Terrorism has led to many problems in Thai societies, not only property damage but also civilian casualties. Predicting terrorism activities in advance can help prepare and manage risk from sabotage by these activities. This paper proposes a framework focusing on event classification in terrorism domain using fuzzy inference systems (FISs). Each FIS is a decision-making model combining fuzzy logic and approximate reasoning. It is generated in five main parts: the input interface, the fuzzification interface, knowledge base unit, decision making unit and output defuzzification interface. Adaptive neuro-fuzzy inference system (ANFIS) is a FIS model adapted by combining the fuzzy logic and neural network. The ANFIS utilizes automatic identification of fuzzy logic rules and adjustment of membership function (MF). Moreover, neural network can directly learn from data set to construct fuzzy logic rules and MF implemented in various applications. FIS settings are evaluated based on two comparisons. The first evaluation is the comparison between unstructured and structured events using the same FIS setting. The second comparison is the model settings between FIS and ANFIS for classifying structured events. The data set consists of news articles related to terrorism events in three southern provinces of Thailand. The experimental results show that the classification performance of the FIS resulting from structured events achieves satisfactory accuracy and is better than the unstructured events. In addition, the classification of structured events using ANFIS gives higher performance than the events using only FIS in the prediction of terrorism events.

Description Logics (DLs) [2] are a logical reconstruction of the so-called frame-based knowledge representation languages, with the aim of providing a simple well-established Tarski-style declarative semantics to capture the meaning of the most popular features of structured representation of knowledge. Nowadays, DLs have gained even more popularity due to their application in 1 the context of the Semantic Web [4]. For example, the current standard language for specifying ontologies, the Web Ontology Language OWL is based on Description Logics. It is very natural to extend DLs to the fuzzy case in order to manage fuzzy/vague/imprecise pieces of knowledge for which a clear and precise definition is not possible. For a good and recent survey on the advances in the field of fuzzy DLs, we refer the reader to [14]. One of the challenges of the research in this community is the fact that different families of fuzzy operators (or fuzzy logics) lead to fuzzy DLs with different properties. In fuzzy logic, there are a lot of families of fuzzy operators (or fuzzy logics). Table 1 shows the connectives involved in what are considered the main four families. The most famous families correspond to the three basic continuous t-norms (i.e., Lukasiewicz, Gödel and Product [10]) together with an R-implication

Recently, Wang et al. discussed the properties of fuzzy information systems under homomorphisms in the paper [C. Wang, D. Chen, L. Zhu, Homomorphisms between fuzzy information systems, Applied Mathematics Letters 22 (2009) 1045-1050], where homomorphisms are based upon the concepts of consistent functions and fuzzy relation mappings. In this paper, we classify consistent functions as predecessor-consistent and successor-consistent, and then proceed to present more properties of consistent functions. In addition, we improve some characterizations of fuzzy relation mappings provided by Wang et al.

The expert opinion is necessary in medical decision making, since there are wide variations in clinical practices. Moreover, the growing need to assess and improve quality of health care has brought to light the possibility of developing and implementing clinical practice guidelines based on expert opinions. Even though the colleague's opinion helps in accessing information about real cases which is another important source of information, an important goal to reach when dealing with real medical cases is to have simultaneous access to the expert's opinion about the same indications of the real case being treated. The increase of the information volume in each medical field, due to the emergence of new discoveries, treatments, medicines and technologies, leads to a frequent need of consulting medical literature and in particular specialized revues and journals. Certainly, due to the huge volume of this information, a classified, targeted, access is necessary. In the field of medicine, Imprecision and Uncertainty play a large role in the process of diagnosis of disease that has most frequently been the focus of these applications. With the increased volume of information available to physicians from new medical technologies, the process of classifying different sets of symptoms under a single name and determining the appropriate therapeutic actions become increasingly difficult.

We introduce the first temporal-difference learning algorithm that is stable with linear function approximation and off-policy training, for any finite Markov decision process, target policy, and exciting behavior policy, and whose complexity scales linearly in the number of parameters. We consider an i.i.d.\ policy-evaluation setting in which the data need not come from on-policy experience. The gradient temporal-difference (GTD) algorithm estimates the expected update vector of the TD(0) algorithm and performs stochastic gradient descent on its L_2 norm. Our analysis proves that its expected update is in the direction of the gradient, assuring convergence under the usual stochastic approximation conditions to the same least-squares solution as found by the LSTD, but without its quadratic computational complexity. GTD is online and incremental, and does not involve multiplying by products of likelihood ratios as in importance-sampling methods.

