Steffen F. Bocklisch

Sometimes, often, and always: exploring the vague meanings of frequency expressions.

The article describes a general two-step procedure for the numerical translation of vague linguistic terms (LTs). The suggested procedure consists of empirical and model components, including (1) participants’ estimates of numerical values corresponding to verbal terms and (2) modeling of the empirical data using fuzzy membership functions (MFs), respectively. The procedure is outlined in two studies for data from N = 89 and N = 109 participants, who were asked to estimate numbers corresponding to 11 verbal frequency expressions (e.g., sometimes). Positions and shapes of the resulting MFs varied considerably in symmetry, vagueness, and overlap and are indicative of the different meanings of the vague frequency expressions. Words were not distributed equidistantly across the numerical scale. This has important implications for the many questionnaires that use verbal rating scales, which consist of frequency expressions and operate on the premise of equidistance. These results are discussed for an exemplar questionnaire (COPSOQ). Furthermore, the variation of the number of prompted LTs (5 vs. 11) showed no influence on the words’ interpretations.

Fuzzy Time Series Analysis

A modeling method is suggested in this paper, which permits building multidimensional fuzzy models of time series consisting of fuzzy prototypes. These models have to be trained in a so-called period of learning and are suitable for short, medium and long range forecasts. The prediction of an incomplete time series is based on fuzzy classification to the prototypes. The results are grades of membership. In principle, these grades and further courses of prototypes are used to forecast the time series.

How to translate words into numbers? a fuzzy approach for the numerical translation of verbal probabilities

The paper describes a general two-step procedure for the numerical translation of linguistic terms using parametric fuzzy potential membership functions. In an empirical study 121 participants estimated numerical values that correspond to 13 verbal probability expressions. Among the estimates are the most typical numerical equivalent and the minimal and maximal values that just correspond to the given linguistic terms. These values serve as foundation for the proposed fuzzy approach. Positions and shapes of the resulting membership functions suggest that the verbal probability expressions are not distributed equidistantly along the probability scale and vary considerably in symmetry, vagueness and overlap. Therefore we recommend the proposed empirical procedure and fuzzy approach for future investigations and applications in the area of decision support.

Adaptive Fuzzy Pattern Classification for the Online Detection of Driver Lane Change Intention

Abstract In this paper we introduce a new fuzzy system using adaptive fuzzy pattern classification (AFPC) for data-based online evolvement. The fuzzy pattern concept represents an efficient tool for handling uncertainty in multi-dimensional data streams and combines powerful performance, flexibility and meaningful interpretability within one consistent framework. We outline AFPC for non-linear, multi-dimensional transition processes, namely, for the identification of lane change intention in car driving. While lane changes are rare, they are highly safety-relevant transition processes, showing high fuzziness and large individual and inter-individual variations (e.g., in lane change duration). The method employs a combined knowledge- and data-based approach, and the underlying fuzzy potential membership function concept models expert knowledge, closely mirroring human cognition. The design of AFPC comprises (I) an initial training phase (off-line and supervised), which generates a meaningful start-classifier, (II) an online application phase, and finally (III) an evolvement phase (online and unsupervised). Here we consider parametric and structural adaptations and discuss prospects and future challenges. Furthermore, we present specific modeling results for such online data from a real driving study. Next-generation advanced driver assistance systems, as well as autonomously driven vehicles need to evolve, in terms of parameters and structure, based on online real-time data. AFPC presents an efficient tool for application in this area and others (e.g., medicine).

Recognition of fuzzy time series patterns using evolving classification results

In some nonstationary time series, where a global model is neither available nor applicable, we may observe recurring patterns that can be extracted to create several local models instead. This article proposes knowledge-based short-time prediction methods for multivariate streaming time series that rely on the early recognition of such local patterns. A parametric fuzzy model for patterns is presented, along with an online, classification-based recognition procedure, which will introduce the notion of evolving classification results. Subsequently, two options are discussed to predict time series employing the fuzzified pattern knowledge, accompanied by an example. Special emphasis is placed on comprehensible models and methods, as well as a seamless interface to data mining algorithms.

