The concept of rough communication based on both-branch fuzzy set is proposed, in which the loss of information may exist, for each agent there has a different language and can not provide precise communication to eac...The concept of rough communication based on both-branch fuzzy set is proposed, in which the loss of information may exist, for each agent there has a different language and can not provide precise communication to each other. The method of information measure in a rough communication based on both-branch fuzzy set is proposed. By using some concepts, such as ｜α｜-both-branch rough communication cut, the relation theorem between rough communication based on both-branch fuzzy concept and rough communication based on classical concept is obtained. Finally, an example of rough communication based on both-branch fuzzy set is given.展开更多
The function of the air target threat evaluation （TE） is the foundation for weapons allocation and senor resources management within the surface air defense. The multi-attribute evaluation methodology is utilized to...The function of the air target threat evaluation （TE） is the foundation for weapons allocation and senor resources management within the surface air defense. The multi-attribute evaluation methodology is utilized to address the issue of the TE in which the tactic features of the detected target are treated as evaluation attributes. Meanwhile, the intuitionistic fuzzy set （IFS） is employed to deal with information uncertainty in the TE process. Furthermore, on the basis of the entropy weight and inclusion-comparison probability, a hybrid TE method is developed. In order to accommodate the demands of naturalistic decision making, the proposed method allows air defense commanders to express their intuitive opinions besides incorporating into the threat features of the detected target. An illustrative example is provided to indicate the feasibility and advantage of the proposed method.展开更多
Multiattribute decision making（MADM） problems, in which the weights and ratings of alternatives are expressed with intuitionistic fuzzy（IF） sets, are investigated.Firstly, the relative degrees of membership and th...Multiattribute decision making（MADM） problems, in which the weights and ratings of alternatives are expressed with intuitionistic fuzzy（IF） sets, are investigated.Firstly, the relative degrees of membership and the relative degrees of non-membership are formulated as IF sets, the weights and values of alternatives on both qualitative and quantitative attributes may be expressed as IF sets in a unified way.Then a MADM method based on generalized ordered weighted averaging operators is proposed.The proposed method is illustrated with a numerical example.展开更多
The aim of this paper is to discuss the approximate rea- soning problems with interval-valued fuzzy environments based on the fully implicational idea. First, this paper constructs a class of interval-valued fuzzy imp...The aim of this paper is to discuss the approximate rea- soning problems with interval-valued fuzzy environments based on the fully implicational idea. First, this paper constructs a class of interval-valued fuzzy implications by means of a type of impli- cations and a parameter on the unit interval, then uses them to establish fully implicational reasoning methods for interval-valued fuzzy modus ponens （IFMP） and interval-valued fuzzy modus tel- lens （IFMT） problems. At the same time the reversibility properties of these methods are analyzed and the reversible conditions are given. It is shown that the existing unified forms of α-triple I （the abbreviation of triple implications） methods for FMP and FMT can be seen as the particular cases of our methods for IFMP and IFMT.展开更多
The evaluation method and its accuracy for evaluating complex systems are considered. In order to evaluate accurately complex systems, the existed evaluating methods are simply analyzed, and a new comprehensive evalua...The evaluation method and its accuracy for evaluating complex systems are considered. In order to evaluate accurately complex systems, the existed evaluating methods are simply analyzed, and a new comprehensive evaluating method is developed. The new method is integration of Delphi approach, analytic hierarchy process, gray interconnect degree and fuzzy evaluation (DHGF). Its theory foundation is the meta-synthesis methodology from qualitative analysis to quantitative analysis. According to fuzzy set approach, using the methods of concordance of evaluation, redundant verify, double models redundant, and limitations of the method etc, the accuracy of evaluating method of DHGF is estimated, and a practical example is given. The result shows that using the method to evaluate complex system projects is feasible and credible.展开更多
This paper presents a general framework for the study of relation-based intuitionistic fuzzy rough sets determined by two intuitionistic fuzzy implicators.By employing two intuitionistic fuzzy implicators I and J,I -l...This paper presents a general framework for the study of relation-based intuitionistic fuzzy rough sets determined by two intuitionistic fuzzy implicators.By employing two intuitionistic fuzzy implicators I and J,I -lower and J-upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined.Properties of(I,J) -intuitionistic fuzzy rough approximation operators are then examined.The connections between special types of intuitionistic fuzzy relations and properties of (I,J)-intuitionistic fuzzy approximation operators are also established.展开更多
