The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity d...The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity degree/relation in multi-scale map spaces and then proposes a model for calculating the degree of spatial similarity between a point cloud at one scale and its gener- alized counterpart at another scale. After validation, the new model features 16 points with map scale change as the x coordinate and the degree of spatial similarity as the y coordinate. Finally, using an application for curve fitting, the model achieves an empirical formula that can calculate the degree of spatial similarity using map scale change as the sole independent variable, and vice versa. This formula can be used to automate algorithms for point feature generalization and to determine when to terminate them during the generalization.展开更多
In presented fuzzy multi-attribute decision-making （FMADM） problems, the information about attribute weights is interval numbers and the decision maker （DM） has fuzzy complementary preference relation on alternati...In presented fuzzy multi-attribute decision-making （FMADM） problems, the information about attribute weights is interval numbers and the decision maker （DM） has fuzzy complementary preference relation on alternatives. Firstly, the decision-making information based on the subjective preference information in the form of the fuzzy complementary judgment matrix is uniform by using a translation function. Then an objective programming model is established. Attribute weights are obtained by solving the model, thus the fuzzy overall values of alternatives are derived by using the additive weighting method. Secondly, the ranking approach of alternatives is proposed based on the degree of similarity between the fuzzy positive ideal solution of alternatives （FPISA） and the fuzzy overall values. The method can sufficiently utilize the objective information of alternatives and meet the subjective requirements of the DM as much as possible. It is easy to be operated and implemented on a computer. Finally, the proposed method is applied to the project evaluation in the venture investment.展开更多
Study of fuzzy entropy and similarity measure on intuitionistic fuzzy sets (IFSs) was proposed and analyzed. Unlike fuzzy set, IFSs contain uncertainty named hesitance, which is contained in fuzzy membership function ...Study of fuzzy entropy and similarity measure on intuitionistic fuzzy sets (IFSs) was proposed and analyzed. Unlike fuzzy set, IFSs contain uncertainty named hesitance, which is contained in fuzzy membership function itself. Hence, designing fuzzy entropy is not easy because of many entropy definitions. By considering different fuzzy entropy definitions, fuzzy entropy on IFSs is designed and discussed. Similarity measure was also presented and its usefulness was verified to evaluate degree of similarity.展开更多
Similarity measure design for discrete data group was proposed. Similarity measure design for continuous membership function was also carried out. Proposed similarity measures were designed based on fuzzy number and d...Similarity measure design for discrete data group was proposed. Similarity measure design for continuous membership function was also carried out. Proposed similarity measures were designed based on fuzzy number and distance measure, and were proved. To calculate the degree of similarity of discrete data, relative degree between data and total distribution was obtained. Discrete data similarity measure was completed with combination of mentioned relative degrees. Power interconnected system with multi characteristics was considered to apply discrete similarity measure. Naturally, similarity measure was extended to multi-dimensional similarity measure case, and applied to bus clustering problem.展开更多
The multiobjective group decision-making problem under risk is common in reality. This paper focuses on the study about risky multiobjective group decision-making problem where the index value is not certain. We give ...The multiobjective group decision-making problem under risk is common in reality. This paper focuses on the study about risky multiobjective group decision-making problem where the index value is not certain. We give indexes classifying method and index normalizing formula of this type problem. By building objective function that minimizes general weighted distance from every alternative to the relatively best and worst alternative, the optimal membership degree of every decision-maker to every alternative can be obtained, and by building another objective function that minimizes general weighted distance from the optimal membership degree of every decision-maker to every alternative to the group optimal alternative and the group inferior alternative, the optimal membership degree of every decision-maker to every alternative can be obtained, which are both based on probability theory and fuzzy theory. Aftermost a model is established which collects group preferences. This method provides a new idea and approach for solving multiobjective decision-making problem among uncertain system, which is applicable for practical problem. Finally a case study shows a satisfactory result.展开更多
