Multi-Criteria Decision Making Based on Bipolar Picture Fuzzy Operators and New Distance Measures

This paper aims to introduce the novel concept of the bipolar picture fuzzy set(BPFS)as a hybrid structure of bipolar fuzzy set(BFS)and picture fuzzy set(PFS).BPFS is a new kind of fuzzy sets to deal with bipolarity(both positive and negative aspects)to each membership degree(belonging-ness),neutral membership(not decided),and non-membership degree(refusal).In this article,some basic properties of bipolar picture fuzzy sets(BPFSs)and their fundamental operations are introduced.The score function,accuracy function and certainty function are suggested to discuss the comparability of bipolar picture fuzzy numbers(BPFNs).Additionally,the concept of new distance measures of BPFSs is presented to discuss geometrical properties of BPFSs.In the context of BPFSs,certain aggregation operators(AOs)named as“bipolar picture fuzzy weighted geometric(BPFWG)operator,bipolar picture fuzzy ordered weighted geometric(BPFOWG)operator and bipolar picture fuzzy hybrid geometric(BPFHG)operator”are defined for information aggregation of BPFNs.Based on the proposed AOs,a new multicriteria decision-making(MCDM)approach is proposed to address uncertain real-life situations.Finally,a practical application of proposed methodology is also illustrated to discuss its feasibility and applicability.

A novel algorithm for distance measurement using stereo camera

Distance estimation can be achieved by using active sensors or with the help of passive sensors such as cameras.The stereo vision system is generally composed of two cameras to mimic the human binocular vision.In this paper,a Python-based algorithm is pro-posed to find the parameters of each camera,rectify the images,create the disparity maps and finally use these maps for distance measurements.Experiments using real-time im-ages,which were captured from our stereo vision system,of different obstacles posi-tioned at multiple distances(60-200 cm)prove the effectiveness of the proposed program and show that the calculated distance to the obstacle is relatively accurate.The accuracy of distance measurement is up to 99.83%.The processing time needed to calculate the distance between the obstacle and the cameras is less than 0.355 s.

Information fusion of train speed and distance measurements based on fuzzy adaptive Kalman filter algorithm

The measurement accuracy of speed and distance in high speed train directly affects the control precision and driving efficiency of train control system. To improve the capability of train self control, a combined speed measurement and positioning method based on speed sensor and radar which is assisted by global positioning system（GPS） is proposed to improve the accuracy of measurement and reduce the dependence on the ground equipment. In consideration of the fact that the filtering precision of Kalman filter will decrease when the statistical characteristics are changing, this paper uses fuzzy comprehensive evaluation method to evaluate the sub filter, and information distribution coefficients are dynamically adjusted according to filtering reliability, which can improve the fusion accuracy and fault tolerance of the system. The sub filter is required to carry on the covariance shaping adaptive filtering when it is in the suboptimal state. The adjustment factor of error covariance is obtained according to the minimized cost function, which can improve the matching degree between the measured residual variance and the system recursive residual. The simulation results show that the improved filter algorithm can track the changes of the system effectively, enhance the filtering accuracy significantly, and improve the measurement accuracies of train speed and distance.

Feature Selection Based on Distance Measurement

Every day we receive a large amount of information through different social media and software,and this data and information can be realized with the advent of data mining methods.In the process of data mining,to solve some high-dimensional problems,feature selection is carried out in limited training samples,and effective features are selected.This paper focuses on two Relief feature selection algorithms:Relief and ReliefF algorithm.The differences between them and their respective applicable scopes are analyzed.Based on Relief algorithm,the high weight feature subset is obtained,and the correlation between features is calculated according to the mutual information distance measure,and the high redundant features are removed to obtain the feature subset with higher quality.Experimental results on six datasets show the effectiveness of our method.

Novel Distance Measures on Hesitant Fuzzy Sets Based on Equal-Probability Transformation and Their Application in Decision Making on Intersection Traffic Control

The purpose of this study is to reduce the uncertainty in the calculation process on hesitant fuzzy sets(HFSs).The innovation of this study is to unify the cardinal numbers of hesitant fuzzy elements(HFEs)in a special way.Firstly,a probability density function is assigned for any given HFE.Thereafter,equal-probability transformation is introduced to transform HFEs with different cardinal numbers on the condition into the same probability density function.The characteristic of this transformation is that the higher the consistency of the membership degrees in HFEs,the higher the credibility of the mentioned membership degrees is,then,the bigger the probability density values for them are.According to this transformation technique,a set of novel distance measures on HFSs is provided.Finally,an illustrative example of intersection traffic control is introduced to show the usefulness of the given distance measures.The example also shows that this study is a good complement to operation theories on HFSs.

