficient than Mixture Regression estimators in no information case.

Mixture Ratio Estimators Using Multi-Auxiliary Variables and Attributes for Two-Phase Sampling

In this paper, we have proposed three classes of mixture ratio estimators for estimating population mean by using information on auxiliary variables and attributes simultaneously in two-phase sampling under full, partial and no information cases and analyzed the properties of the estimators. A simulated study was carried out to compare the performance of the proposed estimators with the existing estimators of finite population mean. It has been found that the mixture ratio estimator in full information case using multiple auxiliary variables and attributes is more efficient than mean per unit, ratio estimator using one auxiliary variable and one attribute, ratio estimator using multiple auxiliary variable and multiple auxiliary attributes and mixture ratio estimators in both partial and no information case in two-phase sampling. A mixture ratio estimator in partial information case is more efficient than mixture ratio estimators in no information case.

Mixture Regression-Cum-Ratio Estimator Using Multi-Auxiliary Variables and Attributes in Single-Phase Sampling

In this paper, we have proposed a class of mixture regression-cum-ratio estimator for estimating population mean by using information on multiple auxiliary variables and attributes simultaneously in single-phase sampling and analyzed the properties of the estimator. An empirical was carried out to compare the performance of the proposed estimator with the existing estimators of finite population mean using simulated population. It was found that the mixture regression-cum-ratio estimator was more efficient than ratio and regression estimators using one auxiliary variable and attribute, ratio and regression estimators using multiple auxiliary variables and attributes and regression-cum-ratio estimators using multiple auxiliary variables and attributes in single-phase sampling for finite population.

Modified Multiple Scale/Segment Entropy （MMPE） Analysis of Heart Rate Variability of NHH, CHF ＆ AF Subjects

Nonlinear analysis of heart rate variability （HRV） has become important as heart behaves as a complex system. In this work, the approximate entropy （ApEn） has been used as a nonlinear measure. A new concept of estimating the ApEn in different segments of long length of the recorded data called modified multiple scale （segment） entropy （MMPE） is introduced. The idea of estimating the approximate entropy in different segments is useful to detect the nonlinear dynamics of the heart present in the entire length of data. The present work has been carried out for three cases namely the normal healthy heart （NHH） data, congestive heart failure （CHF） data and Atrial fibrillation （AF） data and the data are analyzed using MMPE techniques. It is observed that the mean value of ApEn for NHH data is much higher than the mean values for CHF data and AF data. The ApEn profiles of CHF, AF and NHH data for different segments obtained using MPE profiles measures the heart dynamism for the three different cases. Also the power spectral density is obtained using fast fourier transform （FFT） analysis and the ratio of LF/HF （low frequency/high frequency） power are computed on multiple scales/segments namely MPLH （multiple scale low frequency to high frequency） for the NHH data, CHF data and AF data and analyzed using MPLH techniques. The results are presented and discussed in the paper.