Utilizing granular computing to enhance artificial neural network architecture, a newtype of network emerges—thegranular neural network (GNN). GNNs offer distinct advantages over their traditional counterparts: The a...Utilizing granular computing to enhance artificial neural network architecture, a newtype of network emerges—thegranular neural network (GNN). GNNs offer distinct advantages over their traditional counterparts: The ability toprocess both numerical and granular data, leading to improved interpretability. This paper proposes a novel designmethod for constructing GNNs, drawing inspiration from existing interval-valued neural networks built uponNNNs. However, unlike the proposed algorithm in this work, which employs interval values or triangular fuzzynumbers for connections, existing methods rely on a pre-defined numerical network. This new method utilizesa uniform distribution of information granularity to granulate connections with unknown parameters, resultingin independent GNN structures. To quantify the granularity output of the network, the product of two commonperformance indices is adopted: The coverage of numerical data and the specificity of information granules.Optimizing this combined performance index helps determine the optimal parameters for the network. Finally,the paper presents the complete model construction and validates its feasibility through experiments on datasetsfrom the UCIMachine Learning Repository. The results demonstrate the proposed algorithm’s effectiveness andpromising performance.展开更多
Let G be a connected graph of order n and m_(RD)^(L)_(G)I denote the number of reciprocal distance Laplacian eigenvaluesof G in an interval I.For a given interval I,we mainly present several bounds on m_(RD)^(L)_(G)I ...Let G be a connected graph of order n and m_(RD)^(L)_(G)I denote the number of reciprocal distance Laplacian eigenvaluesof G in an interval I.For a given interval I,we mainly present several bounds on m_(RD)^(L)_(G)I in terms of various structuralparameters of the graph G,including vertex-connectivity,independence number and pendant vertices.展开更多
We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists betw...We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.展开更多
The circular chromatic number of a graph is an important parameter of a graph. The distance graph G(Z,D) , with a distance set D , is the infinite graph with vertex set Z={0,±1,±2,...} in which tw...The circular chromatic number of a graph is an important parameter of a graph. The distance graph G(Z,D) , with a distance set D , is the infinite graph with vertex set Z={0,±1,±2,...} in which two vertices x and y are adjacent iff y-x∈D . This paper determines the circular chromatic numbers of two classes of distance graphs G(Z,D m,k,k+1 ) and G(Z,D m,k,k+1,k+2 ).展开更多
A method for ranking complementary judgment matrixes with traspezoidal fuzzy numbers based on Hausdorff metric distance and fuzzy compromise decision approach is proposed. With regard to fuzzy number complementary jud...A method for ranking complementary judgment matrixes with traspezoidal fuzzy numbers based on Hausdorff metric distance and fuzzy compromise decision approach is proposed. With regard to fuzzy number complementary judgment matrixes given by a decider group whose members have various weights, the expert＇s information was aggregated first by means of simple weight average（SWA） method and Bonissone calculational method. Hence a matrix including all the experts＇ preference information was got. Then the matrix＇ column members were added up and the fuzzy evaluation values of the alternatives were got. Lastly, the Hausdorff metric distance and fuzzy compromise decision approach were used to rank the fuzzy evaluation values and then the ranking values of all the alternatives were got. Because exact numbers and triangular fuzzy numbers could all be transformed into trapezoidal fuzzy numbers, the method developed can rank complementary judgment matrixes with trapezoidal fuzzy numbers, triangular fuzzy numbers and exact numbers as well. An illustrative example is also given to verify the developed method and to demonstrate its feasibility and practicality.展开更多
A novel permutation-dependent Baire distance is introduced for multi-channel data. The optimal permutation is given by minimizing the sum of these pairwise distances. It is shown that for most practical cases the mini...A novel permutation-dependent Baire distance is introduced for multi-channel data. The optimal permutation is given by minimizing the sum of these pairwise distances. It is shown that for most practical cases the minimum is attained by a new gradient descent algorithm introduced in this article. It is of biquadratic time complexity: Both quadratic in number of channels and in size of data. The optimal permutation allows us to introduce a novel Baire-distance kernel Support Vector Machine (SVM). Applied to benchmark hyperspectral remote sensing data, this new SVM produces results which are comparable with the classical linear SVM, but with higher kernel target alignment.展开更多
This paper establishes the fuzzy discounted cash flow model to settle the uncertainties of the cash flow and discount rate in two-stage DCF model, to take the imprecise of the time period of the supernormal growth pha...This paper establishes the fuzzy discounted cash flow model to settle the uncertainties of the cash flow and discount rate in two-stage DCF model, to take the imprecise of the time period of the supernormal growth phase with considering the investor＇s attitude to risk. Firstly, the discount rate and the growth rate are fuzzified as triangular fuzzy numbers in this fuzzy discounted cash flow model. Then the intrinsic value of an asset can be evaluated by the arithmetic operation on interval and λ- signed distance method under the framework of DCF approach. Finally, a listed company at Shanghai Stock Exchange is analyzed as the case to demonstrate the process of stock value calculation by the fuzzy discounted cash flow model.展开更多
选择合适的海上风力发电机机型对海上风电场的长期高效运行起着至关重要的作用。针对决策者在风机选型决策过程中存在不确定性和主观偏好等问题,提出一种改进的多准则决策(multi-criteria decision making, MCDM)框架及方法:在权重求解...选择合适的海上风力发电机机型对海上风电场的长期高效运行起着至关重要的作用。针对决策者在风机选型决策过程中存在不确定性和主观偏好等问题,提出一种改进的多准则决策(multi-criteria decision making, MCDM)框架及方法:在权重求解算法中将群体决策和直觉模糊数与层次分析法相结合,提出群体直觉模糊层次分析法(group intuitionistic fuzzy analytic hierarchy process, GIAHP)计算指标权重;在备选方案排序算法中将余弦距离引入接近理想点法(technique for order preference by similarity to an ideal solution, TOPSIS),提出多距离TOPSIS确定备选方案排序。最后以山东省海上风电场风机选型为例,并通过敏感性分析验证框架及方法的鲁棒性。该框架及方法为中国海上风电场风机选型提供理论依据,可确保海上风电场长期稳定运行。展开更多
基金the National Key R&D Program of China under Grant 2018YFB1700104.
