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.

Review of low timing jitter mode-locked fiber lasers and applications in dual-comb absolute distance measurement

Passively mode-locked fiber lasers emit femtosecond pulse trains with excellent short-term stability. The quantum-limited timing jitter of a free running femtosecond erbium-doped fiber laser working at room temperature is considerably below one femtosecond at high Fourier frequency. The ultrashort pulse train with ultralow timing jitter enables absolute time-of-flight measurements based on a dual-comb implementation, which is typically composed of a pair of optical frequency combs generated by femtosecond lasers. Dead-zone-free absolute distance measurement with sub-micrometer precision and kHz update rate has been routinely achieved with a dual-comb configuration, which is promising for a number of precision manufacturing applications, from large step-structure measurements prevalent in microelectronic profilometry to three coordinate measurements in large-scale aerospace manufacturing and shipbuilding. In this paper, we first review the sub-femtosecond precision timing jitter characterization methods and approaches for ultralow timing jitter mode-locked fiber laser design. Then, we provide an overview of the state-of-the-art dual-comb absolute ranging technology in terms of working principles, experimental implementations, and measurement precisions. Finally, we discuss the impact of quantum-limited timing jitter on the dual-comb ranging precision at a high update rate. The route to highprecision dual-comb range finder design based on ultralow jitter femtosecond fiber lasers is proposed.

Distance Measurement Model Based on RSSI in WSN

The relationship between RSSI (Received Signal Strength Indication) values and distance is the foundation and the key of ranging and positioning technologies in wireless sensor networks. Log-normal shadowing model (LNSM), as a more general signal propagation model, can better describe the relationship between the RSSI value and distance, but the parameter of variance in LNSM is depended on experiences without self-adaptability. In this paper, it is found that the variance of RSSI value changes along with distance regu- larly by analyzing a large number of experimental data. Based on the result of analysis, we proposed the relationship function of the variance of RSSI and distance, and established the log-normal shadowing model with dynamic variance (LNSM-DV). At the same time, the method of least squares(LS) was selected to es- timate the coefficients in that model, thus LNSM-DV might be adjusted dynamically according to the change of environment and be self-adaptable. The experimental results show that LNSM-DV can further reduce er- ror, and have strong self-adaptability to various environments compared with the LNSM.

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.

Optimization of measurement distance of (109)~Cd K XRF system for obese subjects

The precision of results obtained from the ^109Cd K XRF in vivo measurement system of bone lead for obses subjects with high BMI( body mass index)was poor.The main factor affecting the precision was the distance between tibia and detector.Compared with the standard phantom,a large phantom was used to simulate the obese subject in the measurements at different distances to the detector.The counts of Compton scattering increased highly because of the tissue overlying and surrounding tibia of the obese subject.When the distance between leg and detector was too small,the instrument would produce the distorted X-ray spectra,so that the obtained data were inaccurate,In order to ensure good measuremtn precision and accuracy,the distance between leg and detector should be maintained at 25mm during the counting period.Meanwhile,the dead time displayed instantly on the instrument should be controlled to around 30%.

On the Probable Cause of the Discrepancies between Hipparcos and VLBI Pleiades Distance Measurements

It will show, a recent extension of special relativity on the grounds of a novel concept of velocity, which also predicts the speed of transversal motions on the plane of the sky to increase with enduring observation time, to fully explain the differences of the observational results of the former experiments referring to the distance of the Pleiades from Earth.

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.

On Similarity Measures and Distance Measures of Fuzzy Soft Sets

In this paper we introduce several new similarity measures and distance measures between fuzzy soft sets, these measures are examined based on the set-theoretic approach and the matching function. Comparative studies of these measures are derived. By introducing two general formulas, we propose a new method to define the similarity measures and the distance measures between two fuzzy soft sets with different parameter sets.

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.

Multi-Attribute Couplings-Based Euclidean and Nominal Distances for Unlabeled Nominal Data

Learning unlabeled data is a significant challenge that needs to han-dle complicated relationships between nominal values and attributes.Increas-ingly,recent research on learning value relations within and between attributes has shown significant improvement in clustering and outlier detection,etc.However,typical existing work relies on learning pairwise value relations but weakens or overlooks the direct couplings between multiple attributes.This paper thus proposes two novel and flexible multi-attribute couplings-based distance(MCD)metrics,which learn the multi-attribute couplings and their strengths in nominal data based on information theories:self-information,entropy,and mutual information,for measuring both numerical and nominal distances.MCD enables the application of numerical and nominal clustering methods on nominal data and quantifies the influence of involving and filtering multi-attribute couplings on distance learning and clustering perfor-mance.Substantial experiments evidence the above conclusions on 15 data sets against seven state-of-the-art distance measures with various feature selection methods for both numerical and nominal clustering.

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 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.

Fuzzy Regression Model Based on Fuzzy Distance Measure

Some existed fuzzy regression methods have some special requirements for the object of study, such as assuming the observed values as symmetric triangular fuzzy numbers or imposing a non-negative constraint of regression parameters. In this paper, we propose a left-right fuzzy regression method, which is applicable to various forms of observed values. We present a fuzzy distance and partial order between two left-right (LR) fuzzy numbers and we let the mean fuzzy distance between the observed and estimated values as the mean fuzzy error, then make the mean fuzzy error minimum to get the regression parameter. We adopt two criteria involving mean fuzzy error (comparative mean fuzzy error based on partial order) and SSE to compare the performance of our proposed method with other methods. Finally four different types of numerical examples are given to illustrate that our proposed method has feasibility and wide applicability.

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.

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.

Criterions and Measures of Route Selection of Shallowly Embedded Long-Distance Oil and Gas Pipeline in Mountain Areas

According to the engineering investigation of long-distance oil and gas pipelines, the criterions and measures of route selection are drawn as follows： the flat landform is the first choice in route alignment. The foot of mountain is the first choice when the route passes by the valley. The route should pass by but the shady and deposited slope and not in sunny and erosive slope as possible as it can. The pipeline should be vertical to contour climbing and descending the mountain except steep slope. Tunnel can be used in crossing foothill. Perpendicularly traversing the river is better than beveling; the worst choice is to put the pipeline along the river. Bypass is the best choice in karsts area. The order of route selection should be pre-choosing, investigation, optimization and adjustment.

Measuring Musical Rhythm Similarity: Further Experiments with the Many-to-Many Minimum-Weight Matching Distance

Musical rhythms are represented as sequences of symbols. The sequences may be composed of binary symbols denoting either silent or monophonic sounded pulses, or ternary symbols denoting silent pulses and two types of sounded pulses made up of low-pitched (dum) and high-pitched (tak) sounds. Experiments are described that compare the effectiveness of the many-to-many minimum-weight matching between two sequences to serve as a measure of similarity that correlates well with human judgements of rhythm similarity. This measure is also compared to the often used edit distance and to the one-to-one minimum-weight matching. New results are reported from experiments performed with three widely different datasets of real- world and artificially generated musical rhythms (including Afro-Cuban rhythms), and compared with results previously reported with a dataset of Middle Eastern dum-tak rhythms.