To identify interactions among evaluation criteria and describe their importance,a new identification method making use of a fuzzy measure is presented.The relative weight and interaction degree of every evaluation cr...To identify interactions among evaluation criteria and describe their importance,a new identification method making use of a fuzzy measure is presented.The relative weight and interaction degree of every evaluation criteria pair are obtained by using the diamond pairwise comparison method.Based on comparison results,the maximum eigenvector method of analytic hierarchy process (AHP),the hierarchical clustering method,and the phi(s) transformation are utilized to generate values of the fuzzy measure for each subset of the evaluation criterion set.Overall evaluation on each supplier is aggregated by Choquet integral with respect to the fuzzy measure.Finally,an illustrative example demonstrates the practical feasibility and validity of the proposed method.展开更多
The ideas of ambiguous bipolar skepticism under algebra and closed skepticism ambiguous bipolar ideals and related features have been developed.The fuzzy measure ideal is described in terms of bipolar ambiguous measur...The ideas of ambiguous bipolar skepticism under algebra and closed skepticism ambiguous bipolar ideals and related features have been developed.The fuzzy measure ideal is described in terms of bipolar ambiguous measure algebra and bipolar skepticism,and the linkages between bipolar fuzzy measure algebra are determined.A bipolar misty ideal’s skepticism is examined.InBCW andBCL-measure algebra,homogeneous ideas and dubious pictures of fuzzy bipolar measure ideas are examined.Also,we gave the relationship between these concepts.Finally,it is given the perfect terms for an occult bipolar doubt to be a measure of ideal fuzzy bipolar closed doubt.展开更多
Profile hidden Markov models (HMMs) based on classical HMMs have been widely applied for protein sequence identification. The formulation of the forward and backward variables in profile HMMs is made under statistic...Profile hidden Markov models (HMMs) based on classical HMMs have been widely applied for protein sequence identification. The formulation of the forward and backward variables in profile HMMs is made under statistical independence assumption of the probability theory. We propose a fuzzy profile HMM to overcome the limitations of that assumption and to achieve an improved alignment for protein sequences belonging to a given family. The proposed model fuzzifies the forward and backward variables by incorporating Sugeno fuzzy measures and Choquet integrals, thus further extends the generalized HMM. Based on the fuzzified forward and backward variables, we propose a fuzzy Baum-Welch parameter estimation algorithm for profiles. The strong correlations and the sequence preference involved in the protein structures make this fuzzy architecture based model as a suitable candidate for building profiles of a given family, since the fuzzy set can handle uncertainties better than classical methods.展开更多
The concept of fuzzy measure was introduced by Sugeno in 1974. A notion of signed fuzzy measure is introduced in this paper, and its elementary properties are briefly discussed. An analogue of Hahn decomposition theo...The concept of fuzzy measure was introduced by Sugeno in 1974. A notion of signed fuzzy measure is introduced in this paper, and its elementary properties are briefly discussed. An analogue of Hahn decomposition theorem is established under the null-null-additive condition. A version of the Jordan decomposition theorem is proved under the null-additive condition.展开更多
Differrent kinds of operations have been proposed in fuzzy set theory although Zadeh's operation is the most popoular. We discuss a new kind of fuzzy set operations which is based on measurement. In the measure b...Differrent kinds of operations have been proposed in fuzzy set theory although Zadeh's operation is the most popoular. We discuss a new kind of fuzzy set operations which is based on measurement. In the measure based operation, there are only two basic operators: operator for intersection and operator for union. These two operators are interrelated with each other, and conditional fuzzy measures(or conditional membership functions) are also included in these operators. Moreover, the operator for complement is not independently defined, and it is derived from the above two basic operators. The measure based operation brings to light some relations between Zadeh's operation and probabilistic operation. We show that both Zadeh's operation and probabilistic operation are special cases of measure based operators.We also discuss the problem of the law of excluded middle and the law of contradiction. It is shown that these laws still hold in fuzzy sets and this conclusion causes no difficulty in explaining the nature of fuzziness.展开更多
