Given a family $${\mathcal {F}}$$ of k-element sets, $$S_1,\ldots ,S_r\in {\mathcal form an r-sunflower if $$S_i \cap S_j =S_{i'} S_{j'}$$ for all $$i \ne j$$ and $$i' j'$$ . According to famous conjecture Erdős Rado (JAMA 35: 85–90, 1960), there is constant $$c=c(r)$$ such that $$|{\mathcal {F}}|\ge c^k$$ , then contains r-sunflower. We come close proving this families bounded Vapnik-Chervonen...

This paper presents an indirect adaptive fuzzy control scheme for a class of single-input-single-output (SISO) nonlinear systems. A Takagi-Sugeno (T-S) fuzzy model is employed as a dynamical model of the partially known nonlinear system. Both the structure and the parameters of the T-S model are identified on-line. A T-S model based feedback linearization controller (FLC) is designed and a Lyap...

In this paper, we present equivalent characterizations of L-closure systems on lower bounded complete L-ordered sets and complete L-lattices, respectively. These results demonstrate the feasibility of notion of fuzzy closure system developed in our previous work (L.-K. Guo, G.-Q. Zhang, Q.-G. Li: Fuzzy closure systems on L-ordered sets. Math. Log. Quart. 57 (3) (2011), 281-291.). Also we develo...

using the notion of “belongingness ($epsilon$)” and “quasi-coincidence (q)” of fuzzy points with fuzzy sets, we introduce the concept of an ($ alpha, beta$)- fuzzyhv-ideal of an hv-ring, where , are any two of {$epsilon$, q,$epsilon$ $vee$ q, $epsilon$ $wedge$ q} with $ alpha$ $neq$ $epsilon$ $wedge$ q. since the concept of ($epsilon$, $epsilon$ $vee$ q)-fuzzy hv-ideals is an important and ...

A digital fuzzy logic filter of type III interacts with a real model signal reference to obtain the best answer in the sense of minimum mean square error of the output. The key part of the filter is a fuzzy mechanism that adaptively selects and emits answer according to the changes of the external reference signal. Based on input signal level, this fuzzy filter selects the best parameter values...

module over a ring is a general mathematical concept for many examples of mathematicalobjects that can be added to each other and multiplied by scalar numbers.in this paper, we consider a module over a ring as a universe and by using the notion of reference points, we provide local approximations for  subsets of the universe.

This paper deals with the stabilization of uncertain nonlinear time-delay systems subject to input saturation. A nonlinear time-delay system is first represented by Takagi-Sugeno (T-S) fuzzy model, a set of fuzzy implications which are used to characterize local dynamics with actuator saturation. Based on a delay independent stability analysis, a domain of attraction in which the admissible ini...

We prove that three independent fuzzy systems can uniformly approximate Bayesian posterior probability density functions by approximating the prior and likelihood probability densities as well as the hyperprior probability densities that underly the priors. This triply fuzzy function approximation extends the recent theorem for uniformly approximating the posterior density by approximating just...

The concept of upper and lower semicontinuity of fuzzy mappings introduced by Bao and Wu [Y.E. Bao, C.X. Wu, Convexity and semicontinuity of fuzzy mappings, Comput. Math. Appl., 51 (2006) 1809–1816] is redefined by using the concept of parameterized triples of fuzzy numbers. On the basis of the linear ordering of fuzzy numbers proposed by Goetschel and Voxman [R. Goetschel, W. Voxman, Elementar...