We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for m...We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for more accurate calculation of the mean exit time by computing large deviation prefactors with the aid of machine learning.More specifically,we design a neural network framework to compute quasipotential,most probable paths and prefactors based on the orthogonal decomposition of a vector field.We corroborate the higher effectiveness and accuracy of our algorithm with two toy models.Numerical experiments demonstrate its powerful functionality in exploring the internal mechanism of rare events triggered by weak random fluctuations.展开更多
M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large devi...M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large deviation principles and moderate deviation upper bounds for stationary m-negatively associated random variables are proved. Kolmogorov-type and Marcinkiewicz-type strong laws of large numbers as well as the three series theorem for m-negatively associated random variables are also given.展开更多
Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove mod...Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove moderate deviations and large deviations for the statistic sup ｜fn（x） - fn（-x） ｜.展开更多
We study moderate deviations for estimators of the drift parameter of the fractional Ornstein-Uhlenbeck process. Two moderate deviation principles are obtained.
The authors consider the moderate deviations of hydrodynamic limit for Ginzburg-Landau models. The moderate deviation principle of hydrodynamic limit for a specific Ginzburg-Landau model is obtained and an explicit fo...The authors consider the moderate deviations of hydrodynamic limit for Ginzburg-Landau models. The moderate deviation principle of hydrodynamic limit for a specific Ginzburg-Landau model is obtained and an explicit formula of the rate function is derived.展开更多
This paper presents a small perturbation Cramer method for obtaining the large deviation principle of a family of measures (β,ε> 0) on a topological vector space. As an application, we obtain the moderate deviati...This paper presents a small perturbation Cramer method for obtaining the large deviation principle of a family of measures (β,ε> 0) on a topological vector space. As an application, we obtain the moderate deviation estimations for uniformly ergodic Markov processes.展开更多
In this article, we obtain the large deviations and moderate deviations for negatively dependent （ND） and non-identically distributed random variables defined on （-∞, ＋∞）. The results show that for some non-ide...In this article, we obtain the large deviations and moderate deviations for negatively dependent （ND） and non-identically distributed random variables defined on （-∞, ＋∞）. The results show that for some non-identical random variables, precise large deviations and moderate deviations remain insensitive to negative dependence structure.展开更多
Advertising English is viewed as an English style with such functional factors as attention value, readability, memorability, selling power. Commercial advertisements are the major concern of this paper. Deviation, na...Advertising English is viewed as an English style with such functional factors as attention value, readability, memorability, selling power. Commercial advertisements are the major concern of this paper. Deviation, namely the violation to the norms of a language, frequently appears in advertisements and can meet requirements of the style of advertising English. Due to limited space, this paper focuses on deviation on the phonological, graphological, lexical, grammatical, and semantic level. Analyzing deviation in advertising English can promote readers' aesthetic and appreciative ability and encourage advertisers to create advertisements with more efficiency, novelty, innovation in more effective language.展开更多
In this paper we prove a central limit theorem and a moderate deviation principle for a class of semilinear stochastic partial differential equations, which contain the stochastic Burgers’ equation and the stochastic...In this paper we prove a central limit theorem and a moderate deviation principle for a class of semilinear stochastic partial differential equations, which contain the stochastic Burgers’ equation and the stochastic reaction-diffusion equation. The weak convergence method plays an important role.展开更多
Song is one of Christina Georgina Rossetti's most outstanding death poems,dealing with the main themes that she concerns:death,love and religion.This paper tries to use the technique of deviation that refers to vi...Song is one of Christina Georgina Rossetti's most outstanding death poems,dealing with the main themes that she concerns:death,love and religion.This paper tries to use the technique of deviation that refers to violations to the standard language and readers'expectations to interpret this poem's stylistic features from the aspects of grammar,phonology,image,theme and narrative point of view.Through the stylistic analysis with the method of deviation,its solemn theme is exposed clearly.展开更多
We give a definition of relative entropy with respect to a sublinear expectation and establish large deviation principle for the empirical measures for independent random variables under the sublinear expectation.
