Fuzzy similarity measures, which are used to judge the closeness of two fuzzy sets, are presented to evaluate the water quality of the Haihe River. Based on the membership functions and coefficient of variation as the...Fuzzy similarity measures, which are used to judge the closeness of two fuzzy sets, are presented to evaluate the water quality of the Haihe River. Based on the membership functions and coefficient of variation as the weights, four fuzzy similarity measures （including Lattice similarity measure, Hamming similarity measure, Euclidean similarity measure and the max-min similarity measure） are used to classify the 299 samples into the proper water quality standard ranks. The results are compared with the traditional distance discriminant methods. The calculation of two traditional distance discriminant methods （both Euclidean distance and absolute value distance） is also based on the use of coefficients of variation as the weights. Without the Lattice similarity measure, for this method loses some information, the correct assignment of samples classified into the same water quality ranks is 75.92% with the other three similarity measures and two distance discriminant methods. This result shows the reliability of the five methods. Only considering the three similarity measures, there were only 1.01% of the samples that did not classify to the same ranks, while the corresponding ratio of the two distance discriminant methods was 5.69%. The results of leave-one-out cross validation show that more than 88% of the samples are classified to the proper ranks, which demonstrates that the similarity measures are suitable to evaluate the water quality of the Haihe River.展开更多
In the context of multivariate regular variation,the authors establish the first-order asymptotics of the spectral risk measure of portfolio loss.Furthermore,by the notion of second-order regular variation,the second-...In the context of multivariate regular variation,the authors establish the first-order asymptotics of the spectral risk measure of portfolio loss.Furthermore,by the notion of second-order regular variation,the second-order asymptotics of the spectral risk measure of portfolio loss is also presented.In order to illustrate the derived results,a numerical example with Monte Carlo simulation is carried out.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
基金supported by the National Natural Science Foundation of China (No.51178018,71031001)
文摘Fuzzy similarity measures, which are used to judge the closeness of two fuzzy sets, are presented to evaluate the water quality of the Haihe River. Based on the membership functions and coefficient of variation as the weights, four fuzzy similarity measures （including Lattice similarity measure, Hamming similarity measure, Euclidean similarity measure and the max-min similarity measure） are used to classify the 299 samples into the proper water quality standard ranks. The results are compared with the traditional distance discriminant methods. The calculation of two traditional distance discriminant methods （both Euclidean distance and absolute value distance） is also based on the use of coefficients of variation as the weights. Without the Lattice similarity measure, for this method loses some information, the correct assignment of samples classified into the same water quality ranks is 75.92% with the other three similarity measures and two distance discriminant methods. This result shows the reliability of the five methods. Only considering the three similarity measures, there were only 1.01% of the samples that did not classify to the same ranks, while the corresponding ratio of the two distance discriminant methods was 5.69%. The results of leave-one-out cross validation show that more than 88% of the samples are classified to the proper ranks, which demonstrates that the similarity measures are suitable to evaluate the water quality of the Haihe River.
基金supported by the Important Natural Science Foundation of Colleges and Universities of Anhui Province under Grant No.KJ2020A0122the Scientific Research Start-up Foundation of Hefei Normal University。
文摘In the context of multivariate regular variation,the authors establish the first-order asymptotics of the spectral risk measure of portfolio loss.Furthermore,by the notion of second-order regular variation,the second-order asymptotics of the spectral risk measure of portfolio loss is also presented.In order to illustrate the derived results,a numerical example with Monte Carlo simulation is carried out.
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.