A dynamic hesitant fuzzy linguistic group decisionmaking(DHFLGDM) problem is studied from the perspective of information reliability based on the theory of hesitant fuzzy linguistic term sets(HFLTSs). First, an approa...A dynamic hesitant fuzzy linguistic group decisionmaking(DHFLGDM) problem is studied from the perspective of information reliability based on the theory of hesitant fuzzy linguistic term sets(HFLTSs). First, an approach is applied to transform the dynamic HFLTSs(DHFLTSs) into a set of proportional linguistic terms to eliminate the time dimension. Second, expert reliability is measured by considering both group similarity and degree of certainty, and an optimization method is employed to quantify the linguistic terms by maximizing the group similarity. Third, through computing the attribute stability as well as its reliability, a combination rule which considers both reliability and weight is proposed to aggregate the information, and then the aggregated grade values and degree of stability are used to make a selection. Finally,the application and feasibility of the proposed method are verified through a case study and method comparison.展开更多
The numerical calculation method is widely used in the evaluation of slope stability,but it cannot take the randomness and fuzziness into account that exist in rock and soil engineering objectively.The fuzzy optimizat...The numerical calculation method is widely used in the evaluation of slope stability,but it cannot take the randomness and fuzziness into account that exist in rock and soil engineering objectively.The fuzzy optimization theory is thus introduced to the evaluation of slope stability by this paper and a method of fuzzy optimal selection of similar slopes is put forward to analyze slope stability.By comparing the relative membership degrees that the evaluated object sample of slope is similar to the source samples of which the stabilities are detected clearly,the source sample with the maximal relative membership degree will be chosen as the best similar one to the object sample,and the stability of the object sample can be evaluated by that of the best similar source sample.In the process many uncertain influential factors are considered and characteristics and knowledge of the source samples are obtained.The practical calculation indicates that it can achieve good results to evaluate slope stability by using this method.展开更多
In order to distinguish with effect different hesitant fuzzy elements(HFEs), we introduce the asymmetrical relative entropy between HFEs as a distance measure for higher discernment. Next,the formula of attribute weig...In order to distinguish with effect different hesitant fuzzy elements(HFEs), we introduce the asymmetrical relative entropy between HFEs as a distance measure for higher discernment. Next,the formula of attribute weights is derived via an optimal model according to TOPSIS from the relative closeness degree constructed by the discerning relative entropy. Then, we propose the concept of cocorrelation degree from the viewpoint of probability theory and develop another new formula of hesitant fuzzy correlation coeffcient, and prove their similar properties to the traditional correlation coeffcient.To make full use of the existing similarity measures including the ones presented by us, we consider aggregation of similarity measures for hesitant fuzzy sets and derive the synthetical similarity formula.Finally, the derived formula is used for netting clustering analysis under hesitant fuzzy information and the effectiveness and superiority are veri?ed through a comparison analysis of clustering results obtained by other clustering algorithms.展开更多
基金funded by the Natural Science Foundation Committee,China(41364001,41371435)
文摘The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity degree/relation in multi-scale map spaces and then proposes a model for calculating the degree of spatial similarity between a point cloud at one scale and its gener- alized counterpart at another scale. After validation, the new model features 16 points with map scale change as the x coordinate and the degree of spatial similarity as the y coordinate. Finally, using an application for curve fitting, the model achieves an empirical formula that can calculate the degree of spatial similarity using map scale change as the sole independent variable, and vice versa. This formula can be used to automate algorithms for point feature generalization and to determine when to terminate them during the generalization.
文摘In presented fuzzy multi-attribute decision-making （FMADM） problems, the information about attribute weights is interval numbers and the decision maker （DM） has fuzzy complementary preference relation on alternatives. Firstly, the decision-making information based on the subjective preference information in the form of the fuzzy complementary judgment matrix is uniform by using a translation function. Then an objective programming model is established. Attribute weights are obtained by solving the model, thus the fuzzy overall values of alternatives are derived by using the additive weighting method. Secondly, the ranking approach of alternatives is proposed based on the degree of similarity between the fuzzy positive ideal solution of alternatives （FPISA） and the fuzzy overall values. The method can sufficiently utilize the objective information of alternatives and meet the subjective requirements of the DM as much as possible. It is easy to be operated and implemented on a computer. Finally, the proposed method is applied to the project evaluation in the venture investment.
基金Project(ER120001) supported by Development of Application Technology BioNano Super Composites, Korea
文摘Study of fuzzy entropy and similarity measure on intuitionistic fuzzy sets (IFSs) was proposed and analyzed. Unlike fuzzy set, IFSs contain uncertainty named hesitance, which is contained in fuzzy membership function itself. Hence, designing fuzzy entropy is not easy because of many entropy definitions. By considering different fuzzy entropy definitions, fuzzy entropy on IFSs is designed and discussed. Similarity measure was also presented and its usefulness was verified to evaluate degree of similarity.