Let （Xi） be a martingale difference sequence and Sn=∑^ni=1Xi Suppose （Xi） i=1 is bounded in L^p. In the case p ≥2, Lesigne and Volny （Stochastic Process. Appl. 96 （2001） 143） obtained the estimation μ（Sn ...Let （Xi） be a martingale difference sequence and Sn=∑^ni=1Xi Suppose （Xi） i=1 is bounded in L^p. In the case p ≥2, Lesigne and Volny （Stochastic Process. Appl. 96 （2001） 143） obtained the estimation μ（Sn 〉 n） ≤ cn^-p/2, Yulin Li （Statist. Probab. Lett. 62 （2003） 317） generalized the result to the case when p ∈ （1,2] and obtained μ（Sn 〉 n） ≤ cn^l-p, these are optimal in a certain sense. In this article, the authors study the large deviation of Sn for some dependent sequences and obtain the same order optimal upper bounds for μ（Sn 〉 n） as those for martingale difference sequence.展开更多
Charles Dickens is one of the greatest critical realist writers of the Victorian Age.In language,he is often compared with William Shakespeare for his adeptness with the vernacular and large vocabulary.Charles Dickens...Charles Dickens is one of the greatest critical realist writers of the Victorian Age.In language,he is often compared with William Shakespeare for his adeptness with the vernacular and large vocabulary.Charles Dickens achieved a recognizable place among English writers through the use of the stylistic features in his fictional language.Oliver Twist is the best representative of Charles Dickens’style,which makes it the most appropriate choice for the present stylistic study on Charles Dickens.No one who has ever read the dehumanizing workhouse scenes of Oliver Twist and the dark,criminal underworld life can forget them.This thesis attempts to investigate Oliver Twist through the approach of modern stylistics,particularly the theory of linguistic devia tion.This thesis consists of an introduction,the main body and a conclusion.The introduction offers a brief summary of the com ments on Charles Dickens and Chapter X of Oliver Twist,introduces the newly rising linguistic deviation theories,and brings about the theories on which this thesis settles.The main body explores the deviation effects produced from four aspects:lexical deviation,grammatical deviation,graphological deviation,and semantic deviation.It endeavors to show Dickens’manipulating language and the effects achieved through this manipulation.The conclusion mainly sums up the previous analysis,and reveals the theme of the novel,positive effect of linguistic deviation and significance of deviation application.展开更多
A class of multi dimensional degenerate diffusion processes X ε(t) in R r(r≥2) are considered and the asymptotic properties of empirical measures are investigated; here X ε(t) saitisfies the stochastic differen...A class of multi dimensional degenerate diffusion processes X ε(t) in R r(r≥2) are considered and the asymptotic properties of empirical measures are investigated; here X ε(t) saitisfies the stochastic differential equation dX ε(t)=σ(X ε(t)) d W(t)+B(X ε(t)) d t+ εσ～(X ε(t)) d W(t),ε>0. X ε(t) are small random perturbations of the degenerate diffusion process X(t), which satisfies the stochastic differential equation dX(t)=σ(X(t)) d W(t)+B(X(t)) d t. A large deviation theorem for projection measures ν on R r-n (n<r) of empirical measures μ are proved展开更多
The size distribution of the broken top coal blocks is an important factor,affecting the recovery ratio and the efficiency of drawing top coal in longwall top coal caving(LTCC)mining panel.The standard deviation of to...The size distribution of the broken top coal blocks is an important factor,affecting the recovery ratio and the efficiency of drawing top coal in longwall top coal caving(LTCC)mining panel.The standard deviation of top coal block size(dt)is one of the main parameters to reflect the size distribution of top coal.To find the effect of dt on the caving mechanism,this study simulates experiments with 9 different dt by using discrete element software PFC.The dt is divided into two stages:uniform distribution stage(UDS)whose dt is less than 0.1(Schemes 1–5),and nonuniform distribution stage(NDS)whose dt is more than 0.1(Schemes 6–9).This research mainly investigates the variation of recovery ratio,drawing body shape,boundary of top coal,and contact force between particles in the two stages,respectively.The results showed that with the increasing dt,the recovery ratio of the panel increases first and then decreases in UDS.It is the largest in Scheme 3,which mainly increases the drawing volume at the side of starting drawing end.However,the recovery ratio decreases first and then increases quickly in NDS,and it is the largest in Scheme 9,where the drawing volume at the side of finishing drawing end are relatively higher.In UDS,the major size of top coal is basically medium,while in NDS,the size varies from medium to small,and then to large,with a distinct difference in shape and volume of the drawing body.When the major size of top coal is medium and small,the cross-section width of the initial boundary of top coal at each height is relatively small.Conversely,when the top coal size is large,the initial boundary of top coal has a larger opening range,the rotating angle of lower boundary is relatively small in the normal drawing stage,which is conducive to the development of drawing body and reduces the residual top coal,and the maximum particle velocity and the particles movement angle are both larger.This study lays a foundation for the prediction of recovery ratio,and suggests that the uniform top coal is more manageable and has a larger recovery ratio.展开更多
This paper is a further investigation into the large deviations for random sums of heavy-tailed,we extended and improved some results in ref. [1] and [2]. These results can applied to some questions in Insurance and F...This paper is a further investigation into the large deviations for random sums of heavy-tailed,we extended and improved some results in ref. [1] and [2]. These results can applied to some questions in Insurance and Finance.展开更多
