Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable ...Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.展开更多
A method with the fuzzy entropy for measuring fuzziness to fuzzy problem in rough sets is proposed. A new sort of the fuzzy entropy is given. The calculating formula and the equivalent expression method with the fuzzy...A method with the fuzzy entropy for measuring fuzziness to fuzzy problem in rough sets is proposed. A new sort of the fuzzy entropy is given. The calculating formula and the equivalent expression method with the fuzzy entropy in rough sets based on equivalence relation are provided, and the properties of the fuzzy entropy are proved. The fuzzy entropy based on equivalent relation is extended to generalize the fuzzy entropy based on general binary relation, and the calculating formula and the equivalent expression of the generalized fuzzy entropy are also given. Finally, an example illustrates the way for getting the fuzzy entropy. Results show that the fuzzy entropy can conveniently measure the fuzziness in rough sets.展开更多
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 ...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.展开更多
The main factors deciding the compressive strength of binder backfill body are tailing density and binder dosage in binder backfill materials. Based on the antecedent of certain pulp density, the method of increasing ...The main factors deciding the compressive strength of binder backfill body are tailing density and binder dosage in binder backfill materials. Based on the antecedent of certain pulp density, the method of increasing the tailing density and reducing the binder dosage, or the manner of cutting down the tailing density and gaining the binder dosage are taken to guarantee the strength of backfill body. The problem that should be solved is how to determine the tailing density and the binder dosage rationally. This paper tries to realize the correct selection of the tailing density and the binder dosage in computer with the method of fuzzy mathematics.展开更多
A new image recognition method based on fuzzy rough sets theory is proposed, and its implementation discussed. The performance of this method as applied to ferrography image recognition is evaluated. It is shown that...A new image recognition method based on fuzzy rough sets theory is proposed, and its implementation discussed. The performance of this method as applied to ferrography image recognition is evaluated. It is shown that the new method gives better results than fuzzy or rough sets method when used alone.展开更多
In this paper, category GIFS of generalized intuitionistic fuzzy sets(GIF) is built up. Topoi properties of category GIFS are studied. Firstly, it is proved that the category GIFS has all topoi properties except that ...In this paper, category GIFS of generalized intuitionistic fuzzy sets(GIF) is built up. Topoi properties of category GIFS are studied. Firstly, it is proved that the category GIFS has all topoi properties except that it has no subobject classifiers, Secondly, it is proved that the category GIFS has middle object and consequently GIFS is a weak topos. Thirdly, by the use of theory of weak topos GIFS, the power object of an object in GIFS is studied.展开更多
At present, most of the association rules algorithms are based on the Boolean attribute and single-level association rules mining. But data of the real world has various types, the multi-level and quantitative attribu...At present, most of the association rules algorithms are based on the Boolean attribute and single-level association rules mining. But data of the real world has various types, the multi-level and quantitative attributes are got more and more attention. And the most important step is to mine frequent sets. In this paper, we propose an algorithm that is called fuzzy multiple-level association （FMA） rules to mine frequent sets. It is based on the improved Eclat algorithm that is different to many researchers’ proposed algorithms thatused the Apriori algorithm. We analyze quantitative data’s frequent sets by using the fuzzy theory, dividing the hierarchy of concept and softening the boundary of attributes’ values and frequency. In this paper, we use the vertical-style data and the improved Eclat algorithm to describe the proposed method, we use this algorithm to analyze the data of Beijing logistics route. Experiments show that the algorithm has a good performance, it has better effectiveness and high efficiency.展开更多
The fuzzy static and dynamic random phenomena in an abstract separable Banach space is discussed in this paper. The representation theorems for fuzzy set valued random sets, fuzzy random elements and fuzzy set value...The fuzzy static and dynamic random phenomena in an abstract separable Banach space is discussed in this paper. The representation theorems for fuzzy set valued random sets, fuzzy random elements and fuzzy set valued stochastic processes are obtained.展开更多