基金Project(2010-0020163) supported by Key Research Institute Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology, Korea
文摘Similarity measure design for discrete data group was proposed. Similarity measure design for continuous membership function was also carried out. Proposed similarity measures were designed based on fuzzy number and distance measure, and were proved. To calculate the degree of similarity of discrete data, relative degree between data and total distribution was obtained. Discrete data similarity measure was completed with combination of mentioned relative degrees. Power interconnected system with multi characteristics was considered to apply discrete similarity measure. Naturally, similarity measure was extended to multi-dimensional similarity measure case, and applied to bus clustering problem.
文摘The multiobjective group decision-making problem under risk is common in reality. This paper focuses on the study about risky multiobjective group decision-making problem where the index value is not certain. We give indexes classifying method and index normalizing formula of this type problem. By building objective function that minimizes general weighted distance from every alternative to the relatively best and worst alternative, the optimal membership degree of every decision-maker to every alternative can be obtained, and by building another objective function that minimizes general weighted distance from the optimal membership degree of every decision-maker to every alternative to the group optimal alternative and the group inferior alternative, the optimal membership degree of every decision-maker to every alternative can be obtained, which are both based on probability theory and fuzzy theory. Aftermost a model is established which collects group preferences. This method provides a new idea and approach for solving multiobjective decision-making problem among uncertain system, which is applicable for practical problem. Finally a case study shows a satisfactory result.
基金supported by the National Natural Science Foundation of China(71171112 71502073+2 种基金 71601002)the Scientific Innovation Research of College Graduates in Jiangsu Province(KYZZ150094)the Anhui Provincial Natural Science Foundation(1708085MG168)
文摘A dynamic hesitant fuzzy linguistic group decisionmaking(DHFLGDM) problem is studied from the perspective of information reliability based on the theory of hesitant fuzzy linguistic term sets(HFLTSs). First, an approach is applied to transform the dynamic HFLTSs(DHFLTSs) into a set of proportional linguistic terms to eliminate the time dimension. Second, expert reliability is measured by considering both group similarity and degree of certainty, and an optimization method is employed to quantify the linguistic terms by maximizing the group similarity. Third, through computing the attribute stability as well as its reliability, a combination rule which considers both reliability and weight is proposed to aggregate the information, and then the aggregated grade values and degree of stability are used to make a selection. Finally,the application and feasibility of the proposed method are verified through a case study and method comparison.
基金Sponsored by the Natural Science Foundation of Liaoning Province in China(Grant No.20022106).
文摘The numerical calculation method is widely used in the evaluation of slope stability,but it cannot take the randomness and fuzziness into account that exist in rock and soil engineering objectively.The fuzzy optimization theory is thus introduced to the evaluation of slope stability by this paper and a method of fuzzy optimal selection of similar slopes is put forward to analyze slope stability.By comparing the relative membership degrees that the evaluated object sample of slope is similar to the source samples of which the stabilities are detected clearly,the source sample with the maximal relative membership degree will be chosen as the best similar one to the object sample,and the stability of the object sample can be evaluated by that of the best similar source sample.In the process many uncertain influential factors are considered and characteristics and knowledge of the source samples are obtained.The practical calculation indicates that it can achieve good results to evaluate slope stability by using this method.
文摘In order to distinguish with effect different hesitant fuzzy elements(HFEs), we introduce the asymmetrical relative entropy between HFEs as a distance measure for higher discernment. Next,the formula of attribute weights is derived via an optimal model according to TOPSIS from the relative closeness degree constructed by the discerning relative entropy. Then, we propose the concept of cocorrelation degree from the viewpoint of probability theory and develop another new formula of hesitant fuzzy correlation coeffcient, and prove their similar properties to the traditional correlation coeffcient.To make full use of the existing similarity measures including the ones presented by us, we consider aggregation of similarity measures for hesitant fuzzy sets and derive the synthetical similarity formula.Finally, the derived formula is used for netting clustering analysis under hesitant fuzzy information and the effectiveness and superiority are veri?ed through a comparison analysis of clustering results obtained by other clustering algorithms.