Let(Z_(n))be a branching process with immigration in a random environmentξ,whereξis an independent and identically distributed sequence of random variables.We show asymptotic properties for all the moments of Z_(n) ...Let(Z_(n))be a branching process with immigration in a random environmentξ,whereξis an independent and identically distributed sequence of random variables.We show asymptotic properties for all the moments of Z_(n) and describe the decay rates of the n-step transition probabilities.As applications,a large deviation principle for the sequence log Z_(n) is established,and related large deviations are also studied.展开更多
This paper presents a non-contact measurement of the realistic catenary geometry deviation in the Norwegian railway network through a laser rangefinder.The random geometry deviation is included in the catenary model ...This paper presents a non-contact measurement of the realistic catenary geometry deviation in the Norwegian railway network through a laser rangefinder.The random geometry deviation is included in the catenary model to investigate its effect on the pantograph–catenary interaction.The dispersion of the longitudinal deviation is assumed to follow a Gaussian distribution.A power spectrum density represents the vertical deviation in the contact wire.Based on the Monte Carlo method,several geometry deviation samples are generated and included in the catenary model.A lumped mass pantograph with flexible collectors is employed to reproduce the high-frequency behaviours.The stochastic analysis results indicate that the catenary geometry deviation causes a significant dispersion of the pantograph–catenary interaction response.The contact force standard deviations measured by the inspection vehicle are within the scope of the simulation results.A critical cut-off frequency that covers 1/16 of the dropper interval is suggested to fully describe the effect of the catenary geometry deviation on the contact force.The statistical minimum contact force is recommended to be modified according to the tolerant contact loss rate at high frequency.An unpleasant interaction performance of the pantograph–catenary can be expected at the catenary top speed when the random catenary geometry deviation is included.展开更多
With the growing needs of prepreg tapes for the automated fiber placement(AFP),the deviation-rectifying of prepreg in slitting process was investigated on a self-developed 16-tow prepreg slitting and winding machine.T...With the growing needs of prepreg tapes for the automated fiber placement(AFP),the deviation-rectifying of prepreg in slitting process was investigated on a self-developed 16-tow prepreg slitting and winding machine.The process of slitting and rewinding of prepreg tape was introduced,and the reason of prepreg tape deviation in slitting process was analyzed.In order to ensure the quality of the narrow prepreg slits,the application of the fuzzy PID algorithm in a closed-loop control system was discussed.A fuzzy PID algorithm was designed by combining fuzzy rules and PID controller.By applying it to precise deviation-rectifying control strategy,the automatic control of rectification could be achieved with accuracy of 0.1 mm,which satisfies the requirement of the prepreg tape both in slitting quality and layup quality for AFP.展开更多
Because of the uncertainty and subjectivity of decision makers in the complex decision-making environment,the evaluation information of alternatives given by decision makers is often fuzzy and uncertain.As a generaliz...Because of the uncertainty and subjectivity of decision makers in the complex decision-making environment,the evaluation information of alternatives given by decision makers is often fuzzy and uncertain.As a generalization of intuitionistic fuzzy set(IFSs)and Pythagoras fuzzy set(PFSs),q-rung orthopair fuzzy set(q-ROFS)is more suitable for expressing fuzzy and uncertain information.But,in actual multiple attribute decision making(MADM)problems,the weights of DMs and attributes are always completely unknown or partly known,to date,the maximizing deviation method is a good tool to deal with such issues.Thus,combine the q-ROFS and conventional maximizing deviation method,we will study the maximizing deviation method under q-ROFSs and q-RIVOFSs in this paper.Firstly,we briefly introduce the basic concept of q-rung orthopair fuzzy sets(q-ROFSs)and q-rung interval-valued orthopair fuzzy sets(q-RIVOFSs).Then,combine the maximizing deviation method with q-rung orthopair fuzzy information,we establish two new decision making models.On this basis,the proposed models are applied to MADM problems with q-rung orthopair fuzzy information.Compared with existing methods,the effectiveness and superiority of the new model are analyzed.This method can effectively solve the MADM problem whose decision information is represented by q-rung orthopair fuzzy numbers(q-ROFNs)and whose attributes are incomplete.展开更多
基金Project supported by the Natural Science Foundation of Jiangsu Province (Grant No.BK20220917)the National Natural Science Foundation of China (Grant Nos.12001213 and 12302035)。
文摘We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for more accurate calculation of the mean exit time by computing large deviation prefactors with the aid of machine learning.More specifically,we design a neural network framework to compute quasipotential,most probable paths and prefactors based on the orthogonal decomposition of a vector field.We corroborate the higher effectiveness and accuracy of our algorithm with two toy models.Numerical experiments demonstrate its powerful functionality in exploring the internal mechanism of rare events triggered by weak random fluctuations.