In order to measure the uncertain information of a type- 2 intuitionistic fuzzy set （T21FS）, an entropy measure of T21FS is presented by using the constructive principles. The proposed entropy measure is also proved...In order to measure the uncertain information of a type- 2 intuitionistic fuzzy set （T21FS）, an entropy measure of T21FS is presented by using the constructive principles. The proposed entropy measure is also proved to satisfy all of the constructive principles. Further, a novel concept of the type-2 triangular in- tuitionistic trapezoidal fuzzy set （T2TITrFS） is developed, and a geometric interpretation of the T2TITrFS is given to comprehend it completely or correctly in a more intuitive way. To deal with a more general uncertain complex system, the constructive principles of an entropy measure of T2TITrFS are therefore proposed on the basis of the axiomatic definition of the type-2 intuitionisic fuzzy entropy measure. This paper elicits a formula of type-2 triangular intuitionistic trapezoidal fuzzy entropy and verifies that it does sa- tisfy the constructive principles. Two examples are given to show the efficiency of the proposed entropy of T2TITrFS in describing the uncertainty of the type-2 intuitionistic fuzzy information and illustrate its application in type-2 triangular intuitionistic trapezodial fuzzy decision making problems.展开更多
Uncertain and hesitant information, widely existing in the real-world qualitative decision making problems, brings great challenges to decision makers. Hesitant fuzzy linguistic term sets(HFLTSs), an effective linguis...Uncertain and hesitant information, widely existing in the real-world qualitative decision making problems, brings great challenges to decision makers. Hesitant fuzzy linguistic term sets(HFLTSs), an effective linguistic computational tool in modeling and eliciting such information, have hence aroused many scholars’ interests and some extensions have been introduced recently.However, these methods are based on the discrete linguistic term framework with the limited expression domain, which actually depict qualitative information using several single values. Therefore,it is hard to ensure the integrity of the semantics representation and the accuracy of the computation results. To deal with this problem, a semantics basis framework called complete linguistic term set(CLTS) is designed, which adopts a separation structure of linguistic scale and expression domain, enriching semantics representation of decision makers. On this basis the concept of fuzzy interval linguistic sets(FILSs) is put forward that employs the interval linguistic term with probability to increase the flexibility of eliciting and representing uncertain and hesitant qualitative information. For practical applications, a fuzzy interval linguistic technique for order preference by similarity to ideal solution(FILTOPSIS) method is developed to deal with multi-attribute group decision making(MAGDM) problems. Through the cases of movie and enterprise resource planning(ERP) system selection, the effectiveness and validity of the proposed method are illustrated.展开更多
The intuitionistic fuzzy set(IFS) based on fuzzy theory,which is of high efficiency to solve the fuzzy problem, has been introduced by Atanassov. Subsequently, he pushed the research one step further from the IFS to t...The intuitionistic fuzzy set(IFS) based on fuzzy theory,which is of high efficiency to solve the fuzzy problem, has been introduced by Atanassov. Subsequently, he pushed the research one step further from the IFS to the interval valued intuitionistic fuzzy set(IVIFS). On the basis of fuzzy set(FS), the IFS is a generalization concept. And the IFS is generalized to the IVIFS.In this paper, the definition of the sixth Cartesian product over IVIFSs is first introduced and its some properties are explored.We prove some equalities based on the operation and the relation over IVIFSs. Finally, we present one geometric interpretation and a numerical example of the sixth Cartesian product over IVIFSs.展开更多
A new method for translating a fuzzy rough set to a fuzzy set is introduced and the fuzzy approximation of a fuzzy rough set is given. The properties of the fuzzy approximation of a fuzzy rough set are studied and a f...A new method for translating a fuzzy rough set to a fuzzy set is introduced and the fuzzy approximation of a fuzzy rough set is given. The properties of the fuzzy approximation of a fuzzy rough set are studied and a fuzzy entropy measure for fuzzy rough sets is proposed. This measure is consistent with similar considerations for ordinary fuzzy sets and is the result of the fuzzy approximation of fuzzy rough sets.展开更多
