An Improved Method Based on TODIM and TOPSIS for Multi-Attribute Decision-Making with Multi-Valued Neutrosophic Sets

Due to the complexity of decision-making problems and the subjectivity of decision-makers in practical application,it is necessary to adopt different forms of information expression according to the actual situation of specific decision-making problems and choose the best method to solve them.Multi-valued neutrosophic set,as an extension of neutrosophic set,can more effectively and accurately describe incomplete,uncertain or inconsistent information.TODIM and TOPSIS methods are two commonly used multi-attribute decision-making methods,each of which has its advantages and disadvantages.This paper proposes a new method based on TODIM and TOPSIS to solve multi-attribute decision-making problems under multi-valued neutrosophic environment.After introducing the related theory of multi-valued neutrosophic set and the traditional TODIM and TOPSIS methods,the new method based on a combination of TODIM and TOPSIS methods is described.And then,two illustrative examples proved the feasibility and validity of the proposed method.Finally,the result has been compared with some existing methods under the same examples and the proposed method’s superiority has been proved.This paper studies this kind of decision-making problem from algorithm idea,algorithm steps and decision-making influencing factors.

Multi-valued responses and dynamic stability of a nonlinear vibro-impact system with a unilateral non-zero offset barrier

In this paper, multi-valued responses and dynamic properties of a nonlinear vibro-impact system with a unilateral nonzero offset barrier are studied. Based on the Krylov-Bogoliubov averaging method and Zhuravlev non-smooth trans- formation, the frequency response, stability conditions, and the equation of backbone curve are derived. Results show that in some conditions impact system may have two or four steady-state solutions, which are interesting and not mentioned for a vibro-impact system with the existence of frequency island phenomena. Then, the classification of the steady-state solutions is discussed, and it is shown that the nontrivial steady-state solutions may lose stability by saddle node bifurcation and Hopf bifurcation. Furthermore, a criterion for avoiding the jump phenomenon is derived and verified. Lastly, it is found that the distance between the system＇s static equilibrium position and the barrier can lead to jump phenomenon under hardening type of nonlinearity stiffness.

Fixed Point of a Countable Family of Uniformly Totally Quasi- <i>&Oslash</i>-Asymptotically Nonexpansive Multi-Valued Mappings in Reflexive Banach Spaces with Applications

The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- ? -asymptotically nonexpansive multi-valued mappings and establish some strong convergence theorems under certain conditions. We utilize the theorems to study a modified Halpern-type iterative algorithm for a system of equilibrium problems. The results improve and extend the corresponding results of Chang et al. (Applied Mathematics and Computation, 218, 6489-6497).

Multi-Valued Neuron with Sigmoid Activation Function for Pattern Classification

Multi-Valued Neuron (MVN) was proposed for pattern classification. It operates with complex-valued inputs, outputs, and weights, and its learning algorithm is based on error-correcting rule. The activation function of MVN is not differentiable. Therefore, we can not apply backpropagation when constructing multilayer structures. In this paper, we propose a new neuron model, MVN-sig, to simulate the mechanism of MVN with differentiable activation function. We expect MVN-sig to achieve higher performance than MVN. We run several classification benchmark datasets to compare the performance of MVN-sig with that of MVN. The experimental results show a good potential to develop a multilayer networks based on MVN-sig.

Importance Analysis of a Multi-state System Based on Direct Partial Logic Derivatives and Multi-valued Decision Diagrams

Importance analysis quantifies the critical degree of individual component. Compared with the traditional binary state system,importance analysis of the multi-state system is more aligned with the practice. Because the multi-valued decision diagram( MDD) can reflect the relationship between the components and the system state bilaterally, it was introduced into the reliability calculation of the multi-state system( MSS). The building method,simplified criteria,and path search and probability algorithm of MSS structure function MDD were given,and the reliability of the system was calculated. The computing methods of importance based on MDD and direct partial logic derivatives( DPLD) were presented. The diesel engine fuel supply system was taken as an example to illustrate the proposed method. The results show that not only the probability of the system in each state can be easily obtained,but also the influence degree of each component and its state on the system reliability can be obtained,which is conducive to the condition monitoring and structure optimization of the system.

MULTI-VALUED TOTALLY QUASI-φ-ASYMPTOTICALLY NONEXPANSIVE SEMI-GROUPS AND STRONG CONVERGENCE THEOREMS IN BANACH SPACES

The purpose of this article is first to introduce the concept of multi-valued to- tally Quasi-φ-asymptotically nonexpansive semi-groups, which contains many kinds of semi- groups as its special cases, and then to modify the Halpern-Mann-type iteration algorithm for multi-valued totally Quasi-cS-asymptotically nonexpansive semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in this article improve and extend the corresponding results announced by many authors recently.

