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Ren B.,Shaoxing University | Cheng X.-P.,Zhejiang Ocean University | Cheng X.-P.,Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province | Lin J.,Zhejiang Normal University
Nonlinear Dynamics | Year: 2016

The nonlocal symmetries for the (Formula presented.)-dimensional Konopelchenko–Dubrovsky equation are obtained with the truncated Painlevé method and the Möbious (conformal) invariant form. The nonlocal symmetries are localized to the Lie point symmetries by introducing auxiliary dependent variables. The finite symmetry transformations are obtained by solving the initial value problem of the prolonged systems. The multi-solitary wave solution is presented with the finite symmetry transformations of a trivial solution. In the meanwhile, symmetry reductions in the enlarged systems are studied by the Lie point symmetry approach. Many explicit interaction solutions between solitons and cnoidal periodic waves are discussed both in analytical and in graphical ways. © 2016 Springer Science+Business Media Dordrecht


Cui Z.,Zhejiang Ocean University | Cui Z.,Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province | Cui Z.,Key Laboratory of Offshore Engineering Technology of Zhejiang Province | Gu S.,Zhejiang Ocean University | And 2 more authors.
International Journal of Control and Automation | Year: 2015

Numerical simulation was conducted for fluid flow past a circular cylinder with triangular control rod in the upstream at low Reynolds numbers. The study focuses on the influences of leg length of rod L, rod-to-cylinder spacing ratio S, vertex angle of triangular a of rod on the vortex shedding and forces. The results show the equilateral triangle rod in the upstream takes effective suppression of not only the lift but also the drag in the range of 0.2R≤L≤0.5R and 3R≤S≤6R(R is the radius of circular cylinder), and the vortex shedding between the two cylinders maybe lead to sharp increasing of the force on the circular cylinder. © 2015 SERSC.


Dechao L.,Zhejiang Ocean University | Dechao L.,Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province | Yongjian X.,Shaanxi Normal University | Youfu J.,Zhejiang Ocean University | Youfu J.,Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province
Fuzzy Optimization and Decision Making | Year: 2015

In this paper, we investigate interval-valued fuzzy negations induced by interval-valued (Formula presented.)-norms, (Formula presented.)-conorms or implications. Some properties of interval-valued fuzzy negations induced by interval-valued sup-morphism (Formula presented.)-norms, inf-morphism (Formula presented.)-conorms or (Formula presented.)-implications are firstly obtained. We also show interval-valued automorphisms acting on the interval-valued fuzzy negations induced by interval-valued (Formula presented.)-norms, (Formula presented.)-conorms or implications. Finally, the relations among the interval-valued fuzzy negations induced by interval-valued (Formula presented.)-norms, (Formula presented.)-conorms or implications are explored. © 2015 Springer Science+Business Media New York


Tan A.,Zhejiang Ocean University | Tan A.,Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province | Wu W.,Zhejiang Ocean University | Wu W.,Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province | And 2 more authors.
Fuzzy Sets and Systems | Year: 2015

Multigranulation rough sets are desirable features in the field of rough set, where this concept is approximated by multiple granular structures. In this study, we employ belief and plausibility functions from evidence theory to characterize the set approximations and attribute reductions in multigranulation rough set theory. First, we show that in an incomplete information system, the pessimistic multigranulation approximations can be measured by belief and plausibility functions, whereas the optimistic multigranulation approximations do not possess this characteristic in general. We also give a sufficient and necessary condition for the numerical measurement of optimistic multigranulation approximations by belief and plausibility functions. Second, in an incomplete decision system, the pessimistic multigranulation approximations are also measured by belief and plausibility functions. In the end, an attribute reduction algorithm for multigranulation rough sets is proposed based on evidence theory, and its efficiency is examined by an example. Thus, belief and plausibility functions can be employed to numerically characterize the attribute reductions and to construct an attribute reduction algorithm for multigranulation rough sets. © 2015 Elsevier B.V.


Li D.,Zhejiang Ocean University | Li D.,Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province
Information Sciences | Year: 2015

In this paper, we mainly investigate T-extension operations of any t-norms and t-conorms on type-2 fuzzy sets' truth values F2 (a set of all functions defined from [0,1] into itself). Based on it, we first construct some type-2 t-norms on the fuzzy truth values F2 with the ordinary partial order ≤ and the partial order ⊂, respectively. The algebraic properties of these type-2 t-norms are then studied. Moreover, the residual operators of some special type-2 t-norms on (F2,≤) and (F2,⊂) are respectively represented. Finally, we briefly discuss the compositional rule of inference based on type-2 t-norms and their residual operators. © 2015 Elsevier Inc. All rights reserved.


