For some complicated graphs obtained by graph operations,it is very difficult to compute resistance distance and Kirchhoff index.Define a new graph operation,and obtain a class of new join graphs:the subdivision-verte...For some complicated graphs obtained by graph operations,it is very difficult to compute resistance distance and Kirchhoff index.Define a new graph operation,and obtain a class of new join graphs:the subdivision-vertex-vertex join G_1* G_2.Then,describe the Laplacian matrix of the graph G_1 * G_2 and use generalized inverse of the Laplacian matrix to get formulas for resistance distance and Kirchhoff index.Through the obtained formulas,the resistance distance of any pairs of vertices and Kirchhoff index of the join graph can be computed.展开更多
This thesis aims to propose a novel distance operator,the probabilistic linguistic term ordered weighted distance(PLTOWD)operator,which enriches the distance theory in probabilistic linguistic term circumstances.The P...This thesis aims to propose a novel distance operator,the probabilistic linguistic term ordered weighted distance(PLTOWD)operator,which enriches the distance theory in probabilistic linguistic term circumstances.The PLTOWD operator is an efficient tool to deal with qualitative evaluation information and their corresponding probabilities or importance degrees.Moreover,some of its desired properties and different families of thePLTOWDoperator are discussed.Meanwhile,the extensions of the PLTOWD operator are also investigated.Then,a method of multiple attribute group decision making(MAGDM)in probabilistic linguistic term information is proposed on the basis of the PLTOWD operator.Finally,a numerical evaluation example in public Eco-environment satisfaction is developed to illustrate the practicability and effectiveness of the given method.Some discussions and comparisons are carried out according to the case results.展开更多
基金National Natural Science Foundation of China(No.11361033)
文摘For some complicated graphs obtained by graph operations,it is very difficult to compute resistance distance and Kirchhoff index.Define a new graph operation,and obtain a class of new join graphs:the subdivision-vertex-vertex join G_1* G_2.Then,describe the Laplacian matrix of the graph G_1 * G_2 and use generalized inverse of the Laplacian matrix to get formulas for resistance distance and Kirchhoff index.Through the obtained formulas,the resistance distance of any pairs of vertices and Kirchhoff index of the join graph can be computed.
基金The study receives funding from National Natural Science Foundation of China[grant numbers 71901088,71701001,and 71901001]Natural Science Foundation of Anhui Province[grant number 1808085QG211]+4 种基金Natural Sciences Research Project of Universities in Anhui[grant number KJ2020A0120]College Excellent Youth Talent Support Program[grant number gxyq2020041]Statistical Science Research Project of China[grant number 2017LZ11]Top Talent Academic Foundation for University Discipline of Anhui Province[grant number gxbjZD2020056]Social Science Innovation andDevelopment Research Project inAnhui Province[grant number 2019CX094].
文摘This thesis aims to propose a novel distance operator,the probabilistic linguistic term ordered weighted distance(PLTOWD)operator,which enriches the distance theory in probabilistic linguistic term circumstances.The PLTOWD operator is an efficient tool to deal with qualitative evaluation information and their corresponding probabilities or importance degrees.Moreover,some of its desired properties and different families of thePLTOWDoperator are discussed.Meanwhile,the extensions of the PLTOWD operator are also investigated.Then,a method of multiple attribute group decision making(MAGDM)in probabilistic linguistic term information is proposed on the basis of the PLTOWD operator.Finally,a numerical evaluation example in public Eco-environment satisfaction is developed to illustrate the practicability and effectiveness of the given method.Some discussions and comparisons are carried out according to the case results.
