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...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.展开更多
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 th...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.展开更多
In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their...In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their logical derivatives of order α.展开更多
This paper discusses the definition and properties of multivalued symmetric functions, points out that a multivalued symmetric function can be decomposed according to the value of the function j. The subfunction Lj co...This paper discusses the definition and properties of multivalued symmetric functions, points out that a multivalued symmetric function can be decomposed according to the value of the function j. The subfunction Lj corresponding to j must be a symmetric function, and it may be expressed as the sum of products form of degenerated multivalued fundamental symmetric functions. Based on this consideration, the circuit realization for the multivalued symmetric functions based on full adders is proposed.展开更多
There are many kinds of special relationships between multiple-valued logical func-tions and their variables, and they are difficult to be judged from their expressions. In thispaper, some sufficient and necessary con...There are many kinds of special relationships between multiple-valued logical func-tions and their variables, and they are difficult to be judged from their expressions. In thispaper, some sufficient and necessary conditions of the independence and statistical independenceof multiple-valued logical functions on their variables are given. Some conditions of algebraicindependence of multiple-valued logical functions on some of their variables and the way to de-generate a function to the greatest extent are proposed, and some applications of these resultsare indicated. All the results are studied by using Chrestenson spectral techniques.展开更多
This paper discusses the best affine approach (BAA) of multi-output m-valued logical functions. First, it gives the spectra of rate of accordance between multi-output m-valued logical functions and their affine func...This paper discusses the best affine approach (BAA) of multi-output m-valued logical functions. First, it gives the spectra of rate of accordance between multi-output m-valued logical functions and their affine functions, then analyzes the BAA of multi-output m-valued logical functions and finally gives the spectral characteristics of BAA of multi-output m-valued logical functions.展开更多
The paper consists in the use of some logical functions decomposition algorithms with application in the implementation of classical circuits like SSI, MSI and PLD. The decomposition methods use the Boolean matrix cal...The paper consists in the use of some logical functions decomposition algorithms with application in the implementation of classical circuits like SSI, MSI and PLD. The decomposition methods use the Boolean matrix calculation. It is calculated the implementation costs emphasizing the most economical solutions. One important aspect of serial decomposition is the task of selecting “best candidate” variables for the G function. Decomposition is essentially a process of substituting two or more input variables with a lesser number of new variables. This substitutes results in the reduction of the number of rows in the truth table. Hence, we look for variables which are most likely to reduce the number of rows in the truth table as a result of decomposition. Let us consider an input variable purposely avoiding all inter-relationships among the input variables. The only available parameter to evaluate its activity is the number of “l”s or “O”s that it has in the truth table. If the variable has only “1” s or “0” s, it is the “best candidate” for decomposition, as it is practically redundant.展开更多
he logical tree methods are used for evaluate quantitatively relationship between frequency and magnitude, and deduce uncertainties of annual occurrence rate of earthquakes in the periods of lower magnitude earthquake...he logical tree methods are used for evaluate quantitatively relationship between frequency and magnitude, and deduce uncertainties of annual occurrence rate of earthquakes in the periods of lower magnitude earthquake. The uncertainties include deviations from the self-similarity of frequency-magnitude relations, different fitting methods, different methods obtained the annual occurrence rate, magnitude step used in fitting, start magnitude, error of magnitude and so on. Taking Xianshuihe River source zone as an example, we analyze uncertainties of occurrence rate of earthquakes M4, which is needed in risk evaluation extrapolating from frequency-magnitude relations of stronger earthquakes. The annual occurrence rate of M4 is usually required for seismic hazard assessment.The sensitivity analysis and examinations indicate that, in the same frequencymagnitude relations fitting method, the most sensitive factor is annual occurrence rate, the second is magnitude step and the following is start magnitude. Effect of magnitude error is rather small.Procedure of estimating the uncertainties is as follows:①Establishing a logical tree described uncertainties in frequencymagnitude relations by available data and knowledge about studied region.② Calculating frequencymagnitude relations for each end branches. ③ Examining sensitivities of each uncertainty factors, amending structure of logical tree and adjusting original weights. ④ Recalculating frequencymagnitude relations of end branches and complementary cumulative distribution function (CCDF) in each magnitude intervals.⑤ Obtaining an annual occurrence rate of M4 earthquakes under given fractiles.Taking fractiles as 20% and 80%, annual occurrence rate of M 4 events in Xianshuihe seismic zone is 0.643 0. The annual occurrence rate is 0.631 8 under fractiles of 50%, which is very close to that under fractiles 20% and 80%.展开更多
