Feature selection methods rooted in rough sets confront two notable limitations:their high computa-tional complexity and sensitivity to noise,rendering them impractical for managing large-scale and noisy datasets.The ...Feature selection methods rooted in rough sets confront two notable limitations:their high computa-tional complexity and sensitivity to noise,rendering them impractical for managing large-scale and noisy datasets.The primary issue stems from these methods’undue reliance on all samples.To overcome these challenges,we introduce the concept of cross-similarity grounded in a robust fuzzy relation and design a rapid and robust feature selection algorithm.Firstly,we construct a robust fuzzy relation by introducing a truncation parameter.Then,based on this fuzzy relation,we propose the concept of cross-similarity,which emphasizes the sample-to-sample similarity relations that uniquely determine feature importance,rather than considering all such relations equally.After studying the manifestations and properties of cross-similarity across different fuzzy granularities,we propose a forward greedy feature selection algorithm that leverages cross-similarity as the foundation for information measurement.This algorithm significantly reduces the time complexity from O(m2n2)to O(mn2).Experimental findings reveal that the average runtime of five state-of-the-art comparison algorithms is roughly 3.7 times longer than our algorithm,while our algorithm achieves an average accuracy that surpasses those of the five comparison algorithms by approximately 3.52%.This underscores the effectiveness of our approach.This paper paves the way for applying feature selection algorithms grounded in fuzzy rough sets to large-scale gene datasets.展开更多
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
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
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
Currently,the international economic situation is becoming increasingly complex,and there is significant downward pressure on the global economy.In recent years,China’s infrastructure sector has experienced rapid gro...Currently,the international economic situation is becoming increasingly complex,and there is significant downward pressure on the global economy.In recent years,China’s infrastructure sector has experienced rapid growth,with the structure of its power engineering business gradually shifting from traditional infrastructure construction to more diversified areas such as production and operation,as well as emergency repairs.As a result,the transformation of mechanized construction in power transmission and transformation projects has become increasingly urgent.This article proposes a post-evaluation model based on game theory to improve comprehensive weighting and fuzzy grey relational projection sorting,which can be used to evaluate the optimal mechanized construction scheme for power transmission and transformation projects.The model begins by considering the entire lifecycle of power transmission and transformation projects.It constructs a post-evaluation index system that covers the planning and design stage,on-site construction stage,operation and maintenance stage,and the decommissioning and disposal stage,with corresponding calculation methods for each index.The fuzzy grey correlation projection sorting method is then employed to evaluate and rank the construction schemes.To validate the model’s effectiveness,a case study of a power transmission and transformation project in a specific region of China is used.The comprehensive benefits of three proposed mechanized construction schemes are evaluated and compared.According to the evaluation results,Scheme 1 is ranked the highest,with a membership degree of 0.870945,excelling in sustainability.These results suggest that the proposed model can effectively evaluate and make decisions regarding the optimal mechanized construction plan for power transmission and transformation projects.展开更多
A modified definition of fuzzy transitivity is given.Several properties of this new definition are obtained.Effect of these new properties of transitivity on equivalence relations is also studied.
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
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
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
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
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
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
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
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
Fuzziness is one of the general characteristics of human thinking and objective things. Introducing fuzzy techniques into decision-making yields very good results. Fuzzy consistent matrix has many excellent characteri...Fuzziness is one of the general characteristics of human thinking and objective things. Introducing fuzzy techniques into decision-making yields very good results. Fuzzy consistent matrix has many excellent characteristics, especially cen- ter-division transitivity conforming to the reality of the human thinking process in decision-making. This paper presents a new approach for creating fuzzy consistent matrix from mutual supplementary matrix in fuzzy decision-making. At the same time, based on the distance between individual fuzzy consistent matrix and average fuzzy consistent matrix, a kind of combined opera- tion for several fuzzy consistent matrixes is presented which reflects most opinions of experienced experts. Finally, a practical example shows its flexibility and practicability further.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
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
Fuzziness is one of the general characteristics of human thinking and objective things.Fuzzy systems are efficient tools to simulate human thinking and execute fuzzy information processing. This paper discusses severa...Fuzziness is one of the general characteristics of human thinking and objective things.Fuzzy systems are efficient tools to simulate human thinking and execute fuzzy information processing. This paper discusses several fundamental problems on methodology of fuzzy systems briefly,including generalized fuzzy entropy, generalized defuzzification strategies and fuzzy consistent relation.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
基金supported by the Anhui Provincial Department of Education University Research Project(2024AH051375)Research Project of Chizhou University(CZ2022ZRZ06)+1 种基金Anhui Province Natural Science Research Project of Colleges and Universities(2024AH051368)Excellent Scientific Research and Innovation Team of Anhui Colleges(2022AH010098).