In power production,gas turbines are commonly used components that generate high amount of energy depending on size and weight.They function as integral parts of helicopters,aircrafts,trains,ships,electrical generator...In power production,gas turbines are commonly used components that generate high amount of energy depending on size and weight.They function as integral parts of helicopters,aircrafts,trains,ships,electrical generators,and tanks.Notably,many researchers are focusing on the design,operation,and maintenance of gas turbines.The focal point of this paper is a DEMATEL approach based on fuzzy sets,with the attempt to use these fuzzy sets explicitly.Using this approach,the cause–effect diagram of gas turbine failures expressed in the literature is generated and aimed to create a perspective for operators.The results of the study show that,"connecting shaft has been broken between turbine and gear box"selected the most important cause factor and"sufficient pressure fuel does not come for fuel pump"is selected the most important effect factor,according to the experts.展开更多
Although the concept of interval fuzzy set and its properties have been defined, its three theorems and their effectiveness are not proved. Therefore, the knowledge presentation and its operation rules of interval fuz...Although the concept of interval fuzzy set and its properties have been defined, its three theorems and their effectiveness are not proved. Therefore, the knowledge presentation and its operation rules of interval fuzzy set are studied firstly, and then the cut set of interval fuzzy set is proposed. Moreover, the decomposition theo- rem, the representation theorem and the extension theorem of interval fuzzy set are presented. Finally, examples are given to demonstrate that the classical fuzzy set is a special case of interval fuzzy set and interval fuzzy set is an effective expansion of the classical fuzzy set.展开更多
A rough set based fuzzy neural network algorithm is proposed to solve the problem of pattern recognition. The least square algorithm (LSA) is used in the learning process of fuzzy neural network to obtain the performa...A rough set based fuzzy neural network algorithm is proposed to solve the problem of pattern recognition. The least square algorithm (LSA) is used in the learning process of fuzzy neural network to obtain the performance of global convergence. In addition, the numbers of rules and the initial weights and structure of fuzzy neural networks are difficult to determine. Here rough sets are introduced to decide the numbers of rules and original weights. Finally, experiment results show the algorithm may get better effect than the BP algorithm.展开更多
Ensemble learning for anomaly detection of data structured into a complex network has been barely studied due to the inconsistent performance of complex network characteristics and the lack of inherent objective funct...Ensemble learning for anomaly detection of data structured into a complex network has been barely studied due to the inconsistent performance of complex network characteristics and the lack of inherent objective function. We propose the intuitionistic fuzzy set（IFS）-based anomaly detection, a new two-phase ensemble method for anomaly detection based on IFS, and apply it to the abnormal behavior detection problem in temporal complex networks.Firstly, it constructs the IFS of a single network characteristic, which quantifies the degree of membership,non-membership and hesitation of each network characteristic to the defined linguistic variables so that makes the unuseful or noise characteristics become part of the detection. To build an objective intuitionistic fuzzy relationship, we propose a Gaussian distribution-based membership function which gives a variable hesitation degree. Then, for the fuzzification of multiple network characteristics, the intuitionistic fuzzy weighted geometric operator is adopted to fuse multiple IFSs and to avoid the inconsistence of multiple characteristics. Finally, the score function and precision function are used to sort the fused IFS. Finally, we carry out extensive experiments on several complex network datasets for anomaly detection, and the results demonstrate the superiority of our method to state-of-the-art approaches, validating the effectiveness of our method.展开更多
This paper gives the definition of λ-cut sets and studies the structure of fuzzy rough sets. Based on the concept of rough sets, this paper proposes the representation theorem of fuzzy rough sets.