The Uniform Convergence Topology On Multi-valued Mapping Space

Some convergences of topology are discussed. The definitions of almost uniform convergence topology and compatible topology are given. It is shown that the quasiuniform convergence and generalized uniform convergence have no compatible topology,but the almost uniform convergence has compatible topology. Moreover, the description of all uniform convergence limits and their mutual relation are investigated[1].

COMMON FIXED POINT THEOREMS FOR MULTI-VALUED MAPS

We establish some results on coincidence and common fixed points for a twopair of multi-valued and single-valued maps in complete metric spaces. Presented theorems generalize recent results of Gordji et al [4] and several results existing in the literature.

Common Fixed Point Theorems of Multi-Valued Maps in Ultra Metric Space

We establish some results on coincidence and common fixed point for a two pair of multi-valued and single-valued maps in ultra metric spaces.

A Fixed Point Theorem for Multi-valued Composite Increasing Operators

In this paper,we give a fixed point theorem for multi-valued composite increasing operators, which generalizes the theorem of the paper [1] under not only multi-valued mappings but also single-valued mappings. And we generalizes the corresponding results of [2]-[5].

A NOVEL MULTI-VALUED BAM MODEL WITH IMPROVED ERROR-CORRECTING CAPABILITY

A Hyperbolic Tangent multi-valued Bi-directional Associative Memory (HTBAM) model is proposed in this letter. Two general energy functions are defined to prove the stability of one class of multi-valued Bi-directional Associative Mernorys(BAMs), with HTBAM being the special case. Simulation results show that HTBAM has a competitive storage capacity and much more error-correcting capability than other multi-valued BAMs.

A Fixed Point Theorem for Multi-valued Composite Increasing Operators in Partially Ordered Spaces

In this paper,we give a fixed point theorem for multi-valued composite increasing operators,in partially ordered spaces,which generalizes the results of [1]-[3] and [5]- [8].

Cotangent Similarity Measure of Consistent Neutrosophic Sets and Application to Multiple Attribute Decision-Making Problems in Neutrosophic Multi-Valued Setting

A neutrosophic multi-valued set(NMVS)is a crucial representation for true,false,and indeterminate multivalued information.Then,a consistent single-valued neutrosophic set(CSVNS)can effectively reflect the mean and consistency degree of true,false,and indeterminate multi-valued sequences and solve the operational issues between different multi-valued sequence lengths in NMVS.However,there has been no research on consistent single-valued neutrosophic similarity measures in the existing literature.This paper proposes cotangent similarity measures and weighted cotangent similarity measures between CSVNSs based on cotangent function in the neutrosophic multi-valued setting.The cosine similarity measures showthe cosine of the angle between two vectors projected into amultidimensional space,rather than their distance.The cotangent similaritymeasures in this study can alleviate several shortcomings of cosine similarity measures in vector space to a certain extent.Then,a decisionmaking approach is presented in viewof the established cotangent similarity measures in the case of NMVSs.Finally,the developed decision-making approach is applied to selection problems of potential cars.The proposed approach has obtained two different results,which have the same sort sequence as the compared literature.The decision results prove its validity and effectiveness.Meantime,it also provides a new manner for neutrosophic multi-valued decision-making issues.

ALGORITHMS FOR A SYSTEM OF GENERALIZED MIXED EQUILIBRIUM PROBLEMS AND A COUNTABLE FAMILY OF SOME NONLINEAR MULTI-VALUED NONEXPANSIVE-TYPE MAPS

In this paper, relaxed iterative algorithms of Krasnoselskii-type and Halpern-type that approximate a solution of a system of a generalized mixed equilibrium problem anda common fixed point of a countable family of totally quasi-C-asymptotically nonexpansivemulti-valued maps are constructed. Strong convergence of the sequence generated by thesealgorithms is proved in uniformly smooth and strictly convex real Banach spaces with Kadec-Klee property. Furthermore, several applications of our theorems are also presented. Finally,our theorems are significant improvements on several important recent results for this classof nonlinear problems.

Reliability Analysis of Satellite Turntable System under Multiple Operation Modes Based on Multi-Valued Decision Diagrams

As a payload support system deployed on satellites,the turntable system is often switched among different working modes during the on-orbit operation,which can experience great state changes.In each mode,the missions to be completed are different,consecutive and non-over-lapping,from which the turntable system can be considered to be a phased-mission system(PMS).Reliability analysis for PMS has been widely studied.However,the system mode cycle characteristic has not been taken into account before.In this paper,reliability analysis method of the satellite turntable system is proposed considering its multiple operation modes and mode cycle characteristic.Firstly,the multi-valued decision diagrams(MDD)manipulation rules between two adjacent mission cycles are proposed.On this basis,MDD models for the turntable system in different states are established and the reliability is calculated using the continuous time Markov chains(CTMC)method.Finally,the comparative study is carried out to show the effectiveness of our proposed method.