some properties of the inclusion variation and the disjoint variation of set functions on T∞-tribe are studied in detail.The absolute continuity and singularity of set functions on T∞-tribe are discussed.The triangu...some properties of the inclusion variation and the disjoint variation of set functions on T∞-tribe are studied in detail.The absolute continuity and singularity of set functions on T∞-tribe are discussed.The triangular norms T∞ and S∞ are considered as the operators of intersection and union between the fuzzy sets.As a result,some important conclusions about the variations and absolute continuity of set functions on T∞-tribe are obtained such as the superadditivity of inclusion variation,the relation between the variations and the equivalence proposition of absolute continuity of set functions on T∞-tribe.In addition,two small mistakes about T∞-measure are pointed out by the counterexamples and are revised.展开更多
With the development of fuzzy measure theory, the integral inequalities based on Sugeno integral are extensively investigated. We concern on the inequalities of Choquuet integral. The main purpose of this paper is to ...With the development of fuzzy measure theory, the integral inequalities based on Sugeno integral are extensively investigated. We concern on the inequalities of Choquuet integral. The main purpose of this paper is to prove the H?lder inequality for any arbitrary fuzzy measure-based Choquet integral whenever any two of these integrated functions f, g and h are comonotone, and there are three weights. Then we prove Minkowski inequality and Lyapunov inequality for Choquet integral. Moreover, when any two of these integrated functions f1, f2, …, fn are comonotone, we also obtain the Hölder inequality, Minkowski inequality and Lyapunov inequality hold for Choquet integral.展开更多
Measure based fuzzy logic, which is constructed on the basis of eight axioms, is a seemingly powerful fuzzy logic. It possesses several remarkable properties. (1) It is an extended Boolean logic, satisfying all the p...Measure based fuzzy logic, which is constructed on the basis of eight axioms, is a seemingly powerful fuzzy logic. It possesses several remarkable properties. (1) It is an extended Boolean logic, satisfying all the properties of Boolean algebra, including the law of excluded middle and the law of contradiction. (2) It is conditional. Conditional membership functions play an important role in this logic. (3) The negation operator is not independently defined with the conjunction and disjunction operators, but on the contrary, it is derived from them. (4) Zadehs fuzzy logic is included in it as a particular case. (5) It gives more hints to the relationship between fuzzy logic and probability logic.展开更多
The accuracy of the statistical learning model depends on the learning technique used which in turn depends on the dataset’s values.In most research studies,the existence of missing values(MVs)is a vital problem.In a...The accuracy of the statistical learning model depends on the learning technique used which in turn depends on the dataset’s values.In most research studies,the existence of missing values(MVs)is a vital problem.In addition,any dataset with MVs cannot be used for further analysis or with any data driven tool especially when the percentage of MVs are high.In this paper,the authors propose a novel algorithm for dealing with MVs depending on the feature selec-tion(FS)of similarity classifier with fuzzy entropy measure.The proposed algo-rithm imputes MVs in cumulative order.The candidate feature to be manipulated is selected using similarity classifier with Parkash’s fuzzy entropy measure.The predictive model to predict MVs within the candidate feature is the Bayesian Ridge Regression(BRR)technique.Furthermore,any imputed features will be incorporated within the BRR equation to impute the MVs in the next chosen incomplete feature.The proposed algorithm was compared against some practical state-of-the-art imputation methods by conducting an experiment on four medical datasets which were gathered from several databases repository with MVs gener-ated from the three missingness mechanisms.The evaluation metrics of mean abso-lute error(MAE),root mean square error(RMSE)and coefficient of determination(R2 score)were used to measure the performance.The results exhibited that perfor-mance vary depending on the size of the dataset,amount of MVs and the missing-ness mechanism type.Moreover,compared to other methods,the results showed that the proposed method gives better accuracy and less error in most cases.展开更多
The fuzzy measure and fuzzy integral are applied to the classification of software defects in this paper. The fuzzy measure of software attributes and attributes' sets are treated by genetic algorithm, and then softw...The fuzzy measure and fuzzy integral are applied to the classification of software defects in this paper. The fuzzy measure of software attributes and attributes' sets are treated by genetic algorithm, and then software attributes are fused by the Choquet fuzzy integral algorithm. Finally, the class labels of soft- ware modules can be output. Experimental results have shown that there are interactions between characteristic attributes of software modules, and also proved that the fuzzy integral fusing method using Fuzzy Measure based on Genetic Algorithm (GA-FM) can significantly improve the accuracy for software defect prediction.展开更多
