Nowadays, picture fuzzy set theory is a flourishing field in mathematics with uncertainty by incorporating the concept of positive, negative and neutral membership degrees of an object. A traditional crisp relation re...Nowadays, picture fuzzy set theory is a flourishing field in mathematics with uncertainty by incorporating the concept of positive, negative and neutral membership degrees of an object. A traditional crisp relation represents the satisfaction or the dissatisfaction of relationship, connection or correspondence between the objects of two or more sets. However, there are some problems that can’t be solved through classical relationships, such as the relationship between two objects being vague. In those situations, picture fuzzy relation over picture fuzzy sets is an important and powerful concept which is suitable for describing correspondences between two vague objects. It represents the strength of association of the elements of picture fuzzy sets. It plays an important role in picture fuzzy modeling, inference and control system and also has important applications in relational databases, approximate reasoning, preference modeling, medical diagnosis, etc. In this article, we define picture fuzzy relations over picture fuzzy sets, including some other fundamental definitions with illustrations. The max-min and min-max compositions of picture fuzzy relations are defined in the light of picture fuzzy sets and discussed some properties related to them. The reflexivity, symmetry and transitivity of a picture fuzzy relation are described over a picture fuzzy set. Finally, various properties are explored related to the picture fuzzy relations over a picture fuzzy set.展开更多
Developing and optimizing fuzzy relation equations are of great relevance in system modeling,which involves analysis of numerous fuzzy rules.As each rule varies with respect to its level of influence,it is advocated t...Developing and optimizing fuzzy relation equations are of great relevance in system modeling,which involves analysis of numerous fuzzy rules.As each rule varies with respect to its level of influence,it is advocated that the performance of a fuzzy relation equation is strongly related to a subset of fuzzy rules obtained by removing those without significant relevance.In this study,we establish a novel framework of developing granular fuzzy relation equations that concerns the determination of an optimal subset of fuzzy rules.The subset of rules is selected by maximizing their performance of the obtained solutions.The originality of this study is conducted in the following ways.Starting with developing granular fuzzy relation equations,an interval-valued fuzzy relation is determined based on the selected subset of fuzzy rules(the subset of rules is transformed to interval-valued fuzzy sets and subsequently the interval-valued fuzzy sets are utilized to form interval-valued fuzzy relations),which can be used to represent the fuzzy relation of the entire rule base with high performance and efficiency.Then,the particle swarm optimization(PSO)is implemented to solve a multi-objective optimization problem,in which not only an optimal subset of rules is selected but also a parameterεfor specifying a level of information granularity is determined.A series of experimental studies are performed to verify the feasibility of this framework and quantify its performance.A visible improvement of particle swarm optimization(about 78.56%of the encoding mechanism of particle swarm optimization,or 90.42%of particle swarm optimization with an exploration operator)is gained over the method conducted without using the particle swarm optimization algorithm.展开更多
The study area, located in the southeast of Tibet along the Sichuan-Tibet highway, is a part of Palongzangbu River basin where mountain hazards take place frequently. On the ground of field surveying, historical data ...The study area, located in the southeast of Tibet along the Sichuan-Tibet highway, is a part of Palongzangbu River basin where mountain hazards take place frequently. On the ground of field surveying, historical data and previous research, a total of 31 debris flow gullies are identified in the study area and 5 factors are chosen as main parameters for evaluating the hazard of debris flows in this study. Spatial analyst functions of geographic information system （GIS） are utilized to produce debris flow inventory and parameter maps. All data are built into a spatial database for evaluating debris flow hazard. Integrated with GIS techniques,the fuzzy relation method is used to calculate the strength of relationship between debris flow inventory and parameters of the database. With this methodology,a hazard map of debris flows is produced. According to this map,6.6% of the study area is classified as very high hazard, 7.3% as high hazard,8.4% as moderate hazard,32. 1% as low hazard and 45.6% as very low hazard or non-hazard areas. After validating the results, this methodology is ultimately confirmed to be available.展开更多
In this paper,the new theory frame and practical methhod for determining all the minimum solutions of Fuzzy matrix equation and transitive closure of Fuzzy relation is described,and it has been carried out on the mier...In this paper,the new theory frame and practical methhod for determining all the minimum solutions of Fuzzy matrix equation and transitive closure of Fuzzy relation is described,and it has been carried out on the miero-computer quickly and accurately.展开更多