Induced and heavy aggregation operators with distance measures

This paper introduces a new aggregation model by using induced and heavy aggregation operators in distances measures such as the Hamming distance.It is called the induced heavy ordered weighted averaging（OWA） distance（IHOWAD） operator.This paper studies some of its main properties and a wide range of particular cases such as the induced heavy OWA（IHOWA） operator,the induced OWA distance（IOWAD） operator and the heavy OWA distance（HOWAD） operator.This approach is generalized by using generalized and quasi-arithmetic means obtaining the induced generalized IHOWAD（IGHOWAD） operator and the Quasi-IHOWAD operator.An application of the new approach in a decision making problem regarding the selection of strategies is developed.

Target Detection Improvement in Distance Measurement System Using Two Rotatable Cameras for FPSO

This paper describes target detection improvement in a distance measurement system using two rotatable cameras for floating production, storage and offloading （FPSO） facilities. The authors have developed a distance measurement system that consists of two rotatable cameras on a ship and a target on a wharf for the automatic berthing of ships. This system measures a distance by detecting and tracking the target on the wharf using the two rotatable cameras on the ship. Our goal is to apply this distance measurement system to an automatic relative positioning system for a ship at an FPSO facility. In this application, the shape of the target in the images captured by the cameras is deformed by their relative positions and attitudes, which increases the measurement errors. To solve this problem, we propose a target detection method that improves the target deformations. The proposed target detection method is able to detect the deformed targets using a target database that is created by image conversion with the perspective projection of a reference target. By using the proposed target detection method, the distance measurement error is decreased. Experimental results on a miniature scale and in an indoor environment confirmed that the measurement error of the relative distance is decreased by using the proposed target detection method.

Rapid and precise distance measurement with hybrid comb lasers

Dual-comb ranging allows rapid and precise distance measurement and can be universally implemented on different comb platforms,e.g.,fiber combs and microcombs.To date,dual-fiber-comb ranging has become a mature and powerful tool for metrology and industry,but the measurement speed is often at a kilohertz level due to the lower repetition rates.Recently,dual-microcomb ranging has given rise to a new opportunity for distance measurement,in consequence of its small footprint and high repetition rates,but full-comb stabilization is challenging.Here,we report a dual-hybrid-comb distance meter capable of ultrarapid and submicrometer precision distance measurement,which can not only leverage the advantage of easy locking inherited from the fiber comb but also sustain ultrarapid measurement speed due to the microcomb.The experimental results show that the measurement precision can reach 3.572μm at 4.136μs and 432 nm at 827.2μs averaging time.Benefiting from the large difference between the repetition rates of the hybrid combs,the measurement speed can be enhanced by 196 folds,in contrast to the dual-fiber-comb system with about a 250 MHz repetition rate.Our work can offer a solution for the fields of rapid dimensional measurement and spectroscopy.

Some new distance measures for type-2 fuzzy sets and distance measure based ranking for group decision making problems

In this paper, we propose some distance measures between type-2 fuzzy sets, and also a new family of utmost distance measures are presented. Several properties of differ- ent proposed distance measures have been introduced. Also, we have introduced a new ranking method for the ordering of type-2 fuzzy sets based on the proposed distance measure. The proposed ranking method satisfies the reasonable prop- erties for the ordering of fuzzy quantities. Some properties such as robustness, order relation have been presented. Lim- itations of existing ranking methods have been studied. Fur- ther for practical use, a new method for selecting the best alternative, for group decision making problems is proposed. This method is illustrated with a numerical example.

An information-volume-based distance measure for decision-making

D-S evidence theory,as a general framework for reasoning with uncertainty,allows combining pieces of evidence from different information sources to derive a degree of belief function that is a type of fuzzy measure.However,the mass assignments given by unknown information sources are disordered.How to measure the difference between the mass assignments has aroused people’s interest.In this paper,inspired by the information volume,a novel distance-based measure is proposed to measure the difference between mass assignments.The method can refine the uncertain information given by experts and compare the refined information to obtain the difference between mass assignments.At the same time,it is verified that the measure not only meets the properties of distance,but also proves the superiority of the proposed Information Volume Distance(IVD)through simulation experiments.Meanwhile,in the process of information fusion,the reliability of each source could be quantified through IVD.Therefore,based on IVD,a new multi-source information algorithm is proposed to solve the problem of multi-source information fusion.Moreover,algorithm is applied to decision-making problem and compare with other methods to verify the effectiveness.