To avoid the decrease of system reliability due to insufficient component maintenance and the resource waste caused by excessive component maintenance,identifying the critical components of complex products is an effe...To avoid the decrease of system reliability due to insufficient component maintenance and the resource waste caused by excessive component maintenance,identifying the critical components of complex products is an effective way to improve the efficiency of maintenance activities.Existing studies on identifying critical components of complex products are mainly from two aspects i.e.,topological properties and functional properties,respectively.In this paper,we combine these two aspects to establish a hybrid intuitionistic fuzzy set to incorporate the different types of attribute values.Considering the mutual correlation between attributes,a combination of AHP(Analytic Hierarchy Process)and Improved Mahalanobis-Taguchi System(MTS)is used to determine the λ-Shapley fuzzy measures for attributes.Then,the λ-Shapley Choquet integral intuitionistic fuzzy TOPSIS(Technique for Order Preference by Similarity to an Ideal Solution)method is proposed for calculating the closeness degrees of components to generate their ranking order.Finally,a case study which is about the right gear of airbus 320 is taken as an example to verify the feasibility and effectiveness of this method.This novel methodology can effectively solve the critical components identification problem with different types of evaluation information and completely unknown weight information of attributes,which provides the implementation of protection measures for the system reliability of complex products.展开更多
In this study a new hybrid aggregation operator named as the generalized intuitionistic fuzzy hybrid Choquet averaging(GIFHCA) operator is defined.Meantime,some desirable properties are studied, and several importan...In this study a new hybrid aggregation operator named as the generalized intuitionistic fuzzy hybrid Choquet averaging(GIFHCA) operator is defined.Meantime,some desirable properties are studied, and several important cases are examined.Furthermore,we define the generalized Shapley GIFHCA (GS-GIFHCA) operator,which does not only overall consider the importance of elements and their ordered positions,but also globally reflect the correlations among them and their ordered positions.In order to simplify the complexity of solving a fuzzy measure,we further define the generalizedλ-Shapley GIFHCA(GλS-GIFHCA) operator.展开更多
A novel concept, called nonadditive set-valued measure, is first defined as a monotone and continuous set function. Then the interconnections between nonadditive set-valued measure and the additive set-valued measur...A novel concept, called nonadditive set-valued measure, is first defined as a monotone and continuous set function. Then the interconnections between nonadditive set-valued measure and the additive set-valued measure as well as the fuzzy measure are discussed. Finally, an approach to construct a nonadditive compact set-valued measure is presented via Aumann fuzzy integral.展开更多
The Choquet integral can serve as a useful tool to aggregate interacting criteria in an uncertain environment. In this paper, a trapezoidal intuitionistic fuzzy aggregation operator based on the Choquet integral is pr...The Choquet integral can serve as a useful tool to aggregate interacting criteria in an uncertain environment. In this paper, a trapezoidal intuitionistic fuzzy aggregation operator based on the Choquet integral is proposed for multi-criteria decision-making problems. The decision information takes the form of trapezoidal intuitionistic fuzzy numbers and both the importance and the interaction information among decision-making criteria are considered. On the basis of the introduction of trapezoidal intuitionistic fuzzy numbers, its operational laws and expected value are defined. A trapezoidal intuitionistic fuzzy aggregation operator based on the Choquet integral is then defined and some of its properties are investigated. A new multi-criteria decision-making method based on a trapezoidal intuitionistic fuzzy Choquet integral operator is proposed. Finally, an illustrative example is used to show the feasibility and availability of the proposed method.展开更多
基金Sponsored by the National Natural Science Foundation of China(7047106370771010)
文摘To identify interactions among evaluation criteria and describe their importance,a new identification method making use of a fuzzy measure is presented.The relative weight and interaction degree of every evaluation criteria pair are obtained by using the diamond pairwise comparison method.Based on comparison results,the maximum eigenvector method of analytic hierarchy process (AHP),the hierarchical clustering method,and the phi(s) transformation are utilized to generate values of the fuzzy measure for each subset of the evaluation criterion set.Overall evaluation on each supplier is aggregated by Choquet integral with respect to the fuzzy measure.Finally,an illustrative example demonstrates the practical feasibility and validity of the proposed method.
