This paper focuses on simplifying the structure of fuzzy systems and improving the precision. By regarding the fuzzy rule base as a mapping from the vague partition on the input universe to the vague partition on the output universe, we first design a new type of fuzzy system using the complete and continuous fuzzy rule base in terms of vague partitions. We then exploit Weierstrass’s approximation theorem to show that this new type of fuzzy system can approximate any real continuous function on a closed interval to arbitrary accuracy and provide the corresponding approximation accuracy with respect to infinite norms. We also provide two numerical examples to illustrate the effectiveness of this new type of fuzzy system. Both theoretical and numerical results show that this new type of fuzzy system achieves the quite approximation effect with a few fuzzy rules.

In this paper, we introduce the property (h) on Banach lattices and present its characterization in terms of disjoint sequences. Then, an example is given to show that an order-to-norm continuous operator may not be σ-order continuous. Suppose T:E→F is an order-bounded operator from Dedekind σ-complete Banach lattice E into Dedekind complete Banach lattice F. We prove that T is σ-order-to-norm continuous if and only if T is both order weakly compact and σ-order continuous. In addition, if E can be represented as an ideal of L0(μ), where (Ω,Σ,μ) is a σ-finite measure space, then T is σ-order-to-norm continuous if and only if T is order-to-norm continuous. As applications, we extend Wickstead’s results on the order continuity of norms on E and E′.