This paper deals with the fuzzy information processing method in the research of the relationship between two variables or among multi-variables, with the undetermined or fuzzy features, different from that in the tr...This paper deals with the fuzzy information processing method in the research of the relationship between two variables or among multi-variables, with the undetermined or fuzzy features, different from that in the traditional statistical method. The reliability and effectiveness of the method have been tested and confirmed in the numerical simulation for a set of man-made data of precursory anomalous parameters and earthquake elements. Finally the relation between the actual monthly frequency of small earthquakes occurring in Huoshan, Anhui Province, China and the magnitude of future stronger earthquakes, as two variables, has been analyzed by the method. It seems to the authors that more reasonable and perfect results could be given with a quantitative analysis of accession degree in fuzzy mathematics by using this method than that of traditional statistical correlation analysis.展开更多
The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzz...The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzzy relation is decomposed into two parts as principal sub-matrices and secondary sub-matrices; an r-ary symmetrical-valued type-2 fuzzy relation model and its corresponding symmetrical-valued type-2 fuzzy relation equation model are established. Then, two algorithms are developed for solving type-2 fuzzy relation equations, one of which gives a theoretical description for general type-2 fuzzy relation equations; the other one can find all the solutions to the symmetrical-valued ones. The results can improve designing type-2 fuzzy controllers, because it provides knowledge to search the optimal solutions or to find the reason if there is no solution. Finally some numerical examples verify the correctness of the results/algorithms.展开更多
We investigate the decision-making problem with a finite set of alternatives,in which the decision information takes the form of a fuzzy preference relation. We develop asimple and practical approach to obtaining the ...We investigate the decision-making problem with a finite set of alternatives,in which the decision information takes the form of a fuzzy preference relation. We develop asimple and practical approach to obtaining the priority vector of a fuzzy preference relation. Theprominent characteristic of the developed approach is that the priority vector can generally beobtained by a simple formula, which is derived from a quadratic programming model. We utilize theconsistency ratio to check the consistency of fuzzy preference relation. If the fuzzy preferencerelation is of unacceptable consistency, then we can return it to the decision maker to reconsiderstructuring a new fuzzy preference relation until the fuzzy preference relation with acceptableconsistency is obtained. We finally illustrate the priority approach by two numerical examples. Thenumerical results show that the developed approach is straightforward, effective, and can easily beperformed on a computer.展开更多
In rough set theory, crisp and/or fuzzy binary relations play an important role in both constructive and axiomatic considerations of various generalized rough sets. This paper considers the uniqueness problem of the ...In rough set theory, crisp and/or fuzzy binary relations play an important role in both constructive and axiomatic considerations of various generalized rough sets. This paper considers the uniqueness problem of the （fuzzy） relation in some generalized rough set model. Our results show that by using the axiomatic approach, the （fuzzy） relation determined by （fuzzy） approximation operators is unique in some （fuzzy） double-universe model.展开更多
Purpose–This paper aims to consider a soft computing approach to pattern classification using the basic tools of fuzzy relational calculus(FRC)and genetic algorithm(GA).Design/methodology/approach–The paper introduc...Purpose–This paper aims to consider a soft computing approach to pattern classification using the basic tools of fuzzy relational calculus(FRC)and genetic algorithm(GA).Design/methodology/approach–The paper introduces a new interpretation of multidimensional fuzzy implication(MFI)to represent the author’s knowledge about the training data set.It also considers the notion of a fuzzy pattern vector(FPV)to handle the fuzzy information granules of the quantized pattern space and to represent a population of training patterns in the quantized pattern space.The construction of the pattern classifier is essentially based on the estimate of a fuzzy relation Ri between the antecedent clause and consequent clause of each one-dimensional fuzzy implication.For the estimation of Ri floating point representation of GA is used.Thus,a set of fuzzy relations is formed from the new interpretation of MFI.This set of fuzzy relations is termed as the core of the pattern classifier.Once the classifier is