The Approximate Linear Programming (ALP) approach to value function approximation for MDPs is a parametric value function approximation method, in that it represents the value function as a linear combination of features which are chosen a priori. Choosing these features can be a difficult challenge in itself. One recent effort, Regularized Approximate Linear Programming (RALP), uses L1 regularization to address this issue by combining a large initial set of features with a regularization penalty that favors a smooth value function with few non-zero weights. Rather than using smoothness as a backhanded way of addressing the feature selection problem, this paper starts with smoothness and develops a non-parametric approach to ALP that is consistent with the smoothness assumption. We show that this new approach has some favorable practical and analytical properties in comparison to (R)ALP.

We describe the Fourier basis, a linear value function approximation scheme based on the Fourier series. We empirically demonstrate that it performs well compared to radial basis functions and the polynomial basis, the two most popular fixed bases for linear value function approximation, and is competitive with learned proto-value functions.

In this work we propose an approach for generalization in continuous domain Reinforcement Learning that, instead of using a single function approximator, tries many different function approximators in parallel, each one defined in a different region of the domain. Associated with each approximator is a relevance function that locally quantifies the quality of its approximation, so that, at each input point, the approximator with highest relevance can be selected. The relevance function is defined using parametric estimations of the variance of the q-values and the density of samples in the input space, which are used to quantify the accuracy and the confidence in the approximation, respectively. These parametric estimations are obtained from a probability density distribution represented as a Gaussian Mixture Model embedded in the input-output space of each approximator. In our experiments, the proposed approach required a lesser number of experiences for learning and produced more stable convergence profiles than when using a single function approximator.

Uncertainty and vagueness are pervasive phenomena in real-life knowledge. They are supported in extended description logics that adapt classical description logics to deal with numerical probabilities or fuzzy truth degrees. While the two concepts are distinguished for good reasons, they combine in the notion of probably, which is ultimately a fuzzy qualification of probabilities. Here, we develop existing propositional logics of fuzzy probability into a full-blown description logic, and we show decidability of several variants of this logic under Lukasiewicz semantics. We obtain these results in a novel generic framework of fuzzy coalgebraic logic; this enables us to extend our results to logics that combine crisp ingredients including standard crisp roles and crisp numerical probabilities with fuzzy roles and fuzzy probabilities.

Fault diagnosis and failure prognosis are essential techniques in improving the safety of many manufacturing systems. Therefore, on-line fault detection and isolation is one of the most important tasks in safety-critical and intelligent control systems. Computational intelligence techniques are being investigated as extension of the traditional fault diagnosis methods. This paper discusses the Temporal Neuro-Fuzzy Systems (TNFS) fault diagnosis within an application study of a manufacturing system. The key issues of finding a suitable structure for detecting and isolating ten realistic actuator faults are described. Within this framework, data-processing interactive software of simulation baptized NEFDIAG (NEuro Fuzzy DIAGnosis) version 1.0 is developed. This software devoted primarily to creation, training and test of a classification Neuro-Fuzzy system of industrial process failures. NEFDIAG can be represented like a special type of fuzzy perceptron, with three layers used to classify patterns and failures. The system selected is the workshop of SCIMAT clinker, cement factory in Algeria.

Abstract--This study proposes a framework of Uncertainty-based Group Decision Support System (UGDSS). It provides a platform for multiple criteria decision analysis in six aspects including (1) decision environment, (2) decision problem, (3) decision group, (4) decision conflict, (5) decision schemes and (6) group negotiation. Based on multiple artificial intelligent technologies, this framework provides reliable support for the comprehensive manipulation of applications and advanced decision approaches through the design of an integrated multi-agents architecture. I. INTRODUCTION Nowadays, since companies are usually working in a rapidly changing and uncertain business environment, more timely and accurate information are required for decision-making, in order to improve customer satisfaction, support profitable business analysis, and increase their competitive advantages. In addition to the use of data and mathematical models, some managerial decisions are qualitative in nature and need judgmental knowledge that resides in human experts. Thus, it is necessary to incorporate such knowledge in developing Decision Support System (DSS). A system that integrates knowledge from experts is called a Knowledge-based Decision Support System (KBDSS) or an Intelligent Decision Support System (IDSS) [1].

