Martin Štěpnička

Analysis of seasonal time series using fuzzy approach

A new methodology for the analysis and forecasting of time series is proposed. It directly employs two soft computing techniques: the fuzzy transform and the perception-based logical deduction. Thanks to the use of both these methods, and to the innovative approach, consisting of the construction of several independent models, the methodology is successfully applicable to robust long-time predictions.

A linguistic approach to time series modeling with the help of F-transform

In this paper, we describe an approach to modeling and forecasting time series that uses the theory of evaluative linguistic expressions, fuzzy/linguistic IF-THEN rules and the fuzzy transform method. We show that the use of a linguistic approach allows better readability and understandability without any significant deterioration in precision.

Fuzzy transform as an additive normal form

In this paper, we recall a class of approximating formulas. Since they arose as a generalization of classical normal forms we denote them by the same term. Moreover, we will show that the fuzzy transform (F-transform) introduced in [Perfilieva, I., Fuzzy approach to solution of differential equations with imprecise data: application to reef growth problem, in: R.V. Demicco, G.J. Klir (Eds.), Fuzzy Logic in Geology, Academic Press, Amsterdam, 2003, pp. 275-300 (Chapter 9), Perfilieva, I., Fuzzy transforms, in: J.F. Peters, A. Skowron (Eds.), Transactions on Rough Sets II. Rough Sets and Fuzzy Sets, Lecture Notes in Computer Science, vol. 3135, 2004, pp. 63-81] as an approximation method for continuous functions can be viewed as a particular case of normal form. Therefore, the results valid for normal forms may be applied to F-transforms as well.

Forecasting seasonal time series with computational intelligence

Accurate time series forecasting is a key issue to support individual and organizational decision making. In this paper, we introduce novel methods for multi-step seasonal time series forecasting. All the presented methods stem from computational intelligence techniques: evolutionary artificial neural networks, support vector machines and genuine linguistic fuzzy rules. Performance of the suggested methods is experimentally justified on seasonal time series from distinct domains on three forecasting horizons. The most important contribution is the introduction of a new hybrid combination using linguistic fuzzy rules and the other computational intelligence methods. This hybrid combination presents competitive forecasts, when compared with the popular ARIMA method. Moreover, such hybrid model is more easy to interpret by decision-makers when modeling trended series.

A neural network approach to the fuzzy transform

The paper deals with the F-transform technique which was introduced as a method for an approximate representation of continuous functions. The same task is solved by many methods from different areas. Neural networks also belong to techniques which have been proved to be powerful for approximation objectives. They provide us with many advantages, especially incremental way of learning parameters. The paper inherits neural approaches to the F-transform method and presents experiments justifying the proposed approach. Incremental way of determination of certain parameters of the F-transform method which were up to now given by batch formula enriches possible areas of application of the method by fast on-line processes. Moreover, the neural approach is demonstrated to be an appropriate one for finding such fuzzy partition of a domain which respects better a given set of measured samples which are to be approximated by a continuous function with no predetermined shape.

Continuity issues of the implicational interpretation of fuzzy rules

The implicational interpretation of fuzzy rules has received little attention in real-world applications so far. This is largely due to the fact that ensuring continuity of the resulting function is not a straightforward task. This paper targets this subject. Departing from consistent linguistic descriptions/rule bases, we introduce sufficient conditions for the continuity of the implicational interpretation with mean of maximum defuzzification. We demonstrate that continuity can be achieved under practically feasible conditions, regardless of the dimensionality of the input.

On redundancies in systems of fuzzy/linguistic IF-THEN rules under perception-based logical deduction inference

In this study, we formally investigate how to determine fuzzy/linguistic IF-THEN rules that are redundant in linguistic descriptions (systems of IF-THEN rules). We present a formal definition of redundancy and show that seemingly redundant rules can in fact be indispensable. These results apply to IF-THEN rules that use evaluative expressions (e.g., small and very big) and the inference method called perception-based logical deduction. However, they are also valid for inference systems with compatible design choices. We also describe an algorithm for the automatic detection and removal of redundant rules. Finally, we present an example of a linguistic description that is learned automatically from data and reduced using our algorithm.

Fuzzy Relational Compositions Based on Generalized Quantifiers

Fuzzy relational compositions have been extensively studied by many authors. Especially, we would like to highlight initial studies of the fuzzy relational compositions motivated by their applications to medical diagnosis by Willis Bandler and Ladislav Kohout. We revisit these types of compositions and introduce new definitions that directly employ generalized quantifiers. The motivation for this step is twofold: first, the application needs for filling a huge gap between the classical existential and universal quantifiers and second, the already existing successful implementation of generalized quantifiers in so called divisions of fuzzy relations, that constitute a database application counterpart of the theory of fuzzy relational compositions. Recall that the latter topic is studied within fuzzy relational databases and flexible querying systems for more than twenty years. This paper is an introductory study that should demonstrate a unifying theoretical framework and introduce that the properties typically valid for fuzzy relational compositions are valid also for the generalized ones, yet sometimes in a weaken form.

Fuzzy rule base ensemble generated from data by linguistic associations mining

As there are many various methods for time series prediction developed but none of them generally outperforms all the others, there always exists a danger of choosing a method that is inappropriate for a given time series. To overcome such a problem, distinct ensemble techniques, that combine several individual forecasts, are being proposed. In this contribution, we employ the so-called Fuzzy Rule-Based Ensemble. This method is constructed as a linear combination of a small number of forecasting methods where the weights of the combination are determined by fuzzy rule bases based on time series features such as trend, seasonality, or stationarity. For identification of fuzzy rule bases, we use the linguistic association mining. A huge experimental justification is provided.

How to Incorporate Excluding Features in Fuzzy Relational Compositions and What for

The aim of this paper is, first, to recall fuzzy relational compositions (products) and, to introduce an idea, how the so-called excluding features could be incorporated into the theoretical background. Apart from rather natural definitions, we provide readers with a theoretical investigation that provides and answer to a rather natural question, under which conditions, in terms of the underlying algebraic structures, the proposed incorporation of excluding features preserves the same properties as the incorporation in the classical relational compositions. The positive impact of the incorporation on reducing the suspicions provided by the basic “circlet” composition without losing the possibly correct suspicion, as in the case of the use of the Bandler-Kohout products, is demonstrated on an example.