Scheme evaluation and selection is an optimum selecting and sequencing problem with multi-objective and multi-level. It can’t follow single objective function or rule. Meanwhile,these objectives are coupled with each...Scheme evaluation and selection is an optimum selecting and sequencing problem with multi-objective and multi-level. It can’t follow single objective function or rule. Meanwhile,these objectives are coupled with each other and the attribution information is fuzzy also. It is necessary to find an effective evaluation method which can consider all conditions and restrictions. In this paper,AHP and rough set theory are applied to fuzzy optimization to determine important weight of each attribution. The rough set fuzzy optimum selection is used to eliminate the useless information. Autonomous underwater vehicle (AUV) is large-scale systems with many coupled design variables and objective functions. Their scheme evaluation and selection are very important,which relate to multiple factors,such as reliability; security,service time; the lifecycle,etc. Results of application in torpedo design indicate that this method is feasible.展开更多
Residuated lattice is an important non-classical logic algebra, and L-fuzzy rough set based on residuated lattice can describe the information with incompleteness, fuzziness and uncomparativity in information systems....Residuated lattice is an important non-classical logic algebra, and L-fuzzy rough set based on residuated lattice can describe the information with incompleteness, fuzziness and uncomparativity in information systems. In this paper, the representation theorems of L-fuzzy rough sets based on residuated lattice are given. The properties and axiomatic definition of the lower and upper approximarion operators in L-fuzzy rough sets are discussed.展开更多
Optimal route selection is an important function of vehicle trac flow guidance system. Its core is to determine the index weight for measuring the route merits and to determine the evaluation method for selecting rout...Optimal route selection is an important function of vehicle trac flow guidance system. Its core is to determine the index weight for measuring the route merits and to determine the evaluation method for selecting route. In this paper, subjective weighting method which relies on driver preference is used to determine the weight and the paper proposes the multi-criteria weighted decision method based on vague sets for selecting the optimal route. Examples show that, the usage of vague sets to describe route index value can provide more decision-making information for route selection.展开更多
The maintenance window scheme(MWS) is one of the most important railway transportation organizational plans and plays an important role in ensuring railway operational safety. However, MWS setting is a very complicate...The maintenance window scheme(MWS) is one of the most important railway transportation organizational plans and plays an important role in ensuring railway operational safety. However, MWS setting is a very complicated process, and most countries currently do so with the help of a computer-aided decision system. In general, a decision system can generate multiple alternatives for MWS within an acceptable time. Therefore, how to choose the best option from the alternatives is a vital decision. This paper presents a novel framework for MWS evaluation based on the Chinese railway system. Specifically, the requirements of each department related to MWS setting are analysed, and we construct an evaluation indicator system for MWS based on the preferences of different departments. Then, we apply the fuzzy soft set theory to MWS evaluation, a method that not only effectively deals with evaluation of uncertain information, but also gives flexibility for experts to input their subjective judgment.Additionally, using the ‘‘AND’’ operation of soft set theory allows combing evaluation information from multiple evaluators to give comprehensive results. Finally, a case study illustrates the proposed framework, showing that the proposed evaluation indicator system and evaluation method are effective and practical.展开更多
文摘Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.
文摘A method with the fuzzy entropy for measuring fuzziness to fuzzy problem in rough sets is proposed. A new sort of the fuzzy entropy is given. The calculating formula and the equivalent expression method with the fuzzy entropy in rough sets based on equivalence relation are provided, and the properties of the fuzzy entropy are proved. The fuzzy entropy based on equivalent relation is extended to generalize the fuzzy entropy based on general binary relation, and the calculating formula and the equivalent expression of the generalized fuzzy entropy are also given. Finally, an example illustrates the way for getting the fuzzy entropy. Results show that the fuzzy entropy can conveniently measure the fuzziness in rough sets.
基金Supported by the National Natural Science Foundation of China（6147323961175044） Supported by the Fundamental Research Funds for the Central Universities of China（2682014ZT28）
文摘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.
文摘The main factors deciding the compressive strength of binder backfill body are tailing density and binder dosage in binder backfill materials. Based on the antecedent of certain pulp density, the method of increasing the tailing density and reducing the binder dosage, or the manner of cutting down the tailing density and gaining the binder dosage are taken to guarantee the strength of backfill body. The problem that should be solved is how to determine the tailing density and the binder dosage rationally. This paper tries to realize the correct selection of the tailing density and the binder dosage in computer with the method of fuzzy mathematics.
文摘A new image recognition method based on fuzzy rough sets theory is proposed, and its implementation discussed. The performance of this method as applied to ferrography image recognition is evaluated. It is shown that the new method gives better results than fuzzy or rough sets method when used alone.