constructed the non-fuzzy features of a test pattern can be classified.Findings–The performance of the proposed scheme is tested on synthetic data.Subsequently,the paper uses the proposed scheme for the vowel classification problem of an Indian language.In all these case studies the recognition score of the proposed method is very good.Finally,a benchmark of performance is established by considering Multilayer Perceptron(MLP),Support Vector Machine(SVM)and the proposed method.The Abalone,Hosse colic and Pima Indians data sets,obtained from UCL database repository are used for the said benchmark study.The benchmark study also establishes the superiority of the proposed method.Originality/value–This new soft computing approach to pattern classification is based on a new interpretation of MFI and a novel notion of FPV.A set of fuzzy relations which is the core of the pattern classifier,is estimated using floating point GA and very effective classification of patterns under vague and imprecise environment is performed.This new approach to pattern classification avoids the curse of high dimensionality of feature vector.It can provide multiple classifications under overlapped classes.展开更多
In 1930 Szpilrajn proved that any strict partial order can be embedded in a strict linear order. This theorem was later refined by Dushnik and Miller (1941), Hansson (1968), Suzumura (1976), Donaldson and Weymark (199...In 1930 Szpilrajn proved that any strict partial order can be embedded in a strict linear order. This theorem was later refined by Dushnik and Miller (1941), Hansson (1968), Suzumura (1976), Donaldson and Weymark (1998), Bossert (1999).Particularly Suzumura introduced the important concept of compatible extension of a (crisp) relation. These extension theorems have an important role in welfare economics. In particular Szpilrajn theorem is the main tool for proving a known theorem of Richter that establishes the equivalence between rational and congruous consumers. In 1999 Duggan proved a general extension theorem that contains all these results.In this paper we introduce the notion of compatible extension of a fuzzy relation and we prove an extension theorem for fuzzy relations. Our result generalizes to fuzzy set theory the main part of Duggan's theorem. As applications we obtain fuzzy versions of the theorems of Szpilrajn, Hansson and Suzumura. We also prove that an asymmetric and transitive fuzzy relation has a compatible extension that is total, asymmetric and transitive.Our results can be useful in the theory of fuzzy consumers. We can prove that any rational fuzzy consumer is congruous, extending to a fuzzy context a part of Richter's theorem. To prove that a congruous fuzzy consumer is rational remains an open problem. A proof of this result can somehow use a fuzzy version of Szpilrajn theorem.展开更多
This paper concentrates on the problem of data redundancy under the extended-possibility-based model. Based on the information gain in data classification, a measure - relation redundancy - is proposed to evaluate the...This paper concentrates on the problem of data redundancy under the extended-possibility-based model. Based on the information gain in data classification, a measure - relation redundancy - is proposed to evaluate the degree of a given relation being redundant in whole. The properties of relation redundancy are also investigated. This new measure is useful in dealing with data redundancy.展开更多
An approach is proposed to solve the problem how to obtain the priorities from interval fuzzy preference relations. Firstly, another expression of interval numbers is given. Then, some basic definitions on consistency...An approach is proposed to solve the problem how to obtain the priorities from interval fuzzy preference relations. Firstly, another expression of interval numbers is given. Then, some basic definitions on consistency and weak transitivity of real and interval fuzzy preference relations are described. Based on these definitions, a two-phase process for determining the priorities from interval fuzzy preference relations is presented. Finally, two exam- ples are used to illustrate the use of the proposed approach.展开更多
In order to enhance catalytic combustion efficiency, a premixed hydrogen /air combustion model of the micro turbine engine is established under different excess air ratio, inlet velocity and heat transfer coefficient....In order to enhance catalytic combustion efficiency, a premixed hydrogen /air combustion model of the micro turbine engine is established under different excess air ratio, inlet velocity and heat transfer coefficient. And effects of inlet velocity, excess air coefficient and heat transfer coefficient on the catalytic combustion efficiency of the hydrogen have been analyzed by the FLUENT with CHEMKIN reaction mechanisms and the fuzzy grey relation theory. It is showed that inlet velocity has a more intuitive influence on the catalytic combustion efficiency of the hydrogen. A higher efficiency can be obtained with a lower inlet velocity. The optimum excess air coefficient is in the range of 0.94 to 1.0, the catalytic combustion efficiency of the hydrogen will be declined if the excess air coefficient exceeded 1.0. The effect of heat transfer coefficient on the catalytic combustion efficiency of the hydrogen mainly embodies in the case of the excess air coefficient exceeded 1.0, however, the effect will be declined if the heat transfer coefficient exceeded 4.0. The fuzzy grey relation degrees of the inlet velocity, heat transfer coefficient and excess air coefficient on the catalytic combustion efficiency of the hydrogen are 0.640945, 0.633214 and 0.547892 respectively.展开更多