文摘The ideas of ambiguous bipolar skepticism under algebra and closed skepticism ambiguous bipolar ideals and related features have been developed.The fuzzy measure ideal is described in terms of bipolar ambiguous measure algebra and bipolar skepticism,and the linkages between bipolar fuzzy measure algebra are determined.A bipolar misty ideal’s skepticism is examined.InBCW andBCL-measure algebra,homogeneous ideas and dubious pictures of fuzzy bipolar measure ideas are examined.Also,we gave the relationship between these concepts.Finally,it is given the perfect terms for an occult bipolar doubt to be a measure of ideal fuzzy bipolar closed doubt.
文摘Profile hidden Markov models (HMMs) based on classical HMMs have been widely applied for protein sequence identification. The formulation of the forward and backward variables in profile HMMs is made under statistical independence assumption of the probability theory. We propose a fuzzy profile HMM to overcome the limitations of that assumption and to achieve an improved alignment for protein sequences belonging to a given family. The proposed model fuzzifies the forward and backward variables by incorporating Sugeno fuzzy measures and Choquet integrals, thus further extends the generalized HMM. Based on the fuzzified forward and backward variables, we propose a fuzzy Baum-Welch parameter estimation algorithm for profiles. The strong correlations and the sequence preference involved in the protein structures make this fuzzy architecture based model as a suitable candidate for building profiles of a given family, since the fuzzy set can handle uncertainties better than classical methods.
基金Supported by the National Natural Science Foundationof China( Nos. 6 0 2 740 5 0 and70 1710 36 )
文摘The concept of fuzzy measure was introduced by Sugeno in 1974. A notion of signed fuzzy measure is introduced in this paper, and its elementary properties are briefly discussed. An analogue of Hahn decomposition theorem is established under the null-null-additive condition. A version of the Jordan decomposition theorem is proved under the null-additive condition.
文摘Differrent kinds of operations have been proposed in fuzzy set theory although Zadeh's operation is the most popoular. We discuss a new kind of fuzzy set operations which is based on measurement. In the measure based operation, there are only two basic operators: operator for intersection and operator for union. These two operators are interrelated with each other, and conditional fuzzy measures(or conditional membership functions) are also included in these operators. Moreover, the operator for complement is not independently defined, and it is derived from the above two basic operators. The measure based operation brings to light some relations between Zadeh's operation and probabilistic operation. We show that both Zadeh's operation and probabilistic operation are special cases of measure based operators.We also discuss the problem of the law of excluded middle and the law of contradiction. It is shown that these laws still hold in fuzzy sets and this conclusion causes no difficulty in explaining the nature of fuzziness.