基金Partly supported by the National Natural Science Foundation of China and the Ministry of Education of ChinaPartly supported by the Science and Technology Research Item of Hubei Provincial Department of Education,Jiaghan University
文摘M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large deviation principles and moderate deviation upper bounds for stationary m-negatively associated random variables are proved. Kolmogorov-type and Marcinkiewicz-type strong laws of large numbers as well as the three series theorem for m-negatively associated random variables are also given.
基金Research supported by the National Natural Science Foundation of China (10271091)
文摘Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove moderate deviations and large deviations for the statistic sup ｜fn（x） - fn（-x） ｜.
基金Research supported by the National Natural Science Foundation of China (10571139)
文摘We study moderate deviations for estimators of the drift parameter of the fractional Ornstein-Uhlenbeck process. Two moderate deviation principles are obtained.
基金Supported by the National Natural Science Foundation of China (10271091)
文摘The authors consider the moderate deviations of hydrodynamic limit for Ginzburg-Landau models. The moderate deviation principle of hydrodynamic limit for a specific Ginzburg-Landau model is obtained and an explicit formula of the rate function is derived.
文摘This paper presents a small perturbation Cramer method for obtaining the large deviation principle of a family of measures (β,ε> 0) on a topological vector space. As an application, we obtain the moderate deviation estimations for uniformly ergodic Markov processes.
基金supported by the Youth Foundation of Hubei Province Department of Education of China (Q200710002)
文摘In this article, we obtain the large deviations and moderate deviations for negatively dependent （ND） and non-identically distributed random variables defined on （-∞, ＋∞）. The results show that for some non-identical random variables, precise large deviations and moderate deviations remain insensitive to negative dependence structure.
文摘Advertising English is viewed as an English style with such functional factors as attention value, readability, memorability, selling power. Commercial advertisements are the major concern of this paper. Deviation, namely the violation to the norms of a language, frequently appears in advertisements and can meet requirements of the style of advertising English. Due to limited space, this paper focuses on deviation on the phonological, graphological, lexical, grammatical, and semantic level. Analyzing deviation in advertising English can promote readers' aesthetic and appreciative ability and encourage advertisers to create advertisements with more efficiency, novelty, innovation in more effective language.
基金supported by NSFF(17BTJ034)The research of WANG was supported by NSFC(11871382,11771161).
文摘In this paper we prove a central limit theorem and a moderate deviation principle for a class of semilinear stochastic partial differential equations, which contain the stochastic Burgers’ equation and the stochastic reaction-diffusion equation. The weak convergence method plays an important role.
文摘Song is one of Christina Georgina Rossetti's most outstanding death poems,dealing with the main themes that she concerns:death,love and religion.This paper tries to use the technique of deviation that refers to violations to the standard language and readers'expectations to interpret this poem's stylistic features from the aspects of grammar,phonology,image,theme and narrative point of view.Through the stylistic analysis with the method of deviation,its solemn theme is exposed clearly.
基金supported by the National Natural Science Foundation of China(11171262)the Specialized Research Fund for the Doctoral Program of Higher Education (200804860048)
文摘We give a definition of relative entropy with respect to a sublinear expectation and establish large deviation principle for the empirical measures for independent random variables under the sublinear expectation.