Intuitionistic fuzzy preference relation(IFPR) is a suitable technique to express fuzzy preference information by decision makers(DMs). This paper aims to provide a group decision making method where DMs use the IFPRs...Intuitionistic fuzzy preference relation(IFPR) is a suitable technique to express fuzzy preference information by decision makers(DMs). This paper aims to provide a group decision making method where DMs use the IFPRs to indicate their preferences with uncertain weights. To begin with, a model to derive weight vectors of alternatives from IFPRs based on multiplicative consistency is presented. Specifically, for any IFPR,by minimizing its absolute deviation from the corresponding consistent IFPR, the weight vectors are generated. Secondly,a method to determine relative weights of DMs depending on preference information is developed. After that we prioritize alternatives based on the obtained weights considering the risk preference of DMs. Finally, this approach is applied to the problem of technical risks assessment of armored equipment to illustrate the applicability and superiority of the proposed method.展开更多
Based on the analyses of existing preference group decision-making(PGDM)methods with intuitionistic fuzzy preference relations(IFPRs),we present a new PGDM framework with incomplete IFPRs.A generalized multiplicative ...Based on the analyses of existing preference group decision-making(PGDM)methods with intuitionistic fuzzy preference relations(IFPRs),we present a new PGDM framework with incomplete IFPRs.A generalized multiplicative consistent for IFPRs is defined,and a mathematical programming model is constructed to supplement the missing values in incomplete IFPRs.Moreover,in this study,another mathematical programming model is constructed to improve the consistency level of unacceptably multiplicative consistent IFPRs.For group decisionmaking(GDM)with incomplete IFPRs,three reliable sources influencing the weights of experts are identified.Subsequently,a method for determining the weights of experts is developed by simultaneously considering three reliable sources.Furthermore,a targeted consensus process(CPR)is developed in this study with reference to the actual situation of the consensus level of each IFPR.Meanwhile,in response to the proposed multiplicative consistency definition,a novel method for determining the optimal priority weights of alternatives is redefined.Lastly,based on the above theory,a novel GDM method with incomplete IFPRs is developed,and the comparative and sensitivity analysis results demonstrate the utility and superiority of this work.展开更多
This paper presents a kind of fuzzy consistent relation, discusses its main properties - center-division transitivity, describes its combined operation. At the same time, introduce the applications of fuzzy consisten...This paper presents a kind of fuzzy consistent relation, discusses its main properties - center-division transitivity, describes its combined operation. At the same time, introduce the applications of fuzzy consistent relation in decision making.展开更多
To overcome the subjectivity of experts in the process of risk response scheme selection, according to the theory of group decision making, a selection method and flow of the risk response schemes for a mining project...To overcome the subjectivity of experts in the process of risk response scheme selection, according to the theory of group decision making, a selection method and flow of the risk response schemes for a mining project was proposed based on fuzzy preference relation and consistency induced ordered weighted averaging (C-IOWA) operator,which can overcome the loss of information in the process of group decision making to a great degree, and improve its efficiency and quality.A numeric example was introduced to illustrate the application of the method, also validating the method as scientific and practicable.展开更多
A fuzzy clustering analysis model based on the quotient space is proposed. Firstly, the conversion from coarse to fine granularity and the hierarchical structure are used to reduce the multidimensional samples. Second...A fuzzy clustering analysis model based on the quotient space is proposed. Firstly, the conversion from coarse to fine granularity and the hierarchical structure are used to reduce the multidimensional samples. Secondly, the fuzzy compatibility relation matrix of the model is converted into fuzzy equivalence relation matrix. Finally, the diagram of clustering genealogy is generated according to the fuzzy equivalence relation matrix, which enables the dynamic selection of different thresholds to effectively solve the problem of cluster analysis of the samples with multi-dimensional attributes.展开更多
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