Aim of this paper is to address the problem of learning Boolean functions from training data with missing values. We present an extension of the BRAIN algorithm, called U-BRAIN (Uncertainty-managing Batch Relevance-based Artificial INtelligence), conceived for learning DNF Boolean formulas from partial truth tables, possibly with uncertain values or missing bits. Such an algorithm is obtained from BRAIN by introducing fuzzy sets in order to manage uncertainty. In the case where no missing bits are present, the algorithm reduces to the original BRAIN.

Description Logics (DLs) are suitable, well-known, logics for managing structured knowledge. They allow reasoning about individuals and well defined concepts, i.e., set of individuals with common properties. The experience in using DLs in applications has shown that in many cases we would like to extend their capabilities. In particular, their use in the context of Multimedia Information Retrieval (MIR) leads to the convincement that such DLs should allow the treatment of the inherent imprecision in multimedia object content representation and retrieval. In this paper we will present a fuzzy extension of ALC, combining Zadeh's fuzzy logic with a classical DL. In particular, concepts becomes fuzzy and, thus, reasoning about imprecise concepts is supported. We will define its syntax, its semantics, describe its properties and present a constraint propagation calculus for reasoning in it.

Bisimulations have been widely used in many areas of computer science to model equivalence between various systems, and to reduce the number of states of these systems, whereas uniform fuzzy relations have recently been introduced as a means to model the fuzzy equivalence between elements of two possible different sets. Here we use the conjunction of these two concepts as a powerful tool in the study of equivalence between fuzzy automata. We prove that a uniform fuzzy relation between fuzzy automata $\cal A$ and $\cal B$ is a forward bisimulation if and only if its kernel and co-kernel are forward bisimulation fuzzy equivalences on $\cal A$ and $\cal B$ and there is a special isomorphism between factor fuzzy automata with respect to these fuzzy equivalences. As a consequence we get that fuzzy automata $\cal A$ and $\cal B$ are UFB-equivalent, i.e., there is a uniform forward bisimulation between them, if and only if there is a special isomorphism between the factor fuzzy automata of $\cal A$ and $\cal B$ with respect to their greatest forward bisimulation fuzzy equivalences. This result reduces the problem of testing UFB-equivalence to the problem of testing isomorphism of fuzzy automata, which is closely related to the well-known graph isomorphism problem. We prove some similar results for backward-forward bisimulations, and we point to fundamental differences. Because of the duality with the studied concepts, backward and forward-backward bisimulations are not considered separately. Finally, we give a comprehensive overview of various concepts on deterministic, nondeterministic, fuzzy, and weighted automata, which are related to bisimulations.

Recently, two types of simulations (forward and backward simulations) and four types of bisimulations (forward, backward, forward-backward, and backward-forward bisimulations) between fuzzy automata have been introduced. If there is at least one simulation/bisimulation of some of these types between the given fuzzy automata, it has been proved that there is the greatest simulation/bisimulation of this kind. In the present paper, for any of the above-mentioned types of simulations/bisimulations we provide an effective algorithm for deciding whether there is a simulation/bisimulation of this type between the given fuzzy automata, and for computing the greatest one, whenever it exists. The algorithms are based on the method developed in [J. Ignjatovi\'c, M. \'Ciri\'c, S. Bogdanovi\'c, On the greatest solutions to certain systems of fuzzy relation inequalities and equations, Fuzzy Sets and Systems 161 (2010) 3081-3113], which comes down to the computing of the greatest post-fixed point, contained in a given fuzzy relation, of an isotone function on the lattice of fuzzy relations.