基金the National Natural Science Foundation of China(10571001)the Innovation Group Foundation of Anhui University
文摘Let （Xi） be a martingale difference sequence and Sn=∑^ni=1Xi Suppose （Xi） i=1 is bounded in L^p. In the case p ≥2, Lesigne and Volny （Stochastic Process. Appl. 96 （2001） 143） obtained the estimation μ（Sn 〉 n） ≤ cn^-p/2, Yulin Li （Statist. Probab. Lett. 62 （2003） 317） generalized the result to the case when p ∈ （1,2] and obtained μ（Sn 〉 n） ≤ cn^l-p, these are optimal in a certain sense. In this article, the authors study the large deviation of Sn for some dependent sequences and obtain the same order optimal upper bounds for μ（Sn 〉 n） as those for martingale difference sequence.
文摘Charles Dickens is one of the greatest critical realist writers of the Victorian Age.In language,he is often compared with William Shakespeare for his adeptness with the vernacular and large vocabulary.Charles Dickens achieved a recognizable place among English writers through the use of the stylistic features in his fictional language.Oliver Twist is the best representative of Charles Dickens’style,which makes it the most appropriate choice for the present stylistic study on Charles Dickens.No one who has ever read the dehumanizing workhouse scenes of Oliver Twist and the dark,criminal underworld life can forget them.This thesis attempts to investigate Oliver Twist through the approach of modern stylistics,particularly the theory of linguistic devia tion.This thesis consists of an introduction,the main body and a conclusion.The introduction offers a brief summary of the com ments on Charles Dickens and Chapter X of Oliver Twist,introduces the newly rising linguistic deviation theories,and brings about the theories on which this thesis settles.The main body explores the deviation effects produced from four aspects:lexical deviation,grammatical deviation,graphological deviation,and semantic deviation.It endeavors to show Dickens’manipulating language and the effects achieved through this manipulation.The conclusion mainly sums up the previous analysis,and reveals the theme of the novel,positive effect of linguistic deviation and significance of deviation application.
文摘A class of multi dimensional degenerate diffusion processes X ε(t) in R r(r≥2) are considered and the asymptotic properties of empirical measures are investigated; here X ε(t) saitisfies the stochastic differential equation dX ε(t)=σ(X ε(t)) d W(t)+B(X ε(t)) d t+ εσ～(X ε(t)) d W(t),ε>0. X ε(t) are small random perturbations of the degenerate diffusion process X(t), which satisfies the stochastic differential equation dX(t)=σ(X(t)) d W(t)+B(X(t)) d t. A large deviation theorem for projection measures ν on R r-n (n<r) of empirical measures μ are proved
基金supported by the National Key R&D Plan of China,China(Grant No.2018YFC0604501)the Natural Science Foundation of China,China(Grant Nos.51934008,51674264,51904305)the Research Fund of the State Key Laboratory of Coal Resources and Safe Mining,CUMT,China(Grant No.SKLCRSM19KF023).
文摘The size distribution of the broken top coal blocks is an important factor,affecting the recovery ratio and the efficiency of drawing top coal in longwall top coal caving(LTCC)mining panel.The standard deviation of top coal block size(dt)is one of the main parameters to reflect the size distribution of top coal.To find the effect of dt on the caving mechanism,this study simulates experiments with 9 different dt by using discrete element software PFC.The dt is divided into two stages:uniform distribution stage(UDS)whose dt is less than 0.1(Schemes 1–5),and nonuniform distribution stage(NDS)whose dt is more than 0.1(Schemes 6–9).This research mainly investigates the variation of recovery ratio,drawing body shape,boundary of top coal,and contact force between particles in the two stages,respectively.The results showed that with the increasing dt,the recovery ratio of the panel increases first and then decreases in UDS.It is the largest in Scheme 3,which mainly increases the drawing volume at the side of starting drawing end.However,the recovery ratio decreases first and then increases quickly in NDS,and it is the largest in Scheme 9,where the drawing volume at the side of finishing drawing end are relatively higher.In UDS,the major size of top coal is basically medium,while in NDS,the size varies from medium to small,and then to large,with a distinct difference in shape and volume of the drawing body.When the major size of top coal is medium and small,the cross-section width of the initial boundary of top coal at each height is relatively small.Conversely,when the top coal size is large,the initial boundary of top coal has a larger opening range,the rotating angle of lower boundary is relatively small in the normal drawing stage,which is conducive to the development of drawing body and reduces the residual top coal,and the maximum particle velocity and the particles movement angle are both larger.This study lays a foundation for the prediction of recovery ratio,and suggests that the uniform top coal is more manageable and has a larger recovery ratio.