Short-time prediction based on recognition of fuzzy time series patterns

This article proposes knowledge-based short-time prediction methods for multivariate streaming time series, relying on the early recognition of local patterns. A parametric, well-interpretable model for such patterns is presented, along with an online, classification-based recognition procedure. Subsequently, two options are discussed to predict time series employing the fuzzified pattern knowledge, accompanied by an example. Special emphasis is placed on comprehensible models and methods, as well as an easy interface to data mining algorithms.

The Fuzziness of Verbal Response Scales:The STAI-T Questionnaire

In this paper we used a two-step procedure for the numerical translation of verbal frequency expressions of the response scale of a questionnaire (STAI-T). In an empirical study, 70 participants estimated numerical equivalents for verbal frequency expressions, data was modeled, and fuzzy membership functions were calculated. Results show that the scale’s visual arrangement does not influence the interpretation of the words’ meanings. We argue that traditional statistics are inappropriate for the analysis of verbal response data and demonstrate the alternative of fuzzy analysis, providing an example.

How medical expertise influences the understanding of symptom intensities - a fuzzy approach

This paper examines the role of imprecision in the interpretation of verbal symptom intensities (e.g., high fever) depending on the level of medical expertise. In a contrastive study we compare low, medium and high level experts (medical students vs. physicians with M = 5.3 vs. M = 24.9 years of experience) concerning their interpretation of symptom intensities. For obtaining and modeling of empirical data a fuzzy approach was used. The resulting fuzzy membership functions (MF) reflect the meanings of the verbal symptom intensities. The two main findings are: (1) with increasing expertise the precision of the MF increase such that low level experts have very vague concepts compared to high level experts and (2) the precision depends on the symptom (e.g., intensities of fever are more precise than pain intensities).

Fuzzy-Pattern-Klassifikatoren als Modelle

ZusammenfassungModelle dienen der Speicherung von Wissen und als Basis für Entscheidungen. Sie finden Anwendung in unterschiedlichsten Bereichen wie Technik, Medizin, Wirtschaft, Psychologie, Umwelt oder Verkehr. Gerade für komplexe Zusammenhänge sind Verfahren, die auf interpretierbaren Mustern beruhen, hoch flexibel und adaptiv. Die Theorie der Fuzzy Sets hat nun das Potenzial, gleitende Übergänge zwischen den Mustern zu beschreiben und damit realitätsnahe Modelle zu entwerfen. In dem Beitrag wird speziell die Fuzzy-Pattern-Klassifikation ausgeführt, die eine parametrische Zugehörigkeitsfunktion nutzt, mit der Muster auch in hochdimensionalen Merkmalsräumen beschrieben werden können. An zwei aktuellen, deutlich unterschiedlichen Anwendungen wird beispielhaft gezeigt, wie das gleiche Modellierungskonzept in humanwissenschaftlichen (psychologischen) und in technischen Bereichen einsetzbar ist. Konkret handelt es sich zum einen um den Einsatz linguistischer Antwortskalen in Fragebogenaktionen und zum anderen um die Zeitreihen-Prognose (konkret des fluktuierenden Energieertrags von Photovoltaikanlagen). Es ist Anliegen, hierbei zumindest exemplarisch den fundamentalen Charakter und damit auch die Transdisziplinarität der Fuzzy Theorie zu zeigen.

Hierarchical Modelling of Data Inherent Structures Using Networks of Fuzzy Classifiers

This work is dedicated to a network oriented modelling approach based on the interconnection of multivariate Fuzzy Pattern Classifier nodes. The main point is the elaboration of a data driven and hierarchical design strategy for such fuzzy classifier network models. In detail two essential issues will be dealt with: the automatic layout of the network and the configuration of the classifier nodes. Both issues are addressed using a multiple cluster analysis approach. Finally the network design and operation ARE illustrated within the scope of an practical example.