Aiming at the problem of abstract and polytype information modeling in product conceptual design, a method of conceptual modeling based on logical expression and evolvement is presented. Based on the logic expressions...Aiming at the problem of abstract and polytype information modeling in product conceptual design, a method of conceptual modeling based on logical expression and evolvement is presented. Based on the logic expressions of the product conceptual design information, a fimction/logic/strucmre mapping model is set up. First, the fimction semantics is transformed into logical expressions through fimction/logic mapping. Second, the methods of logical evolvement are utilized to describe the fimction analysis, fimction/strucmre mapping and structure combination. Last, the logical structure scheme is transformed into geometrical sketch through logic/structure mapping. The conceptual design information and modeling process are described uniformly with logical methods in the model, and an effective method for computer aided conceptual design based on the model is implemented.展开更多
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 (<i>r</i>,<i>φ</i>,<i>ψ</i>)-Suzuki...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 (<i>r</i>,<i>φ</i>,<i>ψ</i>)-Suzuki contraction in such spaces. Around our paper, the function <i>ψ</i> is absolutely continuous, and in this case, the contraction proposed by as has a fixed point.展开更多
Fuzzy logic controller adopting unevenly-distributed membership function was presented with the purpose of enhancing performance of the temperature control precision and robustness for the chamber cooling system.Histo...Fuzzy logic controller adopting unevenly-distributed membership function was presented with the purpose of enhancing performance of the temperature control precision and robustness for the chamber cooling system.Histogram equalization and noise detection were performed to modify the evenly-distributed membership functions of error and error change rate into unevenly-distributed membership functions.Then,the experimental results with evenly and unevenly distributed membership functions were compared under the same outside environment conditions.The experimental results show that the steady-state error is reduced around 40% and the noise disturbance is rejected successfully even though noise range is 60% of the control precision range.The control precision is improved by reducing the steady-state error and the robustness is enhanced by rejecting noise disturbance through the fuzzy logic controller with unevenly-distributed membership function.Moreover,the system energy efficiency and lifetime of electronic expansion valve(EEV) installed in chamber cooling system are improved by adopting the unevenly-distributed membership function.展开更多
The circuit testable realization and its fault detection for logic functions with ESOP (EXOR-Sum-Of-Products) expressions are studied. First of all, for the testable realization by using XOR gate cascade, a test set w...The circuit testable realization and its fault detection for logic functions with ESOP (EXOR-Sum-Of-Products) expressions are studied. First of all, for the testable realization by using XOR gate cascade, a test set with 2 n + m+ 1vectors for the detections of AND bridging faults and a test set with 2n + mvectors for the detections of OR bridging faults are presented. Secondly, for the testable realization by using XOR gate tree, a test set with 2n + mvectors for the detections of AND bridging faults and a test set with 3n + m+ 1vectors for the detections of OR bridging faults are presented. Finally, a single fault test set with n + 5vectors for the XOR gate tree realization is pre- sented. Where n is the number of input variables and m is the number of product terms in a logic function.展开更多
Radial Basis Function Neural Network(RBFNN)ensembles have long suffered from non-efficient training,where incorrect parameter settings can be computationally disastrous.This paper examines different evolutionary algor...Radial Basis Function Neural Network(RBFNN)ensembles have long suffered from non-efficient training,where incorrect parameter settings can be computationally disastrous.This paper examines different evolutionary algorithms for training the Symbolic Radial Basis Function Neural Network(SRBFNN)through the behavior’s integration of satisfiability programming.Inspired by evolutionary algorithms,which can iteratively find the nearoptimal solution,different Evolutionary Algorithms(EAs)were designed to optimize the producer output weight of the SRBFNN that corresponds to the embedded logic programming 2Satisfiability representation(SRBFNN-2SAT).The SRBFNN’s objective function that corresponds to Satisfiability logic programming can be minimized by different algorithms,including Genetic Algorithm(GA),Evolution Strategy Algorithm(ES),Differential Evolution Algorithm(DE),and Evolutionary Programming Algorithm(EP).Each of these methods is presented in the steps in the flowchart form which can be used for its straightforward implementation in any programming language.With the use of SRBFNN-2SAT,a training method based on these algorithms has been presented,then training has been compared among algorithms,which were applied in Microsoft Visual C++software using multiple metrics of performance,including Mean Absolute Relative Error(MARE),Root Mean Square Error(RMSE),Mean Absolute Percentage Error(MAPE),Mean Bias Error(MBE),Systematic Error(SD),Schwarz Bayesian Criterion(SBC),and Central Process Unit time(CPU time).Based on the results,the EP algorithm achieved a higher training rate and simple structure compared with the rest of the algorithms.It has been confirmed that the EP algorithm is quite effective in training and obtaining the best output weight,accompanied by the slightest iteration error,which minimizes the objective function of SRBFNN-2SAT.展开更多
文摘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.