1 INTRODUCTIONIt is well known that much information obtained from biological system is semi-quantitative and linguistic.Experience is a very important source of information,butit is rather subjective,for example,“if...1 INTRODUCTIONIt is well known that much information obtained from biological system is semi-quantitative and linguistic.Experience is a very important source of information,butit is rather subjective,for example,“if the dilution rate is low and growth rate is me-dium then the specific yield is medium”.It is seldom possible to treat this kind ofinformation by using conventional mathematics.Fuzzy set theory can allow effectiveuse of the semi-quantitative and linguistic information. The main application area of fuzzy set theory seems to be modeling of fuzzy rea-soning expressed in natural language,such as the example illustrated above.Zadeh展开更多
文摘Nowadays, picture fuzzy set theory is a flourishing field in mathematics with uncertainty by incorporating the concept of positive, negative and neutral membership degrees of an object. A traditional crisp relation represents the satisfaction or the dissatisfaction of relationship, connection or correspondence between the objects of two or more sets. However, there are some problems that can’t be solved through classical relationships, such as the relationship between two objects being vague. In those situations, picture fuzzy relation over picture fuzzy sets is an important and powerful concept which is suitable for describing correspondences between two vague objects. It represents the strength of association of the elements of picture fuzzy sets. It plays an important role in picture fuzzy modeling, inference and control system and also has important applications in relational databases, approximate reasoning, preference modeling, medical diagnosis, etc. In this article, we define picture fuzzy relations over picture fuzzy sets, including some other fundamental definitions with illustrations. The max-min and min-max compositions of picture fuzzy relations are defined in the light of picture fuzzy sets and discussed some properties related to them. The reflexivity, symmetry and transitivity of a picture fuzzy relation are described over a picture fuzzy set. Finally, various properties are explored related to the picture fuzzy relations over a picture fuzzy set.
基金supported by the National Natural Sci-ence Foundation of China(62006184,62076189,61873277).
文摘Developing and optimizing fuzzy relation equations are of great relevance in system modeling,which involves analysis of numerous fuzzy rules.As each rule varies with respect to its level of influence,it is advocated that the performance of a fuzzy relation equation is strongly related to a subset of fuzzy rules obtained by removing those without significant relevance.In this study,we establish a novel framework of developing granular fuzzy relation equations that concerns the determination of an optimal subset of fuzzy rules.The subset of rules is selected by maximizing their performance of the obtained solutions.The originality of this study is conducted in the following ways.Starting with developing granular fuzzy relation equations,an interval-valued fuzzy relation is determined based on the selected subset of fuzzy rules(the subset of rules is transformed to interval-valued fuzzy sets and subsequently the interval-valued fuzzy sets are utilized to form interval-valued fuzzy relations),which can be used to represent the fuzzy relation of the entire rule base with high performance and efficiency.Then,the particle swarm optimization(PSO)is implemented to solve a multi-objective optimization problem,in which not only an optimal subset of rules is selected but also a parameterεfor specifying a level of information granularity is determined.A series of experimental studies are performed to verify the feasibility of this framework and quantify its performance.A visible improvement of particle swarm optimization(about 78.56%of the encoding mechanism of particle swarm optimization,or 90.42%of particle swarm optimization with an exploration operator)is gained over the method conducted without using the particle swarm optimization algorithm.
文摘The study area, located in the southeast of Tibet along the Sichuan-Tibet highway, is a part of Palongzangbu River basin where mountain hazards take place frequently. On the ground of field surveying, historical data and previous research, a total of 31 debris flow gullies are identified in the study area and 5 factors are chosen as main parameters for evaluating the hazard of debris flows in this study. Spatial analyst functions of geographic information system （GIS） are utilized to produce debris flow inventory and parameter maps. All data are built into a spatial database for evaluating debris flow hazard. Integrated with GIS techniques,the fuzzy relation method is used to calculate the strength of relationship between debris flow inventory and parameters of the database. With this methodology,a hazard map of debris flows is produced. According to this map,6.6% of the study area is classified as very high hazard, 7.3% as high hazard,8.4% as moderate hazard,32. 1% as low hazard and 45.6% as very low hazard or non-hazard areas. After validating the results, this methodology is ultimately confirmed to be available.