Existing value function approximation methods have been successfully used in many applications, but they often lack useful a priori error bounds. We propose approximate bilinear programming, a new formulation of value function approximation thatprovides strong a priori guarantees. In particular, this approach provably finds an approximate value function that minimizes the Bellman residual. Solving a bilinear program optimally is NPhard, but this is unavoidable because the Bellman-residual minimization itself is NPhard. We therefore employ and analyze a common approximate algorithm for bilinear programs. The analysis shows that this algorithm offers a convergent generalization of approximate policy iteration.Finally, we demonstrate that the proposed approach can consistently minimize the Bellman residual on a simple benchmark problem.

We introduce the first temporal-difference learning algorithms that converge with smooth value function approximators, such as neural networks. Conventional temporal-difference (TD) methods, such as TD($\lambda$), Q-learning and Sarsa have been used successfully with function approximation in many applications. However, it is well known that off-policy sampling, as well as nonlinear function approximation, can cause these algorithms to become unstable (i.e., the parameters of the approximator may diverge). Sutton et al (2009a,b) solved the problem of off-policy learning with linear TD algorithms by introducing a new objective function, related to the Bellman-error, and algorithms that perform stochastic gradient-descent on this function. In this paper, we generalize their work to nonlinear function approximation. We present a Bellman error objective function and two gradient-descent TD algorithms that optimize it. We prove the asymptotic almost-sure convergence of both algorithms for any finite Markov decision process and any smooth value function approximator, under usual stochastic approximation conditions. The computational complexity per iteration scales linearly with the number of parameters of the approximator. The algorithms are incremental and are guaranteed to converge to locally optimal solutions.

Relational representation of knowledge makes it possible to perform all the computations and decision making in a uniform relational way by means of special relational compositions called triangle and square products. In this paper some applications in manufacturing related to cost analysis are described. Testing fuzzy relational structures for various relational properties allows us to discover dependencies, hierarchies, similarities, and equivalences of the attributes characterizing technological processes and manufactured artifacts in their relationship to costs and performance. A brief overview of mathematical aspects of BK-relational products is given in Appendix 1 together with further references in the literature.

A fuzzy logic based classification engine has been developed for classifying mass spectra obtained with an imaging internal source Fourier transform mass spectrometer (I^2LD-FTMS). Traditionally, an operator uses the relative abundance of ions with specific mass-to-charge (m/z) ratios to categorize spectra. An operator does this by comparing the spectrum of m/z versus abundance of an unknown sample against a library of spectra from known samples. Automated positioning and acquisition allow I^2LD-FTMS to acquire data from very large grids, this would require classification of up to 3600 spectrum per hour to keep pace with the acquisition. The tedious job of classifying numerous spectra generated in an I^2LD-FTMS imaging application can be replaced by a fuzzy rule base if the cues an operator uses can be encapsulated. We present the translation of linguistic rules to a fuzzy classifier for mineral phases in basalt. This paper also describes a method for gathering statistics on ions, which are not currently used in the rule base, but which may be candidates for making the rule base more accurate and complete or to form new rule bases based on data obtained from known samples. A spatial method for classifying spectra with low membership values, based on neighboring sample classifications, is also presented.

The quality of the ranking function is an important factor that determines the quality of the Information Retrieval system. Each document is assigned a score by the ranking function; the score indicates the likelihood of relevance of the document given a query. In the vector space model, the ranking function is defined by a mathematic expression. We propose a fuzzy logic (FL) approach to defining the ranking function. FL provides a convenient way of converting knowledge expressed in a natural language into fuzzy logic rules. The resulting ranking function could be easily viewed, extended, and verified: * if (tf is high) and (idf is high) > (relevance is high); * if (overlap is high) > (relevance is high). By using above FL rules, we are able to achieve performance approximately equal to the state of the art search engine Apache Lucene (deltaP10 +0.92%; deltaMAP -0.1%). The fuzzy logic approach allows combining the logic-based model with the vector model. The resulting model possesses simplicity and formalism of the logic based model, and the flexibility and performance of the vector model.