This paper is comprised of the modeling and optimization of a multi objective linear programming problem in fuzzy environment in which some goals are fractional and some are linear. Here, we present a new approach for...This paper is comprised of the modeling and optimization of a multi objective linear programming problem in fuzzy environment in which some goals are fractional and some are linear. Here, we present a new approach for its solution by using α-cut of fuzzy numbers. In this proposed method, we first define membership function for goals by introducing non-deviational variables for each of objective functions with effective use of α-cut intervals to deal with uncertain parameters being represented by fuzzy numbers. In the optimization process the under deviational variables are minimized for finding a most satisfactory solution. The developed method has also been implemented on a problem for illustration and comparison.展开更多
Surface accuracy directly affects the surface quality and performance of mechanical parts.Circular hole,especially spatial non-planar hole set is the typical feature and working surface of mechanical parts.Compared wi...Surface accuracy directly affects the surface quality and performance of mechanical parts.Circular hole,especially spatial non-planar hole set is the typical feature and working surface of mechanical parts.Compared with traditional machining methods,additive manufacturing(AM)technology can decrease the surface accuracy errors of circular holes during fabrication.However,an accuracy error may still exist on the surface of circular holes fabricated by AM due to the influence of staircase effect.This study proposes a surface accuracy optimization approach for mechanical parts with multiple circular holes for AM based on triangular fuzzy number(TFN).First,the feature lines on the manifold mesh are extracted using the dihedral angle method and normal tensor voting to detect the circular holes.Second,the optimal AM part build orientation is determined using the genetic algorithm to optimize the surface accuracy of the circular holes by minimizing the weighted volumetric error of the part.Third,the corresponding weights of the circular holes are calculated with the TFN analytic hierarchy process in accordance with the surface accuracy requirements.Lastly,an improved adaptive slicing algorithm is utilized to reduce the entire build time while maintaining the forming surface accuracy of the circular holes using digital twins via virtual printing.The effectiveness of the proposed approach is experimentally validated using two mechanical models.展开更多
Many kinds of uncertainties are involved, such as random, fuzzy, grey, unascertained property and so on, in soil erosion process. To exactly predict the non-point source pollution loads, some uncertainties should be t...Many kinds of uncertainties are involved, such as random, fuzzy, grey, unascertained property and so on, in soil erosion process. To exactly predict the non-point source pollution loads, some uncertainties should be taken into consideration. Aiming at the deficiency of present blind number theory being helpless for fuzziness, a novel blind number, i.e. extended-blind number, was introduced by substituting a set of triangular fuzzy numbers (TFNs), ex- pressed as α-cuts, for interval values in present blind number, and the expected value of extended-blind number was also brought forward by referring to the current blind number theory. On the basis of denoting the parameters of Uni- versal Soil Loss Equation (USLE) as extended-blind parameters, a novel USLE model was established for quantita- tively evaluating soil erosion loss and non-point source pollution loads. As a case, the uncertain USLE was employed for predicting the soil erosion loss and non-point source pollution loads of absorbed nitrogen and phosphorus in a district in the Hangbu-Fengle River basin, in the upstream of Chaohu Lake watershed. The results show that it is feasible in theory to extend blind number into fuzzy environment and reliable on conclusion to apply extended-blind number theory for predicting non-point source pollution loads.展开更多
文摘This paper is comprised of the modeling and optimization of a multi objective linear programming problem in fuzzy environment in which some goals are fractional and some are linear. Here, we present a new approach for its solution by using α-cut of fuzzy numbers. In this proposed method, we first define membership function for goals by introducing non-deviational variables for each of objective functions with effective use of α-cut intervals to deal with uncertain parameters being represented by fuzzy numbers. In the optimization process the under deviational variables are minimized for finding a most satisfactory solution. The developed method has also been implemented on a problem for illustration and comparison.
基金supported by the National Natural Science Foundation of China(Grant Nos.51775494,51821093,and 51935009)the National Key R&D Program of China(Grant No.2018YFB1700701)+1 种基金the Science and Technology Project of Zhejiang Province,China(Grant No.2019C01141)the Zhejiang Provincial Basic Public Welfare Research Project,China(Grant Nos.LGG18E050007 and LGG21E050020).
文摘Surface accuracy directly affects the surface quality and performance of mechanical parts.Circular hole,especially spatial non-planar hole set is the typical feature and working surface of mechanical parts.Compared with traditional machining methods,additive manufacturing(AM)technology can decrease the surface accuracy errors of circular holes during fabrication.However,an accuracy error may still exist on the surface of circular holes fabricated by AM due to the influence of staircase effect.This study proposes a surface accuracy optimization approach for mechanical parts with multiple circular holes for AM based on triangular fuzzy number(TFN).First,the feature lines on the manifold mesh are extracted using the dihedral angle method and normal tensor voting to detect the circular holes.Second,the optimal AM part build orientation is determined using the genetic algorithm to optimize the surface accuracy of the circular holes by minimizing the weighted volumetric error of the part.Third,the corresponding weights of the circular holes are calculated with the TFN analytic hierarchy process in accordance with the surface accuracy requirements.Lastly,an improved adaptive slicing algorithm is utilized to reduce the entire build time while maintaining the forming surface accuracy of the circular holes using digital twins via virtual printing.The effectiveness of the proposed approach is experimentally validated using two mechanical models.
基金Under the auspices of Tackling Key Program for Science and Technology of Anhui Province (No. 07010302165)Natural Science Foundation of Anhui Province (No. 050450303)
文摘Many kinds of uncertainties are involved, such as random, fuzzy, grey, unascertained property and so on, in soil erosion process. To exactly predict the non-point source pollution loads, some uncertainties should be taken into consideration. Aiming at the deficiency of present blind number theory being helpless for fuzziness, a novel blind number, i.e. extended-blind number, was introduced by substituting a set of triangular fuzzy numbers (TFNs), ex- pressed as α-cuts, for interval values in present blind number, and the expected value of extended-blind number was also brought forward by referring to the current blind number theory. On the basis of denoting the parameters of Uni- versal Soil Loss Equation (USLE) as extended-blind parameters, a novel USLE model was established for quantita- tively evaluating soil erosion loss and non-point source pollution loads. As a case, the uncertain USLE was employed for predicting the soil erosion loss and non-point source pollution loads of absorbed nitrogen and phosphorus in a district in the Hangbu-Fengle River basin, in the upstream of Chaohu Lake watershed. The results show that it is feasible in theory to extend blind number into fuzzy environment and reliable on conclusion to apply extended-blind number theory for predicting non-point source pollution loads.