Comments on ＂Some new distance measures for type-2 fuzzy sets and distance measure based ranking for group decision making problems＂

In this article, we have pointed out that some propositions corresponding to the distance measure between the type-2 fuzzy sets （T2FSs） as provided by Singh （Frontiers of Computer Science, 2014, 8（5）, 741-752）, are incorrect by a counterexample. Further, these propositions have been corrected in the present manuscript by giving a correct relation between the T2FSs and validating it with a numerical example.

Optical Frequency Comb Frequency-division Multiplexing Dispersive Interference Multichannel Distance Measurement

An optical frequency comb(OFC)frequency-division multiplexing dispersive interference multichannel distance measurement method is proposed.Based on the OFC dispersive interference,the wide OFC spectrum is divided into multiple channels using a wavelength-division multiplexer.Under the existing light source and spectrometer,a single interference system can realize six channels of the high-precision parallel absolute distance measurement.The influence of the spectrum width and shape on the performance of the distance measurement channel is analyzed.The ranging accuracy of six channels is higher than±4μm under the optimization of a nonuniform discrete Fourier transform and Hanning window.

A Log-Index Weighted Cepstral Distance Measure for Speech Recognition

A log-index weighted cepstral distance measure is proposed and tested in speaker-independent and speaker-dependent isolated word recognition systems using statistic techniques. The weights for the cepstral coefficients of this measure equal the logarithm of the corresponding indices. The experimental results show that this kind of measure works better than any other weighted Euclidean cepstral distance measures on three speech databases. The error rate obtained using this measure is about 1.8 percent for three databases on average, which is a 25% reduction from that obtained using other measures, and a 40% reduction from that obtained using Log Likelihood Ratio (LLR) measure. The experimental results also show that this kind of distance measure works well in both speaker-dependent and speaker-independent speech recognition systems.

ORDERED WEIGHTED DISTANCE MEASURE

The aim of this paper is to develop an ordered weighted distance （OWD） measure, which is the generalization of some widely used distance measures, including the normalized Hamming distance, the normalized Euclidean distance, the normalized geometric distance, the max distance, the median distance and the rain distance, etc. Moreover, the ordered weighted averaging operator, the generalized ordered weighted aggregation operator, the ordered weighted geometric operator, the averaging operator, the geometric mean operator, the ordered weighted square root operator, the square root operator, the max operator, the median operator and the rain operator are also the special cases of the OWD measure. Some methods depending on the input arguments are given to determine the weights associated with the OWD measure. The prominent characteristic of the OWD measure is that it can relieve （or intensify） the influence of unduly large or unduly small deviations on the aggregation results by assigning them low （or high） weights. This desirable characteristic makes the OWD measure very suitable to be used in many actual fields, including group decision making, medical diagnosis, data mining, and pattern recognition, etc. Finally, based on the OWD measure, we develop a group decision making approach, and illustrate it with a numerical example.

Data processing of small samples based on grey distance information approach

Data processing of small samples is an important and valuable research problem in the electronic equipment test. Because it is difficult and complex to determine the probability distribution of small samples, it is difficult to use the traditional probability theory to process the samples and assess the degree of uncertainty. Using the grey relational theory and the norm theory, the grey distance information approach, which is based on the grey distance information quantity of a sample and the average grey distance information quantity of the samples, is proposed in this article. The definitions of the grey distance information quantity of a sample and the average grey distance information quantity of the samples, with their characteristics and algorithms, are introduced. The correlative problems, including the algorithm of estimated value, the standard deviation, and the acceptance and rejection criteria of the samples and estimated results, are also proposed. Moreover, the information whitening ratio is introduced to select the weight algorithm and to compare the different samples. Several examples are given to demonstrate the application of the proposed approach. The examples show that the proposed approach, which has no demand for the probability distribution of small samples, is feasible and effective.

A Quantum Tanimoto Coefficient Fidelity for Entanglement Measurement

Fidelity plays an important role in quantum information processing,which provides a basic scale for comparing two quantum states.At present,one of the most commonly used fidelities is Uhlmann-Jozsa(U-J)fidelity.However,U-J fidelity needs to calculate the square root of the matrix,which is not trivial in the case of large or infinite density matrices.Moreover,U-J fidelity is a measure of overlap,which has limitations in some cases and cannot reflect the similarity between quantum states well.Therefore,a novel quantum fidelity measure called quantum Tanimoto coefficient(QTC)fidelity is proposed in this paper.Unlike other existing fidelities,QTC fidelity not only considers the overlap between quantum states,but also takes into account the separation between quantum states for the first time,which leads to a better performance of measure.Specifically,we discuss the properties of the proposed QTC fidelity.QTC fidelity is compared with some existing fidelities through specific examples,which reflects the effectiveness and advantages of QTC fidelity.In addition,based on the QTC fidelity,three discrimination coefficients d_(1)^(QTC),d_(2)^(QTC),and d_^(3)^(QTC)are defined to measure the difference between quantum states.It is proved that the discrimination coefficient d_(3)^(QTC)is a true metric.Finally,we apply the proposed QTC fidelity-based discrimination coefficients to measure the entanglement of quantum states to show their practicability.