基金Sponsored by the National Natural Science Foundation of China(70471063,70771010)Youth Foundation of Henan University of Science and Technology(2007QN051)
文摘some properties of the inclusion variation and the disjoint variation of set functions on T∞-tribe are studied in detail.The absolute continuity and singularity of set functions on T∞-tribe are discussed.The triangular norms T∞ and S∞ are considered as the operators of intersection and union between the fuzzy sets.As a result,some important conclusions about the variations and absolute continuity of set functions on T∞-tribe are obtained such as the superadditivity of inclusion variation,the relation between the variations and the equivalence proposition of absolute continuity of set functions on T∞-tribe.In addition,two small mistakes about T∞-measure are pointed out by the counterexamples and are revised.
基金supported by the National Natural Science Foundation of China(no.51374199).
文摘With the development of fuzzy measure theory, the integral inequalities based on Sugeno integral are extensively investigated. We concern on the inequalities of Choquuet integral. The main purpose of this paper is to prove the H?lder inequality for any arbitrary fuzzy measure-based Choquet integral whenever any two of these integrated functions f, g and h are comonotone, and there are three weights. Then we prove Minkowski inequality and Lyapunov inequality for Choquet integral. Moreover, when any two of these integrated functions f1, f2, …, fn are comonotone, we also obtain the Hölder inequality, Minkowski inequality and Lyapunov inequality hold for Choquet integral.
文摘Measure based fuzzy logic, which is constructed on the basis of eight axioms, is a seemingly powerful fuzzy logic. It possesses several remarkable properties. (1) It is an extended Boolean logic, satisfying all the properties of Boolean algebra, including the law of excluded middle and the law of contradiction. (2) It is conditional. Conditional membership functions play an important role in this logic. (3) The negation operator is not independently defined with the conjunction and disjunction operators, but on the contrary, it is derived from them. (4) Zadehs fuzzy logic is included in it as a particular case. (5) It gives more hints to the relationship between fuzzy logic and probability logic.
基金funded by the Deanship of Scientific Research(DSR)at King Abdulaziz University(KAU)Jeddah,Saudi Arabia,under grant No.(PH:13-130-1442).
文摘The accuracy of the statistical learning model depends on the learning technique used which in turn depends on the dataset’s values.In most research studies,the existence of missing values(MVs)is a vital problem.In addition,any dataset with MVs cannot be used for further analysis or with any data driven tool especially when the percentage of MVs are high.In this paper,the authors propose a novel algorithm for dealing with MVs depending on the feature selec-tion(FS)of similarity classifier with fuzzy entropy measure.The proposed algo-rithm imputes MVs in cumulative order.The candidate feature to be manipulated is selected using similarity classifier with Parkash’s fuzzy entropy measure.The predictive model to predict MVs within the candidate feature is the Bayesian Ridge Regression(BRR)technique.Furthermore,any imputed features will be incorporated within the BRR equation to impute the MVs in the next chosen incomplete feature.The proposed algorithm was compared against some practical state-of-the-art imputation methods by conducting an experiment on four medical datasets which were gathered from several databases repository with MVs gener-ated from the three missingness mechanisms.The evaluation metrics of mean abso-lute error(MAE),root mean square error(RMSE)and coefficient of determination(R2 score)were used to measure the performance.The results exhibited that perfor-mance vary depending on the size of the dataset,amount of MVs and the missing-ness mechanism type.Moreover,compared to other methods,the results showed that the proposed method gives better accuracy and less error in most cases.
基金Supported by the Natural Science Foundation of Shandong Province(ZR2013FL034)
文摘The fuzzy measure and fuzzy integral are applied to the classification of software defects in this paper. The fuzzy measure of software attributes and attributes' sets are treated by genetic algorithm, and then software attributes are fused by the Choquet fuzzy integral algorithm. Finally, the class labels of soft- ware modules can be output. Experimental results have shown that there are interactions between characteristic attributes of software modules, and also proved that the fuzzy integral fusing method using Fuzzy Measure based on Genetic Algorithm (GA-FM) can significantly improve the accuracy for software defect prediction.
