Research on fast methods for multiplying two n x n Boolean matrices has followed two directions. On the one hand, there are the asymptotically fast methods derived from algorithms to multiply matrices with integer entries. On the other hand, it has been of interest to devise algorithms which, while inferior in the asymptotic sense, are simple enough to be advantageously implemented. This paper ...

the intuitionistic fuzzy set has been applied to game theory very rarely since it was introduced by atanassov in 1983. the aim of this paper is to develop an effective methodology for solving matrix games with payoffs of atanassov’s triangular intuitionistic fuzzy numbers (tifns). in this methodology, the concepts and ranking order relations of atanassov’s tifns are defined. a pair of bi-object...

The intuitionistic fuzzy set has been applied to game theory very rarely since it was introduced by Atanassov in 1983. The aim of this paper is to develop an effective methodology for solving matrix games with payoffs of Atanassov’s triangular intuitionistic fuzzy numbers (TIFNs). In this methodology, the concepts and ranking order relations of Atanassov’s TIFNs are defined. A pair of bi-object...

A Multiple Targets Detection method based on Spatial Smoothing (MTDSS) is proposed to solve the problem of source number estimation under color noise background. Forward-backward smoothing by using signal vectors on specific elements as auxiliary vectors is computed. By spatial smoothing with auxiliary vectors, the correlated signals are decorrelated, and the color noise is partially alleviated...

Point-of-interest (POI) recommendation is the prevalent personalized service in location-based social networks (LBSNs). A single use of matrix factorization (MF) or deep neural cannot effectively capture complex structure user–POI interactions. In addition, to alleviate data-sparsity problem, current methods primarily introduce auxiliary information users and POIs. Auxiliary often judged be equ...

In biological data, it is often the case that observed data are available only for a subset of samples. When a kernel matrix is derived from such data, we have to leave the entries for unavailable samples as missing. In this paper, the missing entries are completed by exploiting an auxiliary kernel matrix derived from another information source. The parametric model of kernel matrices is create...

This paper presents equivalent forms of the Sylvester matrix equations. These equivalent forms allow us to use block linear methods for solving large Sylvester matrix equations. In each step of theses iterative methods we use global FOM or global GMRES algorithm for solving an auxiliary block matrix equations. Also, some numerical experiments for obtaining the numerical approximated solution of...

Matrix factorization is among the most successful techniques for collaborative filtering. One challenge of collaborative filtering is how to utilize available auxiliary information to improve prediction accuracy. In this paper, we study the problem of utilizing auxiliary information as features of factorization and propose formalizing the problem as general functional matrix factorization, whos...

Quadratic Assignment Problems (QAPs) are known to be among the most challenging discrete optimization problems. Recently, a new class of semi-definite relaxation (SDR) models for QAPs based on matrix splitting has been proposed [25, 28]. In this paper, we consider the issue of how to choose an appropriate matrix splitting scheme so that the resulting relaxation model is easy to solve and able t...

A posteriori error estimators based on auxiliary subspace techniques for second order elliptic problems in Rd (d ≥ 2) are considered. In this approach, the solution of a global problem is utilized as the error estimator. As the continuity and coercivity of the problem trivially leads to an efficiency bound, the main focus of this paper is to derive an analogous effectivity bound and to determin...