Jan van den Berg

Constructing an associative concept space for literature-based discovery

Scientific literature is often fragmented, which implies that certain scientific questions can only be answered by combining information from various articles. In this paper, a new algorithm is proposed for finding associations between related concepts present in literature. To this end, concepts are mapped to a multidimensional space by a Hebbian type of learning algorithm using co-occurrence data as input. The resulting concept space allows exploration of the neighborhood of a concept and finding potentially novel relationships between concepts. The obtained information retrieval system is useful for finding literature supporting hypotheses and for discovering previously unknown relationships between concepts. Tests on artificial data show the potential of the proposed methodology. In addition, preliminary tests on a set of Medline abstracts yield promising results.

Financial markets analysis by using a probabilistic fuzzy modelling approach

For successful trading in financial markets, it is important to develop financial models where one can identify different states of the market for modifying one’s actions. In this paper, we propose to use probabilistic fuzzy systems for this purpose. We concentrate on Takagi–Sugeno (TS) probabilistic fuzzy systems that combine interpretability of fuzzy systems with the statistical properties of probabilistic systems. We start by recapitulating the general architecture of TS probabilistic fuzzy rule-based systems and summarize the corresponding reasoning schemes. We mention how probabilities can be estimated from a given data set and how a probability distribution can be approximated using a fuzzy histogram technique. We apply our methodology to financial time series analysis and demonstrate how a probabilistic TS fuzzy system can be identified, assuming that a linguistic term set is given. We illustrate the interpretability of such a system by inspecting the rule bases of our induced models.

Sustainable Rangeland Management using a Multi-Fuzzy Model: How to Deal with Heterogeneous Experts' Knowledge

While fuzzy specialists commonly use homogeneous experts knowledge to construct fuzzy models, it is much more difficult to deal with knowledge elicited from a heterogeneous group of experts. This issue is exemplified in the area of sustainable rangeland management (SRM). One way to deal with the diversity of opinions is to develop a fuzzy system for all experts and to combine all these, the so-called primary systems, into one multi-fuzzy model. To derive each of the primary fuzzy systems, several semi-structured interviews were held in three different areas of the Fars province in Southwest Iran using the knowledge of a group of administrative experts. To obtain the final output of the multi-fuzzy model, we applied different voting methods. The first method simply uses the arithmetic average of the primary outputs as the final output of the multi-fuzzy model. This final output represents an estimation of the right rate of stocking (RRS). We also propose other (un)supervised voting methods. Most importantly, by harmonising the primary outputs such that outliers get less emphasis, we introduce an unsupervised voting method for calculating a weighted estimate of the RRS. This harmonising method is expected to provide a new useful tool for policymakers dealing with heterogenity in experts opinions: it is especially useful where limited field data are available and one is forced to rely on experts knowledge only. By constructing the three fuzzy models based on the elicitation of heterogeneous experts knowledge, our study shows the multidimensional vaguenesses that exist in SRM. Finally, by comparing the final RRS with its common values, this study strongly points to the existence of overgrazing in pastures in the three regions of the Fars province in Southwest Iran.

Probabilistic Reasoning in Fuzzy Rule-Based Systems

We concentrate on Takagi—Sugeno (TS) probabilistic fuzzy systems where interpretability of fuzzy systems is combined with the statistical properties of probabilistic systems. After having sketched the general architecture of TS probabilistic fuzzy systems, we present an appropriate mathematical framework and introduce two probabilistic fuzzy reasoning schemes which have a different interpretation but, eventually, yield the same input-output mapping. We illustrate our theoretical considerations by presenting some simulation results concerning a financial time series analysis.

On the Notion of Statistical Fuzzy Entropy

After a recapitulation of several approaches for defining either statistical or fuzzy entropy and the presentation of an appropriate probabilistic fuzzy framework, we introduce the notion of statistical fuzzy entropy where both fuzzy (or linguistic) uncertainty and probabilistic (and statistical) uncertainty can be modelled and quantified. We investigate certain properties of statistical fuzzy entropy and show its usefulness for developing statistical fuzzy decision trees.

A non-equidistant elastic net algorithm

The statistical mechanical derivation by Simic of the Elastic Net Algorithm (ENA) from a stochastic Hopfield neural network is criticized. In our view, the ENA should be considered a dynamic penalty method. Using a linear distance measure, a Non-equidistant Elastic Net Algorithm (NENA) is presented. Finally, a Hybrid Elastic Net Algorithm (HENA) is discussed.

Some theorems concerning the free energy of (un)constrained stochastic hopfield neural networks

General stochastic binary Hopfield models are viewed from the angle of statistical mechanics. Both the general unconstrained binary stochastic Hopfield model and a certain constrained one are analyzed yielding explicit expressions of the free energy. Moreover, conditions are given for which some of these free energy expressions are Lyapunov functions of the corresponding differential equations. In mean field approximation, either stochastic model appears to coincide with a specific continuous model. Physically, the models are related to spin and to Potts glass models. By means of an alternative derivation, an expression of a ‘complementary’ free energy is presented. Some surveying computational results are reported and an alternative use of the discussed models in resolving constrained optimization problems is discussed.