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Picture Fuzzy Relations over Picture Fuzzy Sets
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作者 Mohammad Kamrul Hasan Abeda Sultana Nirmal Kanti Mitra 《American Journal of Computational Mathematics》 2023年第1期161-184,共24页
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
关键词 Picture fuzzy Sets Picture fuzzy relations Picture fuzzy Binary Rela-tions Composition of Picture fuzzy relations
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Priority approach based on quadratic programming model to fuzzy preference relation 被引量:1
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作者 徐泽水 达庆利 陈琦 《Journal of Southeast University(English Edition)》 EI CAS 2005年第1期108-110,共3页
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
关键词 decision making fuzzy preference relation quadratic programming PRIORITY
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Using Fuzzy Relations and GIS Method to Evaluate Debris Flow Hazard 被引量:10
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作者 SONG Shujun ZHANG Baolei +1 位作者 FENG Wenlan ZHOU Wancun 《Wuhan University Journal of Natural Sciences》 EI CAS 2006年第4期875-881,共7页
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
关键词 fuzzy relations geographic information system (GIS) debris flows hazard evaluation
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New approach to determine the priorities from interval fuzzy preference relations 被引量:7
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作者 Qi Yue Zhiping Fan Lihua Shi 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2011年第2期267-273,共7页
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
关键词 interval fuzzy preference relation CONSISTENCY weaktransitivity priority.
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Effects analysis on catalytic combustion characteristic of hydrogen/air in micro turbine engine by fuzzy grey relation method 被引量:4
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作者 E Jia-qiang WU Jiang-hua +3 位作者 LIU Teng CHEN Jing-wei DENG Yuan-wang PENG Qing-guo 《Journal of Central South University》 SCIE EI CAS CSCD 2019年第8期2214-2223,共10页
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
关键词 micro turbine engine catalytic combustion HYDROGEN fuzzy grey relation theory
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Practical Method for Determining All the Minimum Solutions of Fuzzy Matrix Equation and Transitive Closure of Fuzzy Relation 被引量:2
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作者 阎家杰 赵万忠 《Chinese Quarterly Journal of Mathematics》 CSCD 1993年第4期99-103,共5页
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
关键词 fuzzy matrix equation minimum solution fuzzy relation transitive closure
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On uniqueness of (fuzzy) relation in some generalized rough set model 被引量:1
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作者 PEI Dao-wu 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2014年第3期253-264,共12页
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
关键词 fuzzy relation rough set fuzzy rough set lower approximation operator upper approximationoperator.
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On Methodology of Fuzzy Systems 被引量:1
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作者 Yao Min(Dept. of Computer, Zhejiang University, Hangzhou 310028, P. R. China)Luo Jianhua(Dept. of Biomedical Eng., Shanghai Jiaotong University, 200030, P. R. China) 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 1999年第4期21-26,共6页
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
关键词 fuzzy systems fuzzy entropy Defuzzification strategies fuzzy consistent relation.
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Group Decision Making With Consistency of Intuitionistic Fuzzy Preference Relations Under Uncertainty 被引量:1
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作者 Yang Lin Yingming Wang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2018年第3期741-748,共8页
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
关键词 Group decision making(GDM) intuitionistic fuzzy preference relation(IFPR) intuitionistic fuzzy set(IFS) multiplicative consistency risk preference uncertain weights
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Development of Granular Fuzzy Relation Equations Based on a Subset of Data
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作者 Dan Wang Xiubin Zhu +2 位作者 Witold Pedycz Zhenhua Yu Zhiwu Li 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2021年第8期1416-1427,共12页
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
关键词 A subset of data granular fuzzy relation equations interval-valued fuzzy relation particle swarm optimization(PSO)
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Group Decision-Making Method with Incomplete Intuitionistic Fuzzy Preference Relations Based on a Generalized Multiplicative Consistent Concept
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作者 Xiaoyun Lu Jiuying Dong +1 位作者 Hecheng Li Shuping Wan 《Computer Modeling in Engineering & Sciences》 SCIE EI 2022年第9期881-907,共27页
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
关键词 Intuitionistic fuzzy preference relations multiplicative consistency CONSENSUS optimization model group decision-making
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Fuzzy Consistent Relation and Decision Making
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作者 Yao, Min Huang, Yanjun 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 1998年第2期14-18,共5页
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
关键词 fuzzy consistent relation Center-division transitivity Decision making
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On the Relation Redundancy in Fuzzy Databases
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作者 唐晓辉 陈国青 《Journal of Donghua University(English Edition)》 EI CAS 2006年第6期67-70,83,共5页
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
关键词 fuzzy relational data model CLOSENESS relation redundancy.
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Selection method of risk response schemes for mining project based on fuzzy preference relations
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作者 SUN Bing LUO Hai-tao 《Journal of Coal Science & Engineering(China)》 2010年第2期221-224,共4页
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
关键词 mining project risk response scheme fuzzy preference relation C-IOWA operator
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A NEURAL FUZZY INFERENCE SYSTEM
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作者 Lu Jing 《Journal of Electronics(China)》 2013年第4期401-410,共10页
This paper proposes a new neural fuzzy inference system that mainly consists of four parts. The first part is about how to use neural network to express the relation within a fuzzy rule. The second part is the simplif... This paper proposes a new neural fuzzy inference system that mainly consists of four parts. The first part is about how to use neural network to express the relation within a fuzzy rule. The second part is the simplification of the first part, and experiments show that these simplifications work. On the contrary to the second part, the third part is the enhancement of the first part and it can be used when the first part cannot work very well in the fuzzy inference algorithm, which would be introduced in the fourth part. Finally, the fourth part "neural fuzzy inference algorithm" is been introduced. It can inference the new membership function of the output based on previous fuzzy rules. The accuracy of the fuzzy inference algorithm is dependent on neural network generalization ability. Even if the generalization ability of the neural network we used is good, we still get inaccurate results since the new coming rule may not be related to any of the previous rules. Experiments show this algorithm is successful in situations which satisfy these conditions. 展开更多
关键词 fuzzy logic Neural network relation within fuzzy rule . Graph solution
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Research on the fuzzy relationship between the precursory anomalous elements and earthquake elements
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作者 汪雪泉 郑光 +2 位作者 钱家栋 余华扬 黄显良 《Acta Seismologica Sinica(English Edition)》 CSCD 1999年第6期676-683,727,共8页
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
关键词 earthquake precursors fuzzy information processing fuzzy relation
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The application of fuzzy equivalence relation based on the quotient space in cluster analysis
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作者 SHEN Qin-wei ZHANG Yuan 《International Journal of Technology Management》 2014年第8期58-61,共4页
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
关键词 quotient space hierarchical structure fuzzy compatibility relation fuzzy equivalence relation matrix cluster analysis
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Cardinal Numbers of Fuzzy Sets 被引量:8
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作者 李洪兴 罗承忠 +1 位作者 汪培庄 袁学海 《Chinese Quarterly Journal of Mathematics》 CSCD 1992年第3期101-107,共7页
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
关键词 fuzzy relations fuzzy mappings the cardinal numbers of fuzzy sets
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The construction and combined operation for fuzzy consistent matrixes 被引量:2
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作者 姚敏 沈斌 骆建华 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2005年第1期27-31,共5页
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
关键词 fuzzy consistent matrix fuzzy consistent relation Compound operation
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A MODIFIED FUZZY BIOREACTOR MODEL
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作者 元英进 华刚 胡宗定 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 1994年第3期60-65,共6页
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
关键词 fuzzy set fuzzy relation BIOREACTOR Schweizer- Sklard operator
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