The problem of maximum inner product search (MIPS) is one the most important components in machine learning systems. However, this does not care about diversity, although result diversification can improve user satisfaction. This paper hence considers a new problem, namely categorical diversity-aware IPS which users select preferable categories. Exactly solving needs <inline-formula xmlns:mml="...

in this paper, we investigate the existence of a positive solution of fully fuzzy linear equation systems. this paper mainly to discuss a new decomposition of a nonsingular fuzzy matrix, the symmetric times triangular (st) decomposition. by this decomposition, every nonsingular fuzzy matrix can be represented as a product of a fuzzy symmetric matrix s and a fuzzy triangular matrix t.