Copyright q 2012 Hua-feng Ge. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We obtain new sharp bounds for the Bernoulli numbers: 2 2n !/ π2n 22n − 1 < |B2n| ≤ 2 22k − 1 /22k ζ 2k 2n !/ π2n 22n − 1 , n k, k 1, . . . , k ∈ N , an...

We discuss the role of fuzzy sets in modeling business rules. The technology involved in fuzzy systems modeling is described. We next introduce some ideas from the Dempster-Shafer theory of evidence. We use the Dempster-Shafer framework to provide a machinery for including randomness in the fuzzy systems

In this paper, one conflict context reasoning method based on Dempster-Shafer theory is proposed. Firstly the context conflict problems are illustrated and partitioned based on theory of evidence. Then the context model combined with Dempster-Shafer theory is presented and applied to the reasoning method based on Dempster rule of combination. The effectiveness of this method is verified with a ...

According to the Multi-criteria Decision-making (MCDM) problem with criterion value for triangular fuzzy number, a kind of a MCDM method based on fuzzy number and Dempster-Shafer evidence theory is proposed. By means of the ability to deal with the uncertain information of evidence theory, the method first constructs the evidence body and the Basic Probability Assignment (BPA) function. In the ...

This paper addresses the problem of multi-criteria recommendation in hotel industry. The main focus is to analyze user preferences from different aspects based on ratings and develop a new collaborative filtering method for recommendations. Particularly, proposed system integrates matrix factorization into deep learning model predict ratings, then evidential reasoning approach adopted uncertain...