文摘In this paper,the new theory frame and practical methhod for determining all the minimum solutions of Fuzzy matrix equation and transitive closure of Fuzzy relation is described,and it has been carried out on the miero-computer quickly and accurately.
文摘This paper deals with the fuzzy information processing method in the research of the relationship between two variables or among multi-variables, with the undetermined or fuzzy features, different from that in the traditional statistical method. The reliability and effectiveness of the method have been tested and confirmed in the numerical simulation for a set of man-made data of precursory anomalous parameters and earthquake elements. Finally the relation between the actual monthly frequency of small earthquakes occurring in Huoshan, Anhui Province, China and the magnitude of future stronger earthquakes, as two variables, has been analyzed by the method. It seems to the authors that more reasonable and perfect results could be given with a quantitative analysis of accession degree in fuzzy mathematics by using this method than that of traditional statistical correlation analysis.
基金This work was partially supported by the Natural Science Foundation of China （No. 611 74094） the Tianjin Natural Science Foundation of China （No. 13JCYBJC1 7400） the Program for New Century Excellent Talents in University of China （No. NCET-10-0506）.
文摘The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzzy relation is decomposed into two parts as principal sub-matrices and secondary sub-matrices; an r-ary symmetrical-valued type-2 fuzzy relation model and its corresponding symmetrical-valued type-2 fuzzy relation equation model are established. Then, two algorithms are developed for solving type-2 fuzzy relation equations, one of which gives a theoretical description for general type-2 fuzzy relation equations; the other one can find all the solutions to the symmetrical-valued ones. The results can improve designing type-2 fuzzy controllers, because it provides knowledge to search the optimal solutions or to find the reason if there is no solution. Finally some numerical examples verify the correctness of the results/algorithms.
文摘We investigate the decision-making problem with a finite set of alternatives,in which the decision information takes the form of a fuzzy preference relation. We develop asimple and practical approach to obtaining the priority vector of a fuzzy preference relation. Theprominent characteristic of the developed approach is that the priority vector can generally beobtained by a simple formula, which is derived from a quadratic programming model. We utilize theconsistency ratio to check the consistency of fuzzy preference relation. If the fuzzy preferencerelation is of unacceptable consistency, then we can return it to the decision maker to reconsiderstructuring a new fuzzy preference relation until the fuzzy preference relation with acceptableconsistency is obtained. We finally illustrate the priority approach by two numerical examples. Thenumerical results show that the developed approach is straightforward, effective, and can easily beperformed on a computer.
基金Supported by the National Natural Science Foundation of China(11171308,61379018,51305400)
文摘In rough set theory, crisp and/or fuzzy binary relations play an important role in both constructive and axiomatic considerations of various generalized rough sets. This paper considers the uniqueness problem of the （fuzzy） relation in some generalized rough set model. Our results show that by using the axiomatic approach, the （fuzzy） relation determined by （fuzzy） approximation operators is unique in some （fuzzy） double-universe model.
文摘Purpose–This paper aims to consider a soft computing approach to pattern classification using the basic tools of fuzzy relational calculus(FRC)and genetic algorithm(GA).Design/methodology/approach–The paper introduces a new interpretation of multidimensional fuzzy implication(MFI)to represent the author’s knowledge about the training data set.It also considers the notion of a fuzzy pattern vector(FPV)to handle the fuzzy information granules of the quantized pattern space and to represent a population of training patterns in the quantized pattern space.The construction of the pattern classifier is essentially based on the estimate of a fuzzy relation Ri between the antecedent clause and consequent clause of each one-dimensional fuzzy implication.For the estimation of Ri floating point representation of GA is used.Thus,a set of fuzzy relations is formed from the new interpretation of MFI.This set of fuzzy relations is termed as the core of the pattern classifier.Once the classifier is constructed the non-fuzzy features of a test pattern can be classified.Findings–The performance of the proposed scheme is tested on synthetic data.Subsequently,the paper uses the proposed scheme for the vowel classification problem of an Indian language.In all these case studies the recognition score of the proposed method is very good.Finally,a benchmark of performance is established by considering Multilayer Perceptron(MLP),Support Vector Machine(SVM)and the proposed method.The Abalone,Hosse colic and Pima Indians data sets,obtained from UCL database repository are used for the said benchmark study.The benchmark study also establishes the superiority of the proposed method.Originality/value–This new soft computing approach to pattern classification is based on a new interpretation of MFI and a novel notion of FPV.A set of fuzzy relations which is the core of the pattern classifier,is estimated using floating point GA and very effective classification of patterns under vague and imprecise environment is performed.This new approach to pattern classification avoids the curse of high dimensionality of feature vector.It can provide multiple classifications under overlapped classes.