Learning Dual-Domain Calibration and Distance-Driven Correlation Filter:A Probabilistic Perspective for UAV Tracking

Unmanned Aerial Vehicle(UAV)tracking has been possible because of the growth of intelligent information technology in smart cities,making it simple to gather data at any time by dynamically monitoring events,people,the environment,and other aspects in the city.The traditional filter creates a model to address the boundary effect and time filter degradation issues in UAV tracking operations.But these methods ignore the loss of data integrity terms since they are overly dependent on numerous explicit previous regularization terms.In light of the aforementioned issues,this work suggests a dual-domain Jensen-Shannon divergence correlation filter(DJSCF)model address the probability-based distance measuring issue in the event of filter degradation.The two-domain weighting matrix and JS divergence constraint are combined to lessen the impact of sample imbalance and distortion.Two new tracking models that are based on the perspectives of the actual probability filter distribution and observation probability filter distribution are proposed to translate the statistical distance in the online tracking model into response fitting.The model is roughly transformed into a linear equality constraint issue in the iterative solution,which is then solved by the alternate direction multiplier method(ADMM).The usefulness and superiority of the suggested strategy have been shown by a vast number of experimental findings.

A Novel Incremental Attribute Reduction Algorithm Based on Intuitionistic Fuzzy Partition Distance

Attribute reduction,also known as feature selection,for decision information systems is one of the most pivotal issues in machine learning and data mining.Approaches based on the rough set theory and some extensions were proved to be efficient for dealing with the problemof attribute reduction.Unfortunately,the intuitionistic fuzzy sets based methods have not received much interest,while these methods are well-known as a very powerful approach to noisy decision tables,i.e.,data tables with the low initial classification accuracy.Therefore,this paper provides a novel incremental attribute reductionmethod to dealmore effectivelywith noisy decision tables,especially for highdimensional ones.In particular,we define a new reduct and then design an original attribute reduction method based on the distance measure between two intuitionistic fuzzy partitions.It should be noted that the intuitionistic fuzzypartitiondistance iswell-knownas aneffectivemeasure todetermine important attributes.More interestingly,an incremental formula is also developed to quickly compute the intuitionistic fuzzy partition distance in case when the decision table increases in the number of objects.This formula is then applied to construct an incremental attribute reduction algorithm for handling such dynamic tables.Besides,some experiments are conducted on real datasets to show that our method is far superior to the fuzzy rough set based methods in terms of the size of reduct and the classification accuracy.

Evaluation of an interferometric distance meter

This paper discussed the main parameters contributing to the measurement uncertainty of interferometric distance meter （IDM）. A simple and robust set-up is used to measure distance of about 12 cm with an expanded uncertainty （ k = 2） of ±16.4 μm. The measurement uncertainty is found to be limited by the wavelength measurement accuracy. This set-up can be used to measure distances up to 56 m. It also enables easy determination of the point of equal path difference between the measuring and the reference arms. LabVIEW program is used for counting of the fringes and applying fast Fourier transfor- mation （FFT） to perform frequency selective filtration to the noise. Although the reported uncertainty does not represent the state-of-art uncertainty reached for similar distance, the measurement provides traceable measurement to the unit of length, the meter.

Simultaneous measurement of distance and speed using frequency-modulated continuous-wave self-mixing interferometry and all-phase fast Fourier transform

In this work,we propose a method using frequency-modulated continuous-wave(FMCW)self-mixing interferometry(SMI)and all-phase fast Fourier transform(APFFT)for simultaneous measurement of speed and distance.APFFT offers superior accuracy in frequency determination by mitigating issues like the fence effect and spectrum leakage,contributing to the high-accuracy measurement for speed and distance.Both simulations and experiments have demonstrated relative errors at the levels of 10^(−4) and 10^(−3) for distance and speed measurements,respectively.Furthermore,factors impacting measurement performance have been discussed.The proposed method provides a high-performance and cost-effective solution for distance and speed measurements,applicable across scientific research and various industrial domains.