Tan A.,Zhejiang Ocean University | Tan A.,Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province | Wu W.,Zhejiang Ocean University | Tao Y.,Zhejiang Ocean University
Soft Computing | Year: 2016

In data mining application, the test-cost-sensitive attribute reduction is an important task which aims to decrease the test cost of data. In operational research, the set cover problem is a typical optimization problem and has a long investigation history compared to the attribute reduction problem. In this paper, we employ the methods of set cover problem to deal with the test-cost-sensitive attribute reduction. First, we equivalently transform the test-cost-sensitive reduction problem into the set cover problem by using a constructive approach. It is shown that computing a reduct of a decision system with minimal test cost is equal to computing an optimal solution of the set cover problem. Then, a set-cover-based heuristic algorithm is introduced to solve the test-cost-sensitive reduction problem. In the end, we conduct several numerical experiments on data sets from UCI machine learning repository. Experimental results indicate that the set-cover-based algorithm has superior performances in most cases, and the algorithm is efficient on data sets with many attributes. © 2016 Springer-Verlag Berlin Heidelberg


Qingyuan X.,Zhangzhou Normal University | Anhui T.,Zhejiang Ocean University | Anhui T.,Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province | Jinjin L.,Zhangzhou Normal University
Journal of Intelligent and Fuzzy Systems | Year: 2016

In this paper, we first establish a Multi-Relation Granular Computing model by a given graph, and point out that all the reducts of the constructed Multi-Relation Granular Computing model are exactly all the minimal vertex covers of the corresponding graph. Thus, the vertex cover problem in graph theory can be converted to the knowledge reduction problem in rough set theory. Based on the conversion, we then introduce methods for dealing with the knowledge reduction problem to solve the vertex cover problem. In particular, we introduce a kind of method called the heuristic reduction algorithm based on entropy. © 2016 -IOS Press and the authors. All rights reserved.


Huang H.,Zhejiang Ocean University | Huang H.,Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province | Chen Z.,Iowa State University | Li J.,Shandong Jianzhu University | Yan J.,Iowa State University
Journal of Scientific Computing | Year: 2016

In this paper, we study direct discontinuous Galerkin method (Liu and Yan in SIAM J Numer Anal 47(1):475–698, 2009) and its variations (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010; Vidden and Yan in J Comput Math 31(6):638–662, 2013; Yan in J Sci Comput 54(2–3):663–683, 2013) for 2nd order elliptic problems. A priori error estimate under energy norm is established for all four methods. Optimal error estimate under (Formula presented.) norm is obtained for DDG method with interface correction (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010) and symmetric DDG method (Vidden and Yan in J Comput Math 31(6):638–662, 2013). A series of numerical examples are carried out to illustrate the accuracy and capability of the schemes. Numerically we obtain optimal (Formula presented.)th order convergence for DDG method with interface correction and symmetric DDG method on nonuniform and unstructured triangular meshes. An interface problem with discontinuous diffusion coefficients is investigated and optimal (Formula presented.)th order accuracy is obtained. Peak solutions with sharp transitions are captured well. Highly oscillatory wave solutions of Helmholz equation are well resolved. © 2016 Springer Science+Business Media New York


Yang Y.,Zhejiang Ocean University | Yang Y.,Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province | Yan Z.,CAS Academy of Mathematics and Systems Science | Malomed B.A.,Tel Aviv University
Chaos | Year: 2015

We analytically study rogue-wave (RW) solutions and rational solitons of an integrable fifth-order nonlinear Schrödinger (FONLS) equation with three free parameters. It includes, as particular cases, the usual NLS, Hirota, and Lakshmanan-Porsezian-Daniel equations. We present continuous-wave (CW) solutions and conditions for their modulation instability in the framework of this model. Applying the Darboux transformation to the CW input, novel first- and second-order RW solutions of the FONLS equation are analytically found. In particular, trajectories of motion of peaks and depressions of profiles of the first- and second-order RWs are produced by means of analytical and numerical methods. The solutions also include newly found rational and W-shaped one- and two-soliton modes. The results predict the corresponding dynamical phenomena in extended models of nonlinear fiber optics and other physically relevant integrable systems. © 2015 AIP Publishing LLC.


Chen Z.,Iowa State University | Huang H.,Zhejiang Ocean University | Huang H.,Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province | Yan J.,Iowa State University
Journal of Computational Physics | Year: 2016

We develop 3rd order maximum-principle-satisfying direct discontinuous Galerkin methods [8,9,19,21] for convection diffusion equations on unstructured triangular mesh. We carefully calculate the normal derivative numerical flux across element edges and prove that, with proper choice of parameter pair (β0, β1) in the numerical flux formula, the quadratic polynomial solution satisfies strict maximum principle. The polynomial solution is bounded within the given range and third order accuracy is maintained. There is no geometric restriction on the meshes and obtuse triangles are allowed in the partition. A sequence of numerical examples are carried out to demonstrate the accuracy and capability of the maximum-principle-satisfying limiter. © 2015 Elsevier Inc.

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