The class of multiple attribute decision making （MADM） problems is studied, where the attribute values are intuitionistic fuzzy numbers, and the information about attribute weights is completely unknown. A score fun...The class of multiple attribute decision making （MADM） problems is studied, where the attribute values are intuitionistic fuzzy numbers, and the information about attribute weights is completely unknown. A score function is first used to calculate the score of each attribute value and a score matrix is constructed, and then it is transformed into a normalized score matrix. Based on the normalized score matrix, an entropy-based procedure is proposed to derive attribute weights. Furthermore, the additive weighted averaging operator is utilized to fuse all the normalized scores into the overall scores of alternatives, by which the ranking of all the given alternatives is obtained. This paper is concluded by extending the above results to interval-valued intuitionistic fuzzy set theory, and an illustrative example is also provided.展开更多
Let X be an infinite-dimensional complex Banach space and denote by B（X） the algebra of all bounded linear operators acting on X. It is shown that a surjective additive map Φ from B（X） onto itself preserves simil...Let X be an infinite-dimensional complex Banach space and denote by B（X） the algebra of all bounded linear operators acting on X. It is shown that a surjective additive map Φ from B（X） onto itself preserves similarity in both directions if and only if there exist a scalar c, a bounded invertible linear or conjugate linear operator A and a similarity invariant additive functional ψ on B（X） such that either Φ（T） = cATA^-1 ＋ ψ（T）I for all T, or Φ（T） = cAT＊A^-1 ＋ ψ（T）I for all T. In the case where X has infinite multiplicity, in particular, when X is an infinite-dimensional Hilbert space, the above similarity invariant additive functional ψ is always zero.展开更多
For the first time,we derive the compact forms of normalization factors for photon-added（-subtracted） two-mode squeezed thermal states by using the P-representation and the integration within an ordered product of o...For the first time,we derive the compact forms of normalization factors for photon-added（-subtracted） two-mode squeezed thermal states by using the P-representation and the integration within an ordered product of operators（IWOP） technique.It is found that these two factors are related to the Jacobi polynomials.In addition,some new relationships for Jacobi polynomials are presented.展开更多
In this work,noise removal in digital images is investigated.The importance of this problem lies in the fact that removal of noise is a necessary pre-processing step for other image processing tasks such as edge detec...In this work,noise removal in digital images is investigated.The importance of this problem lies in the fact that removal of noise is a necessary pre-processing step for other image processing tasks such as edge detection,image segmentation,image compression,classification problems,image registration etc.A number of different approaches have been proposed in the literature.In this work,a non-linear PDE-based algorithm is developed based on the ideas proposed by Lysaker,Osher and Tai[IEEE Trans.Image Process.,13(2004),1345-1357].This algorithm consists of two steps:flow field smoothing of the normal vectors,followed by image reconstruction.We propose a finite-difference based additive operator-splitting method that allows for much larger time-steps.This results in an efficient method for noise-removal that is shown to have good visual results.The energy is studied as an objective measure of the algorithm performance.展开更多
This paper presents the iterated addition operation of Petri nets and dis-cusses its application in analysis and synthesis of cycle type systems and star type systems. A group of necessary and sufficient conditions fo...This paper presents the iterated addition operation of Petri nets and dis-cusses its application in analysis and synthesis of cycle type systems and star type systems. A group of necessary and sufficient conditions for analysis of structural properties is obtained. In addition sufficient conditions for general systems are obtained.展开更多
基金supported by the National Science Fund for Distinguished Young Scholars of China(70625005).
文摘The class of multiple attribute decision making （MADM） problems is studied, where the attribute values are intuitionistic fuzzy numbers, and the information about attribute weights is completely unknown. A score function is first used to calculate the score of each attribute value and a score matrix is constructed, and then it is transformed into a normalized score matrix. Based on the normalized score matrix, an entropy-based procedure is proposed to derive attribute weights. Furthermore, the additive weighted averaging operator is utilized to fuse all the normalized scores into the overall scores of alternatives, by which the ranking of all the given alternatives is obtained. This paper is concluded by extending the above results to interval-valued intuitionistic fuzzy set theory, and an illustrative example is also provided.
文摘Let X be an infinite-dimensional complex Banach space and denote by B（X） the algebra of all bounded linear operators acting on X. It is shown that a surjective additive map Φ from B（X） onto itself preserves similarity in both directions if and only if there exist a scalar c, a bounded invertible linear or conjugate linear operator A and a similarity invariant additive functional ψ on B（X） such that either Φ（T） = cATA^-1 ＋ ψ（T）I for all T, or Φ（T） = cAT＊A^-1 ＋ ψ（T）I for all T. In the case where X has infinite multiplicity, in particular, when X is an infinite-dimensional Hilbert space, the above similarity invariant additive functional ψ is always zero.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11264018 and 60978009)the Major Research Plan of the National Natural Science Foundation of China (Grant No. 91121023)+1 种基金the National Basic Research Project of China (Grant No. 2011CBA00200)the Young Talents Foundation of Jiangxi Normal University,China
文摘For the first time,we derive the compact forms of normalization factors for photon-added（-subtracted） two-mode squeezed thermal states by using the P-representation and the integration within an ordered product of operators（IWOP） technique.It is found that these two factors are related to the Jacobi polynomials.In addition,some new relationships for Jacobi polynomials are presented.
文摘In this work,noise removal in digital images is investigated.The importance of this problem lies in the fact that removal of noise is a necessary pre-processing step for other image processing tasks such as edge detection,image segmentation,image compression,classification problems,image registration etc.A number of different approaches have been proposed in the literature.In this work,a non-linear PDE-based algorithm is developed based on the ideas proposed by Lysaker,Osher and Tai[IEEE Trans.Image Process.,13(2004),1345-1357].This algorithm consists of two steps:flow field smoothing of the normal vectors,followed by image reconstruction.We propose a finite-difference based additive operator-splitting method that allows for much larger time-steps.This results in an efficient method for noise-removal that is shown to have good visual results.The energy is studied as an objective measure of the algorithm performance.
文摘This paper presents the iterated addition operation of Petri nets and dis-cusses its application in analysis and synthesis of cycle type systems and star type systems. A group of necessary and sufficient conditions for analysis of structural properties is obtained. In addition sufficient conditions for general systems are obtained.
