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The objective of this paper is to derive some limit theorems of fuzzy random variables under the extension principle associated with continuous Archimedean triangular norms (t-norms). First of all, some convergence theorems for the sum of fuzzy random variables in chance measure and expected value are proved respectively based on the arithmetics of continuous Archimedean triangular norms. Then, a law of large numbers for fuzzy random variables is established by using the obtained convergence theorems. The results of the derived law of large numbers can degenerate to the strong laws of large numbers for random variables and fuzzy variables, respectively.

This paper proposes a 15-bit 10-MS/s pipelined ADC. To implement the incomplete settling principle, the traditional complete settling stage is improved to the incomplete settling structure through dividing the sampling clock of the traditional stage into two parts for discharging the sampling and feedback capacitors and completing the sampling, respectively. It verifies the correction and validity of optimizing ADCs' conversion speed without increasing power consumption through the incomplete settling. It is processed in 0.18pm 1P6M CMOS mixed-mode technology. Simulation results show that 82dB SNDR and 87dB SFDR are obtained at the sampling rate of 10MHz with the input sine frequency of 100KHz and the whole static power dissipation is 21.94mW.I.