文摘In this paper, category GIFS of generalized intuitionistic fuzzy sets(GIF) is built up. Topoi properties of category GIFS are studied. Firstly, it is proved that the category GIFS has all topoi properties except that it has no subobject classifiers, Secondly, it is proved that the category GIFS has middle object and consequently GIFS is a weak topos. Thirdly, by the use of theory of weak topos GIFS, the power object of an object in GIFS is studied.
基金supported by the Fundamental Research Funds for the Central Universities under Grants No.ZYGX2014J051 and No.ZYGX2014J066Science and Technology Projects in Sichuan Province under Grants No.2015JY0178,No.2016FZ0002,No.2014GZ0109,No.2015KZ002 and No.2015JY0030China Postdoctoral Science Foundation under Grant No.2015M572464
文摘At present, most of the association rules algorithms are based on the Boolean attribute and single-level association rules mining. But data of the real world has various types, the multi-level and quantitative attributes are got more and more attention. And the most important step is to mine frequent sets. In this paper, we propose an algorithm that is called fuzzy multiple-level association （FMA） rules to mine frequent sets. It is based on the improved Eclat algorithm that is different to many researchers’ proposed algorithms thatused the Apriori algorithm. We analyze quantitative data’s frequent sets by using the fuzzy theory, dividing the hierarchy of concept and softening the boundary of attributes’ values and frequency. In this paper, we use the vertical-style data and the improved Eclat algorithm to describe the proposed method, we use this algorithm to analyze the data of Beijing logistics route. Experiments show that the algorithm has a good performance, it has better effectiveness and high efficiency.
文摘The fuzzy static and dynamic random phenomena in an abstract separable Banach space is discussed in this paper. The representation theorems for fuzzy set valued random sets, fuzzy random elements and fuzzy set valued stochastic processes are obtained.
文摘In power production,gas turbines are commonly used components that generate high amount of energy depending on size and weight.They function as integral parts of helicopters,aircrafts,trains,ships,electrical generators,and tanks.Notably,many researchers are focusing on the design,operation,and maintenance of gas turbines.The focal point of this paper is a DEMATEL approach based on fuzzy sets,with the attempt to use these fuzzy sets explicitly.Using this approach,the cause–effect diagram of gas turbine failures expressed in the literature is generated and aimed to create a perspective for operators.The results of the study show that,"connecting shaft has been broken between turbine and gear box"selected the most important cause factor and"sufficient pressure fuel does not come for fuel pump"is selected the most important effect factor,according to the experts.
基金Supported by the Aeronautical Science Foundation(20115868009)the Open Project Program of Key Laboratory of Intelligent Computing&Information Processing of Ministry of Education in Xiangtan University(2011ICIP04)+1 种基金the Program of 211 Innovation Engineering on Information in Xiamen University(2009-2011)the College Students Innovation Training Plan of Xianmen University~~
文摘Although the concept of interval fuzzy set and its properties have been defined, its three theorems and their effectiveness are not proved. Therefore, the knowledge presentation and its operation rules of interval fuzzy set are studied firstly, and then the cut set of interval fuzzy set is proposed. Moreover, the decomposition theo- rem, the representation theorem and the extension theorem of interval fuzzy set are presented. Finally, examples are given to demonstrate that the classical fuzzy set is a special case of interval fuzzy set and interval fuzzy set is an effective expansion of the classical fuzzy set.
文摘A rough set based fuzzy neural network algorithm is proposed to solve the problem of pattern recognition. The least square algorithm (LSA) is used in the learning process of fuzzy neural network to obtain the performance of global convergence. In addition, the numbers of rules and the initial weights and structure of fuzzy neural networks are difficult to determine. Here rough sets are introduced to decide the numbers of rules and original weights. Finally, experiment results show the algorithm may get better effect than the BP algorithm.