文摘In 1930 Szpilrajn proved that any strict partial order can be embedded in a strict linear order. This theorem was later refined by Dushnik and Miller (1941), Hansson (1968), Suzumura (1976), Donaldson and Weymark (1998), Bossert (1999).Particularly Suzumura introduced the important concept of compatible extension of a (crisp) relation. These extension theorems have an important role in welfare economics. In particular Szpilrajn theorem is the main tool for proving a known theorem of Richter that establishes the equivalence between rational and congruous consumers. In 1999 Duggan proved a general extension theorem that contains all these results.In this paper we introduce the notion of compatible extension of a fuzzy relation and we prove an extension theorem for fuzzy relations. Our result generalizes to fuzzy set theory the main part of Duggan's theorem. As applications we obtain fuzzy versions of the theorems of Szpilrajn, Hansson and Suzumura. We also prove that an asymmetric and transitive fuzzy relation has a compatible extension that is total, asymmetric and transitive.Our results can be useful in the theory of fuzzy consumers. We can prove that any rational fuzzy consumer is congruous, extending to a fuzzy context a part of Richter's theorem. To prove that a congruous fuzzy consumer is rational remains an open problem. A proof of this result can somehow use a fuzzy version of Szpilrajn theorem.
基金Supported by the National Natural Science Foundation of China(No.70231010/70321001)the Bilateral Scientific and Technological Cooperation between China and Flanders (No.174B0201)
文摘This paper concentrates on the problem of data redundancy under the extended-possibility-based model. Based on the information gain in data classification, a measure - relation redundancy - is proposed to evaluate the degree of a given relation being redundant in whole. The properties of relation redundancy are also investigated. This new measure is useful in dealing with data redundancy.
基金supported by the National Natural Science Foundation for Excellent Innovation Research Group of China (70721001)the National Natural Science Foundation of China (90924016)Fundamental Research Fund for Northeastern University (N090606001)
文摘An approach is proposed to solve the problem how to obtain the priorities from interval fuzzy preference relations. Firstly, another expression of interval numbers is given. Then, some basic definitions on consistency and weak transitivity of real and interval fuzzy preference relations are described. Based on these definitions, a two-phase process for determining the priorities from interval fuzzy preference relations is presented. Finally, two exam- ples are used to illustrate the use of the proposed approach.
基金Project(51776062) supported by the National Natural Science Foundation of ChinaProject(201208430262) supported by the National Studying Abroad Foundation Project of the China Scholarship Council
文摘In order to enhance catalytic combustion efficiency, a premixed hydrogen /air combustion model of the micro turbine engine is established under different excess air ratio, inlet velocity and heat transfer coefficient. And effects of inlet velocity, excess air coefficient and heat transfer coefficient on the catalytic combustion efficiency of the hydrogen have been analyzed by the FLUENT with CHEMKIN reaction mechanisms and the fuzzy grey relation theory. It is showed that inlet velocity has a more intuitive influence on the catalytic combustion efficiency of the hydrogen. A higher efficiency can be obtained with a lower inlet velocity. The optimum excess air coefficient is in the range of 0.94 to 1.0, the catalytic combustion efficiency of the hydrogen will be declined if the excess air coefficient exceeded 1.0. The effect of heat transfer coefficient on the catalytic combustion efficiency of the hydrogen mainly embodies in the case of the excess air coefficient exceeded 1.0, however, the effect will be declined if the heat transfer coefficient exceeded 4.0. The fuzzy grey relation degrees of the inlet velocity, heat transfer coefficient and excess air coefficient on the catalytic combustion efficiency of the hydrogen are 0.640945, 0.633214 and 0.547892 respectively.