On the (<i>r</i>,<i>φ</i>,<i>ψ</i>)-Suzuki Contraction for the Multi-Valued Mappings

In this work we try to give a new contraction type in multi-valued mapping on complete metric spaces. We prove the existence of fixed point for (r,φ,ψ)-Suzuki contraction in such spaces. Around our paper, the function ψ is absolutely continuous, and in this case, the contraction proposed by as has a fixed point.

Assessment of the Southern Ocean Sea Surface Temperature Biases in CMIP5 and CMIP6 Models

This work evaluates the performances of climate models in simulating the Southern Ocean(SO)sea surface temperature(SST)by a large ensemble from phases 5 and 6 of the Coupled Model Intercomparison Project(CMIP5 and CMIP6).By combining models from the same community sharing highly similar SO SST biases and eliminating the effect of global-mean biases on local SST biases,the results reveal that the ensemble-mean SO SST bias at 70°-30°S decreases from 0.38℃ in CMIP5 to 0.28℃ in CMIP6,together with increased intermodel consistency.The dominant mode of the intermodel variations in the zonal-mean SST biases is characterized as a meridional uniform warm bias pattern,explaining 79.1% of the intermodel variance and exhibiting positive principal values for most models.The ocean mixed layer heat budget further demonstrates that the SST biases at 70°-50°S primarily result from the excessive summertime heating effect from surface net heat flux.The biases in surface net heat flux south of 50°S are largely impacted by surface shortwave radiation from cloud and clear sky components at different latitudes.North of 50°S,the underestimated westerlies reduce the northward Ekman transport and hence northward cold advection in models,leading to warm SST biases year-round.In addition,the westerly biases are primarily traced back to the atmosphere-alone model simulations forced by the observed SST and sea ice.These results disclose the thermal origin at the high latitude and dynamical origin at the low latitude of the SO SST biases and underscore the significance of the deficiencies of atmospheric models in producing the SO SST biases.

Vibration and noise mechanism of a 110 kV transformer under DC bias based on finite element method

Global energy and environmental issues are becoming increasingly problematic,and the vibration and noise problem of 110 kV transformers,which are the most widely distributed,have attracted widespread attention from both inside and outside the industry.DC bias is one of the main contributing factors to vibration noise during the normal operation of transformers.To clarify the vibration and noise mechanism of a 110 kV transformer under a DC bias,a multi-field coupling model of a 110 kV transformer was established using the finite element method.The electromagnetic,vibration,and noise characteristics during the DC bias process were compared and quantified through field circuit coupling in parallel with the power frequency of AC,harmonic,and DC power sources.It was found that a DC bias can cause significant distortions in the magnetic flux density,force,and displacement distributions of the core and winding.The contributions of the DC bias effect to the core and winding are different at Kdc=0.85.At this point,the core approached saturation,and the increase in the core force and displacement slowed.However,the saturation of the core increased the leakage flux,and the stress and displacement of the winding increased faster.The sound field distribution characteristics of the 110 kV transformer under a DC bias are related to the force characteristics.When the DC bias coefficient was 1.25,the noise sound pressure level reached 73.6 dB.

Why ecosystem characteristics predicted from remotely sensed data are unbiased and biased at the same time-and how this affects applications

Remotely sensed data are frequently used for predicting and mapping ecosystem characteristics,and spatially explicit wall-to-wall information is sometimes proposed as the best possible source of information for decisionmaking.However,wall-to-wall information typically relies on model-based prediction,and several features of model-based prediction should be understood before extensively relying on this type of information.One such feature is that model-based predictors can be considered both unbiased and biased at the same time,which has important implications in several areas of application.In this discussion paper,we first describe the conventional model-unbiasedness paradigm that underpins most prediction techniques using remotely sensed(or other)auxiliary data.From this point of view,model-based predictors are typically unbiased.Secondly,we show that for specific domains,identified based on their true values,the same model-based predictors can be considered biased,and sometimes severely so.We suggest distinguishing between conventional model-bias,defined in the statistical literature as the difference between the expected value of a predictor and the expected value of the quantity being predicted,and design-bias of model-based estimators,defined as the difference between the expected value of a model-based estimator and the true value of the quantity being predicted.We show that model-based estimators(or predictors)are typically design-biased,and that there is a trend in the design-bias from overestimating small true values to underestimating large true values.Further,we give examples of applications where this is important to acknowledge and to potentially make adjustments to correct for the design-bias trend.We argue that relying entirely on conventional model-unbiasedness may lead to mistakes in several areas of application that use predictions from remotely sensed data.