文摘Feature selection methods rooted in rough sets confront two notable limitations:their high computa-tional complexity and sensitivity to noise,rendering them impractical for managing large-scale and noisy datasets.The primary issue stems from these methods’undue reliance on all samples.To overcome these challenges,we introduce the concept of cross-similarity grounded in a robust fuzzy relation and design a rapid and robust feature selection algorithm.Firstly,we construct a robust fuzzy relation by introducing a truncation parameter.Then,based on this fuzzy relation,we propose the concept of cross-similarity,which emphasizes the sample-to-sample similarity relations that uniquely determine feature importance,rather than considering all such relations equally.After studying the manifestations and properties of cross-similarity across different fuzzy granularities,we propose a forward greedy feature selection algorithm that leverages cross-similarity as the foundation for information measurement.This algorithm significantly reduces the time complexity from O(m2n2)to O(mn2).Experimental findings reveal that the average runtime of five state-of-the-art comparison algorithms is roughly 3.7 times longer than our algorithm,while our algorithm achieves an average accuracy that surpasses those of the five comparison algorithms by approximately 3.52%.This underscores the effectiveness of our approach.This paper paves the way for applying feature selection algorithms grounded in fuzzy rough sets to large-scale gene datasets.
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.
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.
文摘Currently,the international economic situation is becoming increasingly complex,and there is significant downward pressure on the global economy.In recent years,China’s infrastructure sector has experienced rapid growth,with the structure of its power engineering business gradually shifting from traditional infrastructure construction to more diversified areas such as production and operation,as well as emergency repairs.As a result,the transformation of mechanized construction in power transmission and transformation projects has become increasingly urgent.This article proposes a post-evaluation model based on game theory to improve comprehensive weighting and fuzzy grey relational projection sorting,which can be used to evaluate the optimal mechanized construction scheme for power transmission and transformation projects.The model begins by considering the entire lifecycle of power transmission and transformation projects.It constructs a post-evaluation index system that covers the planning and design stage,on-site construction stage,operation and maintenance stage,and the decommissioning and disposal stage,with corresponding calculation methods for each index.The fuzzy grey correlation projection sorting method is then employed to evaluate and rank the construction schemes.To validate the model’s effectiveness,a case study of a power transmission and transformation project in a specific region of China is used.The comprehensive benefits of three proposed mechanized construction schemes are evaluated and compared.According to the evaluation results,Scheme 1 is ranked the highest,with a membership degree of 0.870945,excelling in sustainability.These results suggest that the proposed model can effectively evaluate and make decisions regarding the optimal mechanized construction plan for power transmission and transformation projects.
文摘A modified definition of fuzzy transitivity is given.Several properties of this new definition are obtained.Effect of these new properties of transitivity on equivalence relations is also studied.
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.
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.
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Project (No. 20040335129) supported by the Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP) China
文摘Fuzziness is one of the general characteristics of human thinking and objective things. Introducing fuzzy techniques into decision-making yields very good results. Fuzzy consistent matrix has many excellent characteristics, especially cen- ter-division transitivity conforming to the reality of the human thinking process in decision-making. This paper presents a new approach for creating fuzzy consistent matrix from mutual supplementary matrix in fuzzy decision-making. At the same time, based on the distance between individual fuzzy consistent matrix and average fuzzy consistent matrix, a kind of combined opera- tion for several fuzzy consistent matrixes is presented which reflects most opinions of experienced experts. Finally, a practical example shows its flexibility and practicability further.
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.
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Fuzziness is one of the general characteristics of human thinking and objective things.Fuzzy systems are efficient tools to simulate human thinking and execute fuzzy information processing. This paper discusses several fundamental problems on methodology of fuzzy systems briefly,including generalized fuzzy entropy, generalized defuzzification strategies and fuzzy consistent relation.
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