基金Supported by the Natural Science Foundation of the Education Department of Anhui Province(0505101)
文摘This paper is a further investigation into the large deviations for random sums of heavy-tailed,we extended and improved some results in ref. [1] and [2]. These results can applied to some questions in Insurance and Finance.
基金partially supported by the National Nature Science Foundation of China(11601286,11501146)。
文摘Let(Z_(n))be a branching process with immigration in a random environmentξ,whereξis an independent and identically distributed sequence of random variables.We show asymptotic properties for all the moments of Z_(n) and describe the decay rates of the n-step transition probabilities.As applications,a large deviation principle for the sequence log Z_(n) is established,and related large deviations are also studied.
文摘This paper presents a non-contact measurement of the realistic catenary geometry deviation in the Norwegian railway network through a laser rangefinder.The random geometry deviation is included in the catenary model to investigate its effect on the pantograph–catenary interaction.The dispersion of the longitudinal deviation is assumed to follow a Gaussian distribution.A power spectrum density represents the vertical deviation in the contact wire.Based on the Monte Carlo method,several geometry deviation samples are generated and included in the catenary model.A lumped mass pantograph with flexible collectors is employed to reproduce the high-frequency behaviours.The stochastic analysis results indicate that the catenary geometry deviation causes a significant dispersion of the pantograph–catenary interaction response.The contact force standard deviations measured by the inspection vehicle are within the scope of the simulation results.A critical cut-off frequency that covers 1/16 of the dropper interval is suggested to fully describe the effect of the catenary geometry deviation on the contact force.The statistical minimum contact force is recommended to be modified according to the tolerant contact loss rate at high frequency.An unpleasant interaction performance of the pantograph–catenary can be expected at the catenary top speed when the random catenary geometry deviation is included.
基金financially supported by the National Basic Research Program of China(973Program)the Priority Academic Program Development of Jiangsu Higher Education Institutionsthe Fundamental Research Funds for the Central Universities ( No. 3082615NS2015056)
文摘With the growing needs of prepreg tapes for the automated fiber placement(AFP),the deviation-rectifying of prepreg in slitting process was investigated on a self-developed 16-tow prepreg slitting and winding machine.The process of slitting and rewinding of prepreg tape was introduced,and the reason of prepreg tape deviation in slitting process was analyzed.In order to ensure the quality of the narrow prepreg slits,the application of the fuzzy PID algorithm in a closed-loop control system was discussed.A fuzzy PID algorithm was designed by combining fuzzy rules and PID controller.By applying it to precise deviation-rectifying control strategy,the automatic control of rectification could be achieved with accuracy of 0.1 mm,which satisfies the requirement of the prepreg tape both in slitting quality and layup quality for AFP.
基金supported by the National Natural Science Foundation of China under Grant No.71571128the Humanities and Social Sciences Foundation of Ministry of Education of the People’s Republic of China(No.17XJA630003).
文摘Because of the uncertainty and subjectivity of decision makers in the complex decision-making environment,the evaluation information of alternatives given by decision makers is often fuzzy and uncertain.As a generalization of intuitionistic fuzzy set(IFSs)and Pythagoras fuzzy set(PFSs),q-rung orthopair fuzzy set(q-ROFS)is more suitable for expressing fuzzy and uncertain information.But,in actual multiple attribute decision making(MADM)problems,the weights of DMs and attributes are always completely unknown or partly known,to date,the maximizing deviation method is a good tool to deal with such issues.Thus,combine the q-ROFS and conventional maximizing deviation method,we will study the maximizing deviation method under q-ROFSs and q-RIVOFSs in this paper.Firstly,we briefly introduce the basic concept of q-rung orthopair fuzzy sets(q-ROFSs)and q-rung interval-valued orthopair fuzzy sets(q-RIVOFSs).Then,combine the maximizing deviation method with q-rung orthopair fuzzy information,we establish two new decision making models.On this basis,the proposed models are applied to MADM problems with q-rung orthopair fuzzy information.Compared with existing methods,the effectiveness and superiority of the new model are analyzed.This method can effectively solve the MADM problem whose decision information is represented by q-rung orthopair fuzzy numbers(q-ROFNs)and whose attributes are incomplete.
