http://ieeexplore.ieee.org TOC Alert for Publication# 91 2012 February 10 20 1 C1 C1 105 20 1 C2 C2 42 20 1 1 8 533 20 1 9 21 630 $H_infty$ control is investigated for discrete-time Takagi–Sugeno (T–S) fuzzy systems with infinite-distributed delay and actuator faults. A discrete-time homogeneous Markov chain is used to represent the stochastic behavior of actuator faults. In terms of a stochastic fuzzy Lyapunov functional, a sufficient condition is proposed to ensure that the resultant closed-loop system is exponentially stable in the mean-square sense with an $H_infty$ performance index. Based on the derived condition, the reliable $H_infty$ control problem is solved, and an explicit expression of the desired controller is also given. The case of no failure in the actuator is also considered. A numerical example is given to demonstrate that our results are effective and less conservative.]]> 20 1 22 31 570 20 1 32 45 734 20 1 46 56 332 $top$-equalities that are derived from residual implication functions is proposed. Then, a model that allows us to learn the parametric similarity measures is introduced. This is achieved by an online learning algorithm with an efficient implication-based loss function. Experiments on real datasets show that the learned measures are efficient at a wide range of scales and achieve better results than existing fuzzy similarity measures. Moreover, the learning algorithm is fast so that it can be used in real-world applications, where computation times are a key feature when one chooses an inference system.]]> 20 1 57 68 809 20 1 69 81 1117 20 1 82 95 1024 $alpha$-cut separately. The problem, thus, reduces to finding the endpoints of these $alpha$-cuts, which amounts to a number of interwoven optimization problems. In the case of a non-monotone continuous function, however, these optimization problems are non-trivial. In this paper, different optimization algorithms are applied for that purpose: Gradient Descent based on Sequential Quadratic Programming, Simplex–Simulated Annealing, Particle Swarm Optimization, and Particle Swarm Optimization combined with Gradient Descent. In addition, two approaches are followed to determine a suitable number of $alpha$-cuts: either a fixed, predetermined number is used, or an initially (very) small number is chosen that is subsequently increased according to a linearity criterion. Both a non-parallel and a parallel implementation are designed. The parallel version is restricted to work with Particle Swarm Optimization and employs communication to optimize its (internal) performance by exploiting the dependence between the various optimization problems. Different configurations are evaluated on a set of benchmark functions in terms of the mean area under the output fuzzy interval and the number of function evaluations. Particle Swarm Optimization combined with Gradient Descent starting from a small number of $alpha$-cuts leads to the most accurate fuzzy intervals at the cost of a relatively large number of function evaluations.]]> 20 1 96 108 840 20 1 109 119 417 20 1 120 134 888 20 1 135 152 872 $I$ , we give out the sufficient and necessary conditions of solutions for the distributive equation of implication $I(x,T_1(y,z))=T_2(I(x,y),I(x,z))$, when $T_1$ is a continuous but not Archimedean triangular norm, $T_2$ is a continuous and Archimedean triangular norm, and $I$ is an unknown function. This obtained characterizations indicate that there are no continuous solutions for the previous functional equation, satisfying the boundary conditions of implications. However, under the assumptions that $I$ is continuous except for the point (0,0), we get its complete characterizations. Here, it should be pointed out that these results make differences with recent results that are obtained by Baczyński and Qin. Moreover, our method can still apply to the three other functional equations that are related closely to the distributive equation of implication.]]> 20 1 153 167 462 20 1 168 180 663 20 1 181 186 554 20 1 187 192 384 20 1 192 200 426 20 1 201 201 651 20 1 202 202 320 20 1 203 204 1564 20 1 C3 C3 37 20 1 C4 C4 29