In this paper, two-person matrix games is considered whose elements of pay-off matrix are triangular fuzzy numbers (TFNs). To solve such game a new method based on α-cut of TFN is developed for each of the players. In this method, two auxiliary bi-objective linear programming (BOLP) models are derived. Then using average weighted approach these two BOLP models are decomposed into two auxiliary ...

Auxiliary matrix exponential method is used to derive simple and numerically efficient general expressions for the following, historically rather cumbersome, and hard to compute, theoretical methods: (1) average Hamiltonian theory following interaction representation transformations; (2) Bloch-Redfield-Wangsness theory of nuclear and electron relaxation; (3) gradient ascent pulse engineering ve...

For differential-algebraic power systems, saddle-noddle bifurcation and Hopf bifurcation are both of universally existent phenomena in power systems. Usually Newton iteration method could be applied to the Moore-Spence system to compute saddle-noddle and Hopf bifurcation points directly. But the Moore-Spence system has very high dimension and causes much complexity in Jacobian matrix factorizat...

Non-negative Matrix Factorization (NMF) is a traditional unsupervised machine learning technique for decomposing a matrix into a set of bases and coefficients under the non-negative constraint. NMF with sparse constraints is also known for extracting reasonable components from noisy data. However, NMF tends to give undesired results in the case of highly sparse data, because the information inc...

The sparsity problem in collaborative filtering (CF) is a major bottleneck for most CF methods. In this paper, we consider a novel approach for alleviating the sparsity problem in CF by transferring useritem rating patterns from a dense auxiliary rating matrix in other domains (e.g., a popular movie rating website) to a sparse rating matrix in a target domain (e.g., a new book rating website). ...

In this report a general approach to algebraic multigrid methods for problems arising from the nite element discretization of a second order, self-adjoint, elliptic partial diierential equation is proposed. Special attention is paid to the coarsening process and the transfer operators. In order to construct a more exible method an auxiliary matrix is introduced which represents a virtual nite e...

the purpose of this paper is to develop a methodology for solving a new type of matrix games in which payoffs are expressed with triangular intuitionistic fuzzy numbers (tifns). in this methodology, the concept of solutions for matrix games with payoffs of tifns is introduced. a pair of auxiliary intuitionistic fuzzy programming models for players are established to determine optimal strategies...

Quantum 3D R – matrix in the classical (i. e. functional) limit gives a symplectic map of dynamical variables. The corresponding 3D evolution model is considered. An auxiliary problem for it is a system of linear equations playing the role of the monodromy matrix in 2D models. A generating function for the integrals of motion is constructed as a determinant of the auxiliary system. PACS: 05.50;...

In this paper, a reduced-rank scheme with joint iterative optimization is presented for direction of arrival estimation. A rank-reduction matrix and an auxiliary reduced-rank parameter vector are jointly optimized to calculate the output power with respect to each scanning angle. Subspace algorithms to estimate the rank-reduction matrix and the auxiliary vector are proposed. Simulations are per...