基金National Natural Science Foundation of China(No.61164009)the Science and Technology Research Project,Department of Education of Jiangxi Province,China(No.GJJ14420)Natural Science Foundation of Jiangxi Province,China(No.20132BAB206026)
文摘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.
文摘In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their logical derivatives of order α.
文摘This paper discusses the definition and properties of multivalued symmetric functions, points out that a multivalued symmetric function can be decomposed according to the value of the function j. The subfunction Lj corresponding to j must be a symmetric function, and it may be expressed as the sum of products form of degenerated multivalued fundamental symmetric functions. Based on this consideration, the circuit realization for the multivalued symmetric functions based on full adders is proposed.
文摘There are many kinds of special relationships between multiple-valued logical func-tions and their variables, and they are difficult to be judged from their expressions. In thispaper, some sufficient and necessary conditions of the independence and statistical independenceof multiple-valued logical functions on their variables are given. Some conditions of algebraicindependence of multiple-valued logical functions on some of their variables and the way to de-generate a function to the greatest extent are proposed, and some applications of these resultsare indicated. All the results are studied by using Chrestenson spectral techniques.
基金Supported by the Opening Research Foundation of the State Key Laboratory of Information Security (2005-01-02)
文摘This paper discusses the best affine approach (BAA) of multi-output m-valued logical functions. First, it gives the spectra of rate of accordance between multi-output m-valued logical functions and their affine functions, then analyzes the BAA of multi-output m-valued logical functions and finally gives the spectral characteristics of BAA of multi-output m-valued logical functions.
文摘The paper consists in the use of some logical functions decomposition algorithms with application in the implementation of classical circuits like SSI, MSI and PLD. The decomposition methods use the Boolean matrix calculation. It is calculated the implementation costs emphasizing the most economical solutions. One important aspect of serial decomposition is the task of selecting “best candidate” variables for the G function. Decomposition is essentially a process of substituting two or more input variables with a lesser number of new variables. This substitutes results in the reduction of the number of rows in the truth table. Hence, we look for variables which are most likely to reduce the number of rows in the truth table as a result of decomposition. Let us consider an input variable purposely avoiding all inter-relationships among the input variables. The only available parameter to evaluate its activity is the number of “l”s or “O”s that it has in the truth table. If the variable has only “1” s or “0” s, it is the “best candidate” for decomposition, as it is practically redundant.
文摘he logical tree methods are used for evaluate quantitatively relationship between frequency and magnitude, and deduce uncertainties of annual occurrence rate of earthquakes in the periods of lower magnitude earthquake. The uncertainties include deviations from the self-similarity of frequency-magnitude relations, different fitting methods, different methods obtained the annual occurrence rate, magnitude step used in fitting, start magnitude, error of magnitude and so on. Taking Xianshuihe River source zone as an example, we analyze uncertainties of occurrence rate of earthquakes M4, which is needed in risk evaluation extrapolating from frequency-magnitude relations of stronger earthquakes. The annual occurrence rate of M4 is usually required for seismic hazard assessment.The sensitivity analysis and examinations indicate that, in the same frequencymagnitude relations fitting method, the most sensitive factor is annual occurrence rate, the second is magnitude step and the following is start magnitude. Effect of magnitude error is rather small.Procedure of estimating the uncertainties is as follows:①Establishing a logical tree described uncertainties in frequencymagnitude relations by available data and knowledge about studied region.② Calculating frequencymagnitude relations for each end branches. ③ Examining sensitivities of each uncertainty factors, amending structure of logical tree and adjusting original weights. ④ Recalculating frequencymagnitude relations of end branches and complementary cumulative distribution function (CCDF) in each magnitude intervals.⑤ Obtaining an annual occurrence rate of M4 earthquakes under given fractiles.Taking fractiles as 20% and 80%, annual occurrence rate of M 4 events in Xianshuihe seismic zone is 0.643 0. The annual occurrence rate is 0.631 8 under fractiles of 50%, which is very close to that under fractiles 20% and 80%.