基金supported by National Natural Science Foundation of China under Grant Nos.71471146,71501158 and 71871182General Program of Humanities and Social Sciences Research of Ministry of Education of China under Grant No.20XJA630003+1 种基金Fundamental Research Funds for the Central Universities under Grant No.3102020JC06Inno-vation Foundation for Doctor Dissertation of Northwestern Polytechnical University under Grant No.CX2021095.
文摘To avoid the decrease of system reliability due to insufficient component maintenance and the resource waste caused by excessive component maintenance,identifying the critical components of complex products is an effective way to improve the efficiency of maintenance activities.Existing studies on identifying critical components of complex products are mainly from two aspects i.e.,topological properties and functional properties,respectively.In this paper,we combine these two aspects to establish a hybrid intuitionistic fuzzy set to incorporate the different types of attribute values.Considering the mutual correlation between attributes,a combination of AHP(Analytic Hierarchy Process)and Improved Mahalanobis-Taguchi System(MTS)is used to determine the λ-Shapley fuzzy measures for attributes.Then,the λ-Shapley Choquet integral intuitionistic fuzzy TOPSIS(Technique for Order Preference by Similarity to an Ideal Solution)method is proposed for calculating the closeness degrees of components to generate their ranking order.Finally,a case study which is about the right gear of airbus 320 is taken as an example to verify the feasibility and effectiveness of this method.This novel methodology can effectively solve the critical components identification problem with different types of evaluation information and completely unknown weight information of attributes,which provides the implementation of protection measures for the system reliability of complex products.
基金supported by the National Natural Science Foundation of China(Nos.71201089,71201110, 71071018 and 71271217)the Natural Science Foundation Youth Project of Shandong Province,China (ZR2012GQ005)the Specialized Research Fund for the Doctoral Program of Higher Education(No. 20111101110036)
文摘In this study a new hybrid aggregation operator named as the generalized intuitionistic fuzzy hybrid Choquet averaging(GIFHCA) operator is defined.Meantime,some desirable properties are studied, and several important cases are examined.Furthermore,we define the generalized Shapley GIFHCA (GS-GIFHCA) operator,which does not only overall consider the importance of elements and their ordered positions,but also globally reflect the correlations among them and their ordered positions.In order to simplify the complexity of solving a fuzzy measure,we further define the generalizedλ-Shapley GIFHCA(GλS-GIFHCA) operator.
基金Supported by the National Natural Science Foundationof China ( No. 6 0 1740 49) and Sino- French JointL aboratory for Research in Com puter Science,Controland Applied Mathem atics ( L IAMA)
文摘A novel concept, called nonadditive set-valued measure, is first defined as a monotone and continuous set function. Then the interconnections between nonadditive set-valued measure and the additive set-valued measure as well as the fuzzy measure are discussed. Finally, an approach to construct a nonadditive compact set-valued measure is presented via Aumann fuzzy integral.
基金supported by the National Natural Science Foundation of China(Nos.7143100671401184)+2 种基金Key Project of Philosophy and Social Sciences Research,Ministry of Education,PRC(No.13JZD0016)China Postdoctoral Science Foundation(No.2014M552169)Central South University Business Management Postdoctoral Research Station
文摘The Choquet integral can serve as a useful tool to aggregate interacting criteria in an uncertain environment. In this paper, a trapezoidal intuitionistic fuzzy aggregation operator based on the Choquet integral is proposed for multi-criteria decision-making problems. The decision information takes the form of trapezoidal intuitionistic fuzzy numbers and both the importance and the interaction information among decision-making criteria are considered. On the basis of the introduction of trapezoidal intuitionistic fuzzy numbers, its operational laws and expected value are defined. A trapezoidal intuitionistic fuzzy aggregation operator based on the Choquet integral is then defined and some of its properties are investigated. A new multi-criteria decision-making method based on a trapezoidal intuitionistic fuzzy Choquet integral operator is proposed. Finally, an illustrative example is used to show the feasibility and availability of the proposed method.