Intelligent wars can take place not only in the physical domain and information domain but also in the cognitive domain.The cognitive domain will become the key domain to win in the future intelligent war.A Lanchester...Intelligent wars can take place not only in the physical domain and information domain but also in the cognitive domain.The cognitive domain will become the key domain to win in the future intelligent war.A Lanchester equation considering cognitive domain is proposed to fit the development tendency intelligent wars in this paper.One party is considered to obtain the exponential enhancement advantage on combat forces in combat if it can gain an advantage in the cognitive domain over the other party according to the systemic advantage function.The operational effectiveness of the cognitive domain in war is considered to consist of a series of indicators.Hesitant fuzzy sets and linguistic term sets are powerful tools when evaluating indicators,hence the indicators are scored by experts using hesitant fuzzy linguistic terms sets here.A unique hesitant fuzzy hybrid arithmetical averaging operator is used to aggregate the evaluation.展开更多
The fundamental principle for differentiating water masses is a strict consideration of their relative "interior homogeneity" and obvious "exterior differences" with others in characteristics. The ...The fundamental principle for differentiating water masses is a strict consideration of their relative "interior homogeneity" and obvious "exterior differences" with others in characteristics. The conceptions of water type, water mass and water system are dealt with on the basis of the theory of fuzzy sets. A proposal to apply the theory of fuzzy sets to define the water mass and its core, independent area, boundary and mixing area is put forward.As an example, the membership function of the surface water masses in the Yellow Sea and East China Sea in August, 1979, are considered. Their cores, independent areas, boundaries, mixing areas and the approximation degrees between different water masses are calculated respectively. The water masses are ranged according to their fuzzy degrees.展开更多
Scheme evaluation and selection is an optimum selecting and sequencing problem with multi-objective and multi-level. It can’t follow single objective function or rule. Meanwhile,these objectives are coupled with each...Scheme evaluation and selection is an optimum selecting and sequencing problem with multi-objective and multi-level. It can’t follow single objective function or rule. Meanwhile,these objectives are coupled with each other and the attribution information is fuzzy also. It is necessary to find an effective evaluation method which can consider all conditions and restrictions. In this paper,AHP and rough set theory are applied to fuzzy optimization to determine important weight of each attribution. The rough set fuzzy optimum selection is used to eliminate the useless information. Autonomous underwater vehicle (AUV) is large-scale systems with many coupled design variables and objective functions. Their scheme evaluation and selection are very important,which relate to multiple factors,such as reliability; security,service time; the lifecycle,etc. Results of application in torpedo design indicate that this method is feasible.展开更多
To investigate the judging problem of optimal dividing matrix among several fuzzy dividing matrices in fuzzy dividing space, correspondingly, which is determined by the various choices of cluster samples in the totali...To investigate the judging problem of optimal dividing matrix among several fuzzy dividing matrices in fuzzy dividing space, correspondingly, which is determined by the various choices of cluster samples in the totality sample space, two algorithms are proposed on the basis of the data analysis method in rough sets theory： information system discrete algorithm （algorithm 1） and samples representatives judging algorithm （algorithm 2）. On the principle of the farthest distance, algorithm 1 transforms continuous data into discrete form which could be transacted by rough sets theory. Taking the approximate precision as a criterion, algorithm 2 chooses the sample space with a good representative. Hence, the clustering sample set in inducing and computing optimal dividing matrix can be achieved. Several theorems are proposed to provide strict theoretic foundations for the execution of the algorithm model. An applied example based on the new algorithm model is given, whose result verifies the feasibility of this new algorithm model.展开更多
Environmental risk assessment of tailings reservoir assessment system is complex and has many index factors.In order to accurately judge surrounding environmental risks of tailings reservoirs and determinate the corre...Environmental risk assessment of tailings reservoir assessment system is complex and has many index factors.In order to accurately judge surrounding environmental risks of tailings reservoirs and determinate the corresponding prevention and control work,multi-hierarchical fuzzy judgment and nested dominance relation of rough set theory are implemented to evaluate them and find out the rules of this evaluation system with 14 representative cases.The methods of multi-hierarchical fuzzy evaluation can overall consider each influence factor of risk assessment system and their mutual impact,and the index weight based on the analytic hierarchy process is relatively reasonable.Rough set theory based on dominance relation reduces each index attribute from the top down,largely simplifies the complexity of the original evaluation system,and considers the preferential information in each index.Furthermore,grey correlation theory is applied to analysis of importance of each reducted condition attribute.The results demonstrate the feasibility of the proposed safety evaluation system and the application potential.展开更多