基金This project is supported by National Natural Science Foundation of China (No. 50405037)Provincial Natural Science Foundation of Zhejiang, China (No. Y105256)Specialized Research Fund for the Doctoral Program of Higher Education, China (No. 20040335060)
文摘Aiming at the problem of abstract and polytype information modeling in product conceptual design, a method of conceptual modeling based on logical expression and evolvement is presented. Based on the logic expressions of the product conceptual design information, a fimction/logic/strucmre mapping model is set up. First, the fimction semantics is transformed into logical expressions through fimction/logic mapping. Second, the methods of logical evolvement are utilized to describe the fimction analysis, fimction/strucmre mapping and structure combination. Last, the logical structure scheme is transformed into geometrical sketch through logic/structure mapping. The conceptual design information and modeling process are described uniformly with logical methods in the model, and an effective method for computer aided conceptual design based on the model is implemented.
文摘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 (<i>r</i>,<i>φ</i>,<i>ψ</i>)-Suzuki contraction in such spaces. Around our paper, the function <i>ψ</i> is absolutely continuous, and in this case, the contraction proposed by as has a fixed point.
文摘Fuzzy logic controller adopting unevenly-distributed membership function was presented with the purpose of enhancing performance of the temperature control precision and robustness for the chamber cooling system.Histogram equalization and noise detection were performed to modify the evenly-distributed membership functions of error and error change rate into unevenly-distributed membership functions.Then,the experimental results with evenly and unevenly distributed membership functions were compared under the same outside environment conditions.The experimental results show that the steady-state error is reduced around 40% and the noise disturbance is rejected successfully even though noise range is 60% of the control precision range.The control precision is improved by reducing the steady-state error and the robustness is enhanced by rejecting noise disturbance through the fuzzy logic controller with unevenly-distributed membership function.Moreover,the system energy efficiency and lifetime of electronic expansion valve(EEV) installed in chamber cooling system are improved by adopting the unevenly-distributed membership function.
基金Supported by the National Natural Science Foundation of China (No.60006002)the Education Department of Guangdong Province of China (No.02019).
文摘The circuit testable realization and its fault detection for logic functions with ESOP (EXOR-Sum-Of-Products) expressions are studied. First of all, for the testable realization by using XOR gate cascade, a test set with 2 n + m+ 1vectors for the detections of AND bridging faults and a test set with 2n + mvectors for the detections of OR bridging faults are presented. Secondly, for the testable realization by using XOR gate tree, a test set with 2n + mvectors for the detections of AND bridging faults and a test set with 3n + m+ 1vectors for the detections of OR bridging faults are presented. Finally, a single fault test set with n + 5vectors for the XOR gate tree realization is pre- sented. Where n is the number of input variables and m is the number of product terms in a logic function.
基金This work is supported by Ministry of Higher Education(MOHE)through Fundamental Research Grant Scheme(FRGS)(FRGS/1/2020/STG06/UTHM/03/7).
文摘Radial Basis Function Neural Network(RBFNN)ensembles have long suffered from non-efficient training,where incorrect parameter settings can be computationally disastrous.This paper examines different evolutionary algorithms for training the Symbolic Radial Basis Function Neural Network(SRBFNN)through the behavior’s integration of satisfiability programming.Inspired by evolutionary algorithms,which can iteratively find the nearoptimal solution,different Evolutionary Algorithms(EAs)were designed to optimize the producer output weight of the SRBFNN that corresponds to the embedded logic programming 2Satisfiability representation(SRBFNN-2SAT).The SRBFNN’s objective function that corresponds to Satisfiability logic programming can be minimized by different algorithms,including Genetic Algorithm(GA),Evolution Strategy Algorithm(ES),Differential Evolution Algorithm(DE),and Evolutionary Programming Algorithm(EP).Each of these methods is presented in the steps in the flowchart form which can be used for its straightforward implementation in any programming language.With the use of SRBFNN-2SAT,a training method based on these algorithms has been presented,then training has been compared among algorithms,which were applied in Microsoft Visual C++software using multiple metrics of performance,including Mean Absolute Relative Error(MARE),Root Mean Square Error(RMSE),Mean Absolute Percentage Error(MAPE),Mean Bias Error(MBE),Systematic Error(SD),Schwarz Bayesian Criterion(SBC),and Central Process Unit time(CPU time).Based on the results,the EP algorithm achieved a higher training rate and simple structure compared with the rest of the algorithms.It has been confirmed that the EP algorithm is quite effective in training and obtaining the best output weight,accompanied by the slightest iteration error,which minimizes the objective function of SRBFNN-2SAT.