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.
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.
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.
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