基金partly supported by the National Natural Science Foundation of China(71371053)the Social Science Foundation of Fujian Province(FJ2015C111)
文摘Intuitionistic fuzzy preference relation(IFPR) is a suitable technique to express fuzzy preference information by decision makers(DMs). This paper aims to provide a group decision making method where DMs use the IFPRs to indicate their preferences with uncertain weights. To begin with, a model to derive weight vectors of alternatives from IFPRs based on multiplicative consistency is presented. Specifically, for any IFPR,by minimizing its absolute deviation from the corresponding consistent IFPR, the weight vectors are generated. Secondly,a method to determine relative weights of DMs depending on preference information is developed. After that we prioritize alternatives based on the obtained weights considering the risk preference of DMs. Finally, this approach is applied to the problem of technical risks assessment of armored equipment to illustrate the applicability and superiority of the proposed method.
基金supported by the National Natural Science Foundation of China(Nos.71740021,11861034,and 61966030)the Humanities Social Science Programming Project of Ministry of Education of China(No.20YJA630059)+1 种基金the Natural Science Foundation of Jiangxi Province of China(No.20192BAB207012)the Natural Science Foundation of Qinghai Province of China(No.2019-ZJ-7086).
文摘Based on the analyses of existing preference group decision-making(PGDM)methods with intuitionistic fuzzy preference relations(IFPRs),we present a new PGDM framework with incomplete IFPRs.A generalized multiplicative consistent for IFPRs is defined,and a mathematical programming model is constructed to supplement the missing values in incomplete IFPRs.Moreover,in this study,another mathematical programming model is constructed to improve the consistency level of unacceptably multiplicative consistent IFPRs.For group decisionmaking(GDM)with incomplete IFPRs,three reliable sources influencing the weights of experts are identified.Subsequently,a method for determining the weights of experts is developed by simultaneously considering three reliable sources.Furthermore,a targeted consensus process(CPR)is developed in this study with reference to the actual situation of the consensus level of each IFPR.Meanwhile,in response to the proposed multiplicative consistency definition,a novel method for determining the optimal priority weights of alternatives is redefined.Lastly,based on the above theory,a novel GDM method with incomplete IFPRs is developed,and the comparative and sensitivity analysis results demonstrate the utility and superiority of this work.
文摘This paper presents a kind of fuzzy consistent relation, discusses its main properties - center-division transitivity, describes its combined operation. At the same time, introduce the applications of fuzzy consistent relation in decision making.
文摘To overcome the subjectivity of experts in the process of risk response scheme selection, according to the theory of group decision making, a selection method and flow of the risk response schemes for a mining project was proposed based on fuzzy preference relation and consistency induced ordered weighted averaging (C-IOWA) operator,which can overcome the loss of information in the process of group decision making to a great degree, and improve its efficiency and quality.A numeric example was introduced to illustrate the application of the method, also validating the method as scientific and practicable.
文摘A fuzzy clustering analysis model based on the quotient space is proposed. Firstly, the conversion from coarse to fine granularity and the hierarchical structure are used to reduce the multidimensional samples. Secondly, the fuzzy compatibility relation matrix of the model is converted into fuzzy equivalence relation matrix. Finally, the diagram of clustering genealogy is generated according to the fuzzy equivalence relation matrix, which enables the dynamic selection of different thresholds to effectively solve the problem of cluster analysis of the samples with multi-dimensional attributes.
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1 INTRODUCTIONIt is well known that much information obtained from biological system is semi-quantitative and linguistic.Experience is a very important source of information,butit is rather subjective,for example,“if the dilution rate is low and growth rate is me-dium then the specific yield is medium”.It is seldom possible to treat this kind ofinformation by using conventional mathematics.Fuzzy set theory can allow effectiveuse of the semi-quantitative and linguistic information. The main application area of fuzzy set theory seems to be modeling of fuzzy rea-soning expressed in natural language,such as the example illustrated above.Zadeh
