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Abstract: In this paper, the convexity properties of fuzzy nets on the Euclidean space is investigated. [Copyright &y& Elsevier]

Abstract: An adaptive fuzzy control approach is proposed for a class of multiple-input–multiple-output (MIMO) nonlinear systems with completely unknown nonaffine functions. The MIMO systems are composed of n subsystems and each of subsystems is in the nested lower triangular form. It is difficult and complicated to control this class of systems due to the existence of unknown nonaffine functions and the couplings among the nested subsystems. This difficulty is overcome by introducing some special type Lyapunov functions and taking advantage of the mean-value theorem, the backstepping design method and the approximation property of the fuzzy systems. The proposed control approach can guarantee that all the signals in the closed-loop system are bounded. A simulation experiment is utilized to verify the feasibility of the proposed approach. [Copyright &y& Elsevier]

Feed-forward neural networks used for pattern classification generally have one input layer, one output layer and several hidden layers. The hidden layers in these networks add extra non-linearity for realization of precise functional mapping between the input and the output layers, but semantic relations of the hidden layers with their predecessor and successor layers cannot be justified. This paper presents a novel scheme for supervised learning on a fuzzy Petri net that provides semantic justification of the hidden layers, and is capable of approximate reasoning and learning from noisy training instances. An algorithm for training a feed-forward fuzzy Petri net and an analysis of its convergence have been presented in the paper. The paper also examines the scope of the learning algorithm in object recognition from 2D geometric views. [ABSTRACT FROM AUTHOR]

This paper presents a new model for unsupervised learning and reasoning on a special type of cognitive maps realized with Petri nets. The unsupervised learning process in the present context adapts the weights of the directed arcs from transitions to places in the Petri net. A Hebbian-type learning algorithm with a natural decay in weights is employed to study the dynamic behavior of the algorithm. The algorithm is conditionally stable for a suitable range of the mortality rate. After convergence of the learning algorithm, the network may be used for computing the beliefs of the desired propositions from the supplied beliefs of the axioms (places with no input arcs). Because of the conditional stability of the algorithm, it may be used in complex decision-making and learning such as automated car driving in an accident-prone environment. The paper also presents a new model for knowledge refinement by adaptation of weights in a fuzzy Petri net using a different form of Hebbian learning. This second model converges to stable points in both encoding and recall phases. [ABSTRACT FROM AUTHOR]

This note aims to correct a complexity result in our paper that investigates the verification of diagnosability for unbounded Petri nets. The main result of [1] is Theorem IV.1, which shows that the diagnosability verification problem can be reduced to a Petri net model checking problem called Yen's problem [2]. This main reduction is still correct. However, it was pointed out by Atig and Habermehl [3] that Yen's original complexity result is not completely correct 1. Specifically, they showed that: (i) in general, Yen's problem is still decidable, but it is as hard as the reachability problem, which corrects the original EXPSPACE-completeness claim in [2]; and (ii) for a special case called the increasing fragment, Yen's problem can be solved in EXPSPACE. [ABSTRACT FROM AUTHOR]