This paper combines interval-valued intuitionistic fuzzy sets and rough sets.It studies rougheness in interval-valued intuitionistic fuzzy sets and proposes one kind of interval-valued intuitionistic fuzzy-rough sets ...This paper combines interval-valued intuitionistic fuzzy sets and rough sets.It studies rougheness in interval-valued intuitionistic fuzzy sets and proposes one kind of interval-valued intuitionistic fuzzy-rough sets models under the equivalence relation in crisp sets.That extends the classical rough set defined by Pawlak.展开更多
This paper is a purely mathematical one dealing with a common possible foundation of Fuzzy Set Theory and Rough Set Theory.It begins with a generalization of Obtulowicz's paper,rough sets and Heyting algebra value...This paper is a purely mathematical one dealing with a common possible foundation of Fuzzy Set Theory and Rough Set Theory.It begins with a generalization of Obtulowicz's paper,rough sets and Heyting algebra valued sets,published in Bull.Polish Acad Sc.(math),198.In this paper Obtulowicz proposes a special subcategory展开更多
Based on rough similarity degree of rough sets and close degree of fuzzy sets, the definitions of rough similarity degree and rough close degree of rough fuzzy sets are given, which can be used to measure the similar ...Based on rough similarity degree of rough sets and close degree of fuzzy sets, the definitions of rough similarity degree and rough close degree of rough fuzzy sets are given, which can be used to measure the similar degree between two rough fuzzy sets. The properties and theorems are listed. Using the two new measures, the method of clustering in the rough fuzzy system can be obtained. After clustering, the new fuzzy sample can be recognized by the principle of maximal similarity degree.展开更多
In order to solve the problem of uncertainty and fuzzy information in the process of weapon equipment system selec-tion,a multi-attribute decision-making(MADM)method based on probabilistic hesitant fuzzy set(PHFS)is p...In order to solve the problem of uncertainty and fuzzy information in the process of weapon equipment system selec-tion,a multi-attribute decision-making(MADM)method based on probabilistic hesitant fuzzy set(PHFS)is proposed.Firstly,we introduce the concept of probability and fuzzy entropy to mea-sure the ambiguity,hesitation and uncertainty of probabilistic hesitant fuzzy elements(PHFEs).Sequentially,the expert trust network is constructed,and the importance of each expert in the network can be obtained by calculating the cumulative trust value under multiple trust propagation paths,so as to obtain the expert weight vector.Finally,we put forward an MADM method combining the probabilistic hesitant fuzzy entropy and grey rela-tion analysis(GRA)model,and an illustrative case is employed to prove the feasibility and effectiveness of the method when solving the weapon system selection decision-making problem.展开更多
基金supported by the National Natural Science Foundation of China (61070241)the Natural Science Foundation of Shandong Province (ZR2010 FM035)the Science Research Foundation of University of Jinan (XKYK31)
文摘The concept of rough communication based on both-branch fuzzy set is proposed, in which the loss of information may exist, for each agent there has a different language and can not provide precise communication to each other. The method of information measure in a rough communication based on both-branch fuzzy set is proposed. By using some concepts, such as ｜α｜-both-branch rough communication cut, the relation theorem between rough communication based on both-branch fuzzy concept and rough communication based on classical concept is obtained. Finally, an example of rough communication based on both-branch fuzzy set is given.
基金supported by the National Natural Science Foundation of China (70871117 70571086)the Development Foundation of Dalian Naval Academy
文摘The function of the air target threat evaluation （TE） is the foundation for weapons allocation and senor resources management within the surface air defense. The multi-attribute evaluation methodology is utilized to address the issue of the TE in which the tactic features of the detected target are treated as evaluation attributes. Meanwhile, the intuitionistic fuzzy set （IFS） is employed to deal with information uncertainty in the TE process. Furthermore, on the basis of the entropy weight and inclusion-comparison probability, a hybrid TE method is developed. In order to accommodate the demands of naturalistic decision making, the proposed method allows air defense commanders to express their intuitive opinions besides incorporating into the threat features of the detected target. An illustrative example is provided to indicate the feasibility and advantage of the proposed method.