基金Supported by the National Natural Science Foundation of China under Grant No 61671142the Fundamental Research Funds for the Central Universities under Grant No 02190022117021
文摘Ensemble learning for anomaly detection of data structured into a complex network has been barely studied due to the inconsistent performance of complex network characteristics and the lack of inherent objective function. We propose the intuitionistic fuzzy set（IFS）-based anomaly detection, a new two-phase ensemble method for anomaly detection based on IFS, and apply it to the abnormal behavior detection problem in temporal complex networks.Firstly, it constructs the IFS of a single network characteristic, which quantifies the degree of membership,non-membership and hesitation of each network characteristic to the defined linguistic variables so that makes the unuseful or noise characteristics become part of the detection. To build an objective intuitionistic fuzzy relationship, we propose a Gaussian distribution-based membership function which gives a variable hesitation degree. Then, for the fuzzification of multiple network characteristics, the intuitionistic fuzzy weighted geometric operator is adopted to fuse multiple IFSs and to avoid the inconsistence of multiple characteristics. Finally, the score function and precision function are used to sort the fused IFS. Finally, we carry out extensive experiments on several complex network datasets for anomaly detection, and the results demonstrate the superiority of our method to state-of-the-art approaches, validating the effectiveness of our method.
基金Supported by the National Natural Science Foundation of China (No. 69803007)
文摘This paper gives the definition of λ-cut sets and studies the structure of fuzzy rough sets. Based on the concept of rough sets, this paper proposes the representation theorem of fuzzy rough sets.
文摘Scheme evaluation and selection is an optimum selecting and sequencing problem with multi-objective and multi-level. It can’t follow single objective function or rule. Meanwhile,these objectives are coupled with each other and the attribution information is fuzzy also. It is necessary to find an effective evaluation method which can consider all conditions and restrictions. In this paper,AHP and rough set theory are applied to fuzzy optimization to determine important weight of each attribution. The rough set fuzzy optimum selection is used to eliminate the useless information. Autonomous underwater vehicle (AUV) is large-scale systems with many coupled design variables and objective functions. Their scheme evaluation and selection are very important,which relate to multiple factors,such as reliability; security,service time; the lifecycle,etc. Results of application in torpedo design indicate that this method is feasible.
基金The National Natural Science Foundation of China (No60474022)
文摘Residuated lattice is an important non-classical logic algebra, and L-fuzzy rough set based on residuated lattice can describe the information with incompleteness, fuzziness and uncomparativity in information systems. In this paper, the representation theorems of L-fuzzy rough sets based on residuated lattice are given. The properties and axiomatic definition of the lower and upper approximarion operators in L-fuzzy rough sets are discussed.
基金Supported by the Provincial Government Decision-making Tender Subject(2013B318)Supported by the Educational Committee of Henan Province of China(15A520004)
文摘Optimal route selection is an important function of vehicle trac flow guidance system. Its core is to determine the index weight for measuring the route merits and to determine the evaluation method for selecting route. In this paper, subjective weighting method which relies on driver preference is used to determine the weight and the paper proposes the multi-criteria weighted decision method based on vague sets for selecting the optimal route. Examples show that, the usage of vague sets to describe route index value can provide more decision-making information for route selection.
基金supported by the National Natural Science Foundation of China (Project Nos.61273242,61403317)Science and Technology Plan of Sichuan province (Project No.2017015)Service Science and Innovation Key Laboratory of Sichuan Province (KL1701)
文摘The maintenance window scheme(MWS) is one of the most important railway transportation organizational plans and plays an important role in ensuring railway operational safety. However, MWS setting is a very complicated process, and most countries currently do so with the help of a computer-aided decision system. In general, a decision system can generate multiple alternatives for MWS within an acceptable time. Therefore, how to choose the best option from the alternatives is a vital decision. This paper presents a novel framework for MWS evaluation based on the Chinese railway system. Specifically, the requirements of each department related to MWS setting are analysed, and we construct an evaluation indicator system for MWS based on the preferences of different departments. Then, we apply the fuzzy soft set theory to MWS evaluation, a method that not only effectively deals with evaluation of uncertain information, but also gives flexibility for experts to input their subjective judgment.Additionally, using the ‘‘AND’’ operation of soft set theory allows combing evaluation information from multiple evaluators to give comprehensive results. Finally, a case study illustrates the proposed framework, showing that the proposed evaluation indicator system and evaluation method are effective and practical.
