We give a definition of relative entropy with respect to a sublinear expectation and establish large deviation principle for the empirical measures for independent random variables under the sublinear expectation.
To study the problems of multi-attribute decision making in which the attribute values are given in the form of linguistic fuzzy numbers and the information of attribute weights are incomplete, a new multi-attribute d...To study the problems of multi-attribute decision making in which the attribute values are given in the form of linguistic fuzzy numbers and the information of attribute weights are incomplete, a new multi-attribute decision making model is presented based on the optimal membership and the relative entropy. Firstly, the definitions of the optimal membership and the relative entropy are given. Secondly, for all alternatives, a set of preference weight vectors are obtained by solving a set of linear programming models whose goals axe all to maximize the optimal membership. Thirdly, a relative entropy model is established to aggregate the preference weight vectors, thus an optimal weight vector is determined. Based on this optimal weight vector, the algorithm of deviation degree minimization is proposed to rank all the alternatives. Finally, a decision making example is given to demonstrate the feasibility and rationality of this new model.展开更多
Let （Xn）n∈EN be a sequence of arbitrary continuous random variables, by the notion of relative entropy hμ^μ（w） as a measure of dissimilarity between probability measure # and reference measure μ, the explicit,...Let （Xn）n∈EN be a sequence of arbitrary continuous random variables, by the notion of relative entropy hμ^μ（w） as a measure of dissimilarity between probability measure # and reference measure μ, the explicit, general bounds for the partial sums of arbitrary continuous random variables under suitable conditions are developed. The argument uses the known and elementary lcmma of convergence for likelihood ratio.展开更多
An experimental study was undertaken to express the hardening Swift law according to friction stir welding （FSW） aluminum alloy 2017. Tensile tests of welded joints were run in accordance with face centered composit...An experimental study was undertaken to express the hardening Swift law according to friction stir welding （FSW） aluminum alloy 2017. Tensile tests of welded joints were run in accordance with face centered composite design. Two types of identified models based on least square method and response surface method were used to assess the contribution of FSW independent factors on the hardening parameters. These models were introduced into finite-element code ＂Abaqus＂ to simulate tensile tests of welded joints. The relative average deviation criterion, between the experimental data and the numerical simulations of tension-elongation of tensile tests, shows good agreement between the experimental results and the predicted hardening models. These results can be used to perform multi-criteria optimization for carrying out specific welds or conducting numerical simulation of plastic deformation of forming process of FSW parts such as hydroforming, bending and forging.展开更多
The distribution performance of the gravity-type liquid distributor(GTLD) significantly affects column operation efficiency and the consequent product quality. In industrial settings, maldistribution is normally consi...The distribution performance of the gravity-type liquid distributor(GTLD) significantly affects column operation efficiency and the consequent product quality. In industrial settings, maldistribution is normally considered to be caused by vertical positional or coplanarity errors stemming from deflections associated with manufacture and installation, or even by excessive weight. The lack ofestimation protocols or standards impedes the description ofthis error, which influences the corresponding outflow rates. Given this situation, the paper proposes a lumped parameter, orifice position deviation(OPD), to facilitate the calculation of the relative discharge rate error(RDRE)based on a formula derivation, which allows the systematic analysis of the influence ofa single orifice or weir OPD.The paper introduces a sensitivity factor K as a concise and unified expression in theoretical RDREs for calibrating the influence of OPD on the RDREs ofgeometrically different orifices and weirs. With respect to the GTLD, a larger K indicates the need for more strict OPD requirements. The paper verifies that the extent of GTLD outflow nonuniformity is associated with diverging tendencies regarding its morphology, especially in the orifice and weir, which can be determined using our proposed procedures.展开更多
基金supported by the National Natural Science Foundation of China(11171262)the Specialized Research Fund for the Doctoral Program of Higher Education (200804860048)
文摘We give a definition of relative entropy with respect to a sublinear expectation and establish large deviation principle for the empirical measures for independent random variables under the sublinear expectation.
基金supported by the National Natural Science Foundation of China(70771041)Chinese Astronautics SupportTechnology Foundation and the Excellent Youth Project of Hubei Provincial Department of Education(Q20082705)
文摘To study the problems of multi-attribute decision making in which the attribute values are given in the form of linguistic fuzzy numbers and the information of attribute weights are incomplete, a new multi-attribute decision making model is presented based on the optimal membership and the relative entropy. Firstly, the definitions of the optimal membership and the relative entropy are given. Secondly, for all alternatives, a set of preference weight vectors are obtained by solving a set of linear programming models whose goals axe all to maximize the optimal membership. Thirdly, a relative entropy model is established to aggregate the preference weight vectors, thus an optimal weight vector is determined. Based on this optimal weight vector, the algorithm of deviation degree minimization is proposed to rank all the alternatives. Finally, a decision making example is given to demonstrate the feasibility and rationality of this new model.
基金Supported by the NNSF of China(10571076) Anhui High Education Research Grant( 2006Kj246B).
文摘Let （Xn）n∈EN be a sequence of arbitrary continuous random variables, by the notion of relative entropy hμ^μ（w） as a measure of dissimilarity between probability measure # and reference measure μ, the explicit, general bounds for the partial sums of arbitrary continuous random variables under suitable conditions are developed. The argument uses the known and elementary lcmma of convergence for likelihood ratio.
文摘An experimental study was undertaken to express the hardening Swift law according to friction stir welding （FSW） aluminum alloy 2017. Tensile tests of welded joints were run in accordance with face centered composite design. Two types of identified models based on least square method and response surface method were used to assess the contribution of FSW independent factors on the hardening parameters. These models were introduced into finite-element code ＂Abaqus＂ to simulate tensile tests of welded joints. The relative average deviation criterion, between the experimental data and the numerical simulations of tension-elongation of tensile tests, shows good agreement between the experimental results and the predicted hardening models. These results can be used to perform multi-criteria optimization for carrying out specific welds or conducting numerical simulation of plastic deformation of forming process of FSW parts such as hydroforming, bending and forging.
文摘The distribution performance of the gravity-type liquid distributor(GTLD) significantly affects column operation efficiency and the consequent product quality. In industrial settings, maldistribution is normally considered to be caused by vertical positional or coplanarity errors stemming from deflections associated with manufacture and installation, or even by excessive weight. The lack ofestimation protocols or standards impedes the description ofthis error, which influences the corresponding outflow rates. Given this situation, the paper proposes a lumped parameter, orifice position deviation(OPD), to facilitate the calculation of the relative discharge rate error(RDRE)based on a formula derivation, which allows the systematic analysis of the influence ofa single orifice or weir OPD.The paper introduces a sensitivity factor K as a concise and unified expression in theoretical RDREs for calibrating the influence of OPD on the RDREs ofgeometrically different orifices and weirs. With respect to the GTLD, a larger K indicates the need for more strict OPD requirements. The paper verifies that the extent of GTLD outflow nonuniformity is associated with diverging tendencies regarding its morphology, especially in the orifice and weir, which can be determined using our proposed procedures.