文摘Utilizing granular computing to enhance artificial neural network architecture, a newtype of network emerges—thegranular neural network (GNN). GNNs offer distinct advantages over their traditional counterparts: The ability toprocess both numerical and granular data, leading to improved interpretability. This paper proposes a novel designmethod for constructing GNNs, drawing inspiration from existing interval-valued neural networks built uponNNNs. However, unlike the proposed algorithm in this work, which employs interval values or triangular fuzzynumbers for connections, existing methods rely on a pre-defined numerical network. This new method utilizesa uniform distribution of information granularity to granulate connections with unknown parameters, resultingin independent GNN structures. To quantify the granularity output of the network, the product of two commonperformance indices is adopted: The coverage of numerical data and the specificity of information granules.Optimizing this combined performance index helps determine the optimal parameters for the network. Finally,the paper presents the complete model construction and validates its feasibility through experiments on datasetsfrom the UCIMachine Learning Repository. The results demonstrate the proposed algorithm’s effectiveness andpromising performance.
基金supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“Graph problems of topological parameters based on the spectra of graph matrices”(2021D01C069)the National Natural Science Foundation of the People's Republic of China“The investigation of spectral properties of graph operations and their related problems”(12161085)。
文摘Let G be a connected graph of order n and m_(RD)^(L)_(G)I denote the number of reciprocal distance Laplacian eigenvaluesof G in an interval I.For a given interval I,we mainly present several bounds on m_(RD)^(L)_(G)I in terms of various structuralparameters of the graph G,including vertex-connectivity,independence number and pendant vertices.
文摘We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.
文摘The circular chromatic number of a graph is an important parameter of a graph. The distance graph G(Z,D) , with a distance set D , is the infinite graph with vertex set Z={0,±1,±2,...} in which two vertices x and y are adjacent iff y-x∈D . This paper determines the circular chromatic numbers of two classes of distance graphs G(Z,D m,k,k+1 ) and G(Z,D m,k,k+1,k+2 ).
文摘A method for ranking complementary judgment matrixes with traspezoidal fuzzy numbers based on Hausdorff metric distance and fuzzy compromise decision approach is proposed. With regard to fuzzy number complementary judgment matrixes given by a decider group whose members have various weights, the expert＇s information was aggregated first by means of simple weight average（SWA） method and Bonissone calculational method. Hence a matrix including all the experts＇ preference information was got. Then the matrix＇ column members were added up and the fuzzy evaluation values of the alternatives were got. Lastly, the Hausdorff metric distance and fuzzy compromise decision approach were used to rank the fuzzy evaluation values and then the ranking values of all the alternatives were got. Because exact numbers and triangular fuzzy numbers could all be transformed into trapezoidal fuzzy numbers, the method developed can rank complementary judgment matrixes with trapezoidal fuzzy numbers, triangular fuzzy numbers and exact numbers as well. An illustrative example is also given to verify the developed method and to demonstrate its feasibility and practicality.
文摘A novel permutation-dependent Baire distance is introduced for multi-channel data. The optimal permutation is given by minimizing the sum of these pairwise distances. It is shown that for most practical cases the minimum is attained by a new gradient descent algorithm introduced in this article. It is of biquadratic time complexity: Both quadratic in number of channels and in size of data. The optimal permutation allows us to introduce a novel Baire-distance kernel Support Vector Machine (SVM). Applied to benchmark hyperspectral remote sensing data, this new SVM produces results which are comparable with the classical linear SVM, but with higher kernel target alignment.
基金Supported by the Natural Science Foundation of Anhui Province （Item No： 070416276X）.
文摘This paper establishes the fuzzy discounted cash flow model to settle the uncertainties of the cash flow and discount rate in two-stage DCF model, to take the imprecise of the time period of the supernormal growth phase with considering the investor＇s attitude to risk. Firstly, the discount rate and the growth rate are fuzzified as triangular fuzzy numbers in this fuzzy discounted cash flow model. Then the intrinsic value of an asset can be evaluated by the arithmetic operation on interval and λ- signed distance method under the framework of DCF approach. Finally, a listed company at Shanghai Stock Exchange is analyzed as the case to demonstrate the process of stock value calculation by the fuzzy discounted cash flow model.
文摘选择合适的海上风力发电机机型对海上风电场的长期高效运行起着至关重要的作用。针对决策者在风机选型决策过程中存在不确定性和主观偏好等问题,提出一种改进的多准则决策(multi-criteria decision making, MCDM)框架及方法:在权重求解算法中将群体决策和直觉模糊数与层次分析法相结合,提出群体直觉模糊层次分析法(group intuitionistic fuzzy analytic hierarchy process, GIAHP)计算指标权重;在备选方案排序算法中将余弦距离引入接近理想点法(technique for order preference by similarity to an ideal solution, TOPSIS),提出多距离TOPSIS确定备选方案排序。最后以山东省海上风电场风机选型为例,并通过敏感性分析验证框架及方法的鲁棒性。该框架及方法为中国海上风电场风机选型提供理论依据,可确保海上风电场长期稳定运行。