基金supported by the National Natural Science Foundation of China (70871117 70571086)
文摘Multiattribute decision making（MADM） problems, in which the weights and ratings of alternatives are expressed with intuitionistic fuzzy（IF） sets, are investigated.Firstly, the relative degrees of membership and the relative degrees of non-membership are formulated as IF sets, the weights and values of alternatives on both qualitative and quantitative attributes may be expressed as IF sets in a unified way.Then a MADM method based on generalized ordered weighted averaging operators is proposed.The proposed method is illustrated with a numerical example.
基金supported by the National Natural Science Foundation of China(60774100)the Natural Science Foundation of Shandong Province of China(Y2007A15)
文摘The aim of this paper is to discuss the approximate rea- soning problems with interval-valued fuzzy environments based on the fully implicational idea. First, this paper constructs a class of interval-valued fuzzy implications by means of a type of impli- cations and a parameter on the unit interval, then uses them to establish fully implicational reasoning methods for interval-valued fuzzy modus ponens （IFMP） and interval-valued fuzzy modus tel- lens （IFMT） problems. At the same time the reversibility properties of these methods are analyzed and the reversible conditions are given. It is shown that the existing unified forms of α-triple I （the abbreviation of triple implications） methods for FMP and FMT can be seen as the particular cases of our methods for IFMP and IFMT.
文摘The evaluation method and its accuracy for evaluating complex systems are considered. In order to evaluate accurately complex systems, the existed evaluating methods are simply analyzed, and a new comprehensive evaluating method is developed. The new method is integration of Delphi approach, analytic hierarchy process, gray interconnect degree and fuzzy evaluation (DHGF). Its theory foundation is the meta-synthesis methodology from qualitative analysis to quantitative analysis. According to fuzzy set approach, using the methods of concordance of evaluation, redundant verify, double models redundant, and limitations of the method etc, the accuracy of evaluating method of DHGF is estimated, and a practical example is given. The result shows that using the method to evaluate complex system projects is feasible and credible.
基金supported by grants from the National Natural Science Foundation of China(Nos.61075120, 60673096 and 60773174)the Natural Science Foundation of Zhejiang Province in China(No.Y107262).
文摘This paper presents a general framework for the study of relation-based intuitionistic fuzzy rough sets determined by two intuitionistic fuzzy implicators.By employing two intuitionistic fuzzy implicators I and J,I -lower and J-upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined.Properties of(I,J) -intuitionistic fuzzy rough approximation operators are then examined.The connections between special types of intuitionistic fuzzy relations and properties of (I,J)-intuitionistic fuzzy approximation operators are also established.
基金supported by the National Natural Science Foundation of China(7137115670971017)the Research Grants Council of the Hong Kong Special Administrative Region,China(City U112111)
文摘In order to measure the uncertain information of a type- 2 intuitionistic fuzzy set （T21FS）, an entropy measure of T21FS is presented by using the constructive principles. The proposed entropy measure is also proved to satisfy all of the constructive principles. Further, a novel concept of the type-2 triangular in- tuitionistic trapezoidal fuzzy set （T2TITrFS） is developed, and a geometric interpretation of the T2TITrFS is given to comprehend it completely or correctly in a more intuitive way. To deal with a more general uncertain complex system, the constructive principles of an entropy measure of T2TITrFS are therefore proposed on the basis of the axiomatic definition of the type-2 intuitionisic fuzzy entropy measure. This paper elicits a formula of type-2 triangular intuitionistic trapezoidal fuzzy entropy and verifies that it does sa- tisfy the constructive principles. Two examples are given to show the efficiency of the proposed entropy of T2TITrFS in describing the uncertainty of the type-2 intuitionistic fuzzy information and illustrate its application in type-2 triangular intuitionistic trapezodial fuzzy decision making problems.
