Numerical solution of a fuzzy time-optimal control problem

In this paper, we consider a time-optimal control problem with uncertainties. Dynamics of controlled object is expressed by crisp linear system of differential equations with fuzzy initial and final states. We introduce a notion of fuzzy optimal time and reduce its calculation to two crisp optimal control problems. We examine the proposed approach on an example.Comment: 11 pages, 3 figure

A new curve fitting based rating prediction algorithm for recommender systems

summary:The most algorithms for Recommender Systems (RSs) are based on a Collaborative Filtering (CF) approach, in particular on the Probabilistic Matrix Factorization (PMF) method. It is known that the PMF method is quite successful for the rating prediction. In this study, we consider the problem of rating prediction in RSs. We propose a new algorithm which is also in the CF framework; however, it is completely different from the PMF-based algorithms. There are studies in the literature that can increase the accuracy of rating prediction by using additional information. However, we seek the answer to the question that if the input data does not contain additional information, how we can increase the accuracy of rating prediction. In the proposed algorithm, we construct a curve (a low-degree polynomial) for each user using the sparse input data and by this curve, we predict the unknown ratings of items. The proposed algorithm is easy to implement. The main advantage of the algorithm is that the running time is polynomial, namely it is $\theta(n^2)$, for sparse matrices. Moreover, in the experiments we get slightly more accurate results compared to the known rating prediction algorithms