基金supported by the National Natural Science Foundation of China(61273275)
文摘Uncertain and hesitant information, widely existing in the real-world qualitative decision making problems, brings great challenges to decision makers. Hesitant fuzzy linguistic term sets(HFLTSs), an effective linguistic computational tool in modeling and eliciting such information, have hence aroused many scholars’ interests and some extensions have been introduced recently.However, these methods are based on the discrete linguistic term framework with the limited expression domain, which actually depict qualitative information using several single values. Therefore,it is hard to ensure the integrity of the semantics representation and the accuracy of the computation results. To deal with this problem, a semantics basis framework called complete linguistic term set(CLTS) is designed, which adopts a separation structure of linguistic scale and expression domain, enriching semantics representation of decision makers. On this basis the concept of fuzzy interval linguistic sets(FILSs) is put forward that employs the interval linguistic term with probability to increase the flexibility of eliciting and representing uncertain and hesitant qualitative information. For practical applications, a fuzzy interval linguistic technique for order preference by similarity to ideal solution(FILTOPSIS) method is developed to deal with multi-attribute group decision making(MAGDM) problems. Through the cases of movie and enterprise resource planning(ERP) system selection, the effectiveness and validity of the proposed method are illustrated.
基金supported by the National Natural Science Foundation of China(61373174)
文摘The intuitionistic fuzzy set(IFS) based on fuzzy theory,which is of high efficiency to solve the fuzzy problem, has been introduced by Atanassov. Subsequently, he pushed the research one step further from the IFS to the interval valued intuitionistic fuzzy set(IVIFS). On the basis of fuzzy set(FS), the IFS is a generalization concept. And the IFS is generalized to the IVIFS.In this paper, the definition of the sixth Cartesian product over IVIFSs is first introduced and its some properties are explored.We prove some equalities based on the operation and the relation over IVIFSs. Finally, we present one geometric interpretation and a numerical example of the sixth Cartesian product over IVIFSs.
基金the National Natural Science Foundation of China (60364001, 70461001)Hainan ProvincialNatural Science Foundation of China (80401).
文摘A new method for translating a fuzzy rough set to a fuzzy set is introduced and the fuzzy approximation of a fuzzy rough set is given. The properties of the fuzzy approximation of a fuzzy rough set are studied and a fuzzy entropy measure for fuzzy rough sets is proposed. This measure is consistent with similar considerations for ordinary fuzzy sets and is the result of the fuzzy approximation of fuzzy rough sets.
基金supported by the National Natural Science Foundation of China (61703426)the National Social Science Foundation of China.
文摘Intelligent wars can take place not only in the physical domain and information domain but also in the cognitive domain.The cognitive domain will become the key domain to win in the future intelligent war.A Lanchester equation considering cognitive domain is proposed to fit the development tendency intelligent wars in this paper.One party is considered to obtain the exponential enhancement advantage on combat forces in combat if it can gain an advantage in the cognitive domain over the other party according to the systemic advantage function.The operational effectiveness of the cognitive domain in war is considered to consist of a series of indicators.Hesitant fuzzy sets and linguistic term sets are powerful tools when evaluating indicators,hence the indicators are scored by experts using hesitant fuzzy linguistic terms sets here.A unique hesitant fuzzy hybrid arithmetical averaging operator is used to aggregate the evaluation.
文摘The fundamental principle for differentiating water masses is a strict consideration of their relative "interior homogeneity" and obvious "exterior differences" with others in characteristics. The conceptions of water type, water mass and water system are dealt with on the basis of the theory of fuzzy sets. A proposal to apply the theory of fuzzy sets to define the water mass and its core, independent area, boundary and mixing area is put forward.As an example, the membership function of the surface water masses in the Yellow Sea and East China Sea in August, 1979, are considered. Their cores, independent areas, boundaries, mixing areas and the approximation degrees between different water masses are calculated respectively. The water masses are ranged according to their fuzzy degrees.
文摘Scheme evaluation and selection is an optimum selecting and sequencing problem with multi-objective and multi-level. It can’t follow single objective function or rule. Meanwhile,these objectives are coupled with each other and the attribution information is fuzzy also. It is necessary to find an effective evaluation method which can consider all conditions and restrictions. In this paper,AHP and rough set theory are applied to fuzzy optimization to determine important weight of each attribution. The rough set fuzzy optimum selection is used to eliminate the useless information. Autonomous underwater vehicle (AUV) is large-scale systems with many coupled design variables and objective functions. Their scheme evaluation and selection are very important,which relate to multiple factors,such as reliability; security,service time; the lifecycle,etc. Results of application in torpedo design indicate that this method is feasible.
文摘To investigate the judging problem of optimal dividing matrix among several fuzzy dividing matrices in fuzzy dividing space, correspondingly, which is determined by the various choices of cluster samples in the totality sample space, two algorithms are proposed on the basis of the data analysis method in rough sets theory： information system discrete algorithm （algorithm 1） and samples representatives judging algorithm （algorithm 2）. On the principle of the farthest distance, algorithm 1 transforms continuous data into discrete form which could be transacted by rough sets theory. Taking the approximate precision as a criterion, algorithm 2 chooses the sample space with a good representative. Hence, the clustering sample set in inducing and computing optimal dividing matrix can be achieved. Several theorems are proposed to provide strict theoretic foundations for the execution of the algorithm model. An applied example based on the new algorithm model is given, whose result verifies the feasibility of this new algorithm model.
基金Project(51374242)supported by the National Natural Science Foundation of ChinaProject(200449)supported by National Outstanding Doctoral Dissertations Special Fund of ChinaProject(2012QNZT028)supported by the Free Exploration Fund of Central South University,China
文摘Environmental risk assessment of tailings reservoir assessment system is complex and has many index factors.In order to accurately judge surrounding environmental risks of tailings reservoirs and determinate the corresponding prevention and control work,multi-hierarchical fuzzy judgment and nested dominance relation of rough set theory are implemented to evaluate them and find out the rules of this evaluation system with 14 representative cases.The methods of multi-hierarchical fuzzy evaluation can overall consider each influence factor of risk assessment system and their mutual impact,and the index weight based on the analytic hierarchy process is relatively reasonable.Rough set theory based on dominance relation reduces each index attribute from the top down,largely simplifies the complexity of the original evaluation system,and considers the preferential information in each index.Furthermore,grey correlation theory is applied to analysis of importance of each reducted condition attribute.The results demonstrate the feasibility of the proposed safety evaluation system and the application potential.
基金supported by grants from the National Natural Science Foundation of China(Nos.10971185 and 10971186)the Natural Science Foundation of Fujiang Province in China(No.2008F5066).
文摘This paper combines interval-valued intuitionistic fuzzy sets and rough sets.It studies rougheness in interval-valued intuitionistic fuzzy sets and proposes one kind of interval-valued intuitionistic fuzzy-rough sets models under the equivalence relation in crisp sets.That extends the classical rough set defined by Pawlak.
文摘This paper is a purely mathematical one dealing with a common possible foundation of Fuzzy Set Theory and Rough Set Theory.It begins with a generalization of Obtulowicz's paper,rough sets and Heyting algebra valued sets,published in Bull.Polish Acad Sc.(math),198.In this paper Obtulowicz proposes a special subcategory
基金the Fujian Provincial Natural Science Foundation of China (Z0510492006J0391)
文摘Based on rough similarity degree of rough sets and close degree of fuzzy sets, the definitions of rough similarity degree and rough close degree of rough fuzzy sets are given, which can be used to measure the similar degree between two rough fuzzy sets. The properties and theorems are listed. Using the two new measures, the method of clustering in the rough fuzzy system can be obtained. After clustering, the new fuzzy sample can be recognized by the principle of maximal similarity degree.
基金supported by the National Natural Science Foundation of China(71901214).
文摘In order to solve the problem of uncertainty and fuzzy information in the process of weapon equipment system selec-tion,a multi-attribute decision-making(MADM)method based on probabilistic hesitant fuzzy set(PHFS)is proposed.Firstly,we introduce the concept of probability and fuzzy entropy to mea-sure the ambiguity,hesitation and uncertainty of probabilistic hesitant fuzzy elements(PHFEs).Sequentially,the expert trust network is constructed,and the importance of each expert in the network can be obtained by calculating the cumulative trust value under multiple trust propagation paths,so as to obtain the expert weight vector.Finally,we put forward an MADM method combining the probabilistic hesitant fuzzy entropy and grey rela-tion analysis(GRA)model,and an illustrative case is employed to prove the feasibility and effectiveness of the method when solving the weapon system selection decision-making problem.
