Von Fuzzy-Sets zu Computing-with-Words

Dieser Artikel bietet einen Überblick über die Entwicklung und Zusammenhänge der einzelnen Elemente der Fuzzy-Logik, wovon Fuzzy-Set-Theorie die Grundlage bildet. Die Grundproblematik besteht in der Handhabung von linguistischen Informationen, die häufig durch Ungenauigkeit gekennzeichnet sind. Die verschiedenen technischen Anwendungen von Fuzzy-Logik bieten eine Möglichkeit, intelligentere Computersysteme zu konstruieren, die mit unpräzisen Informationen umgehen können. Solche Systeme sind Indizien für die Entstehung einer neuen Ära des Cognitive-Computing, di in diesemArtikel ebenfalls zur Sprache kommt. Für das bessere Verständnis wird der Artikel mit einem Beispiel aus der Meteorologie (d. h. Schnee in Adelboden) begleitet.

Modelling the system behaviour of wet snow avalanches using an expert system approach for risk management on high alpine traffic roads

The presented approach describes a model for a rule-based expert system calculating the temporal variability of the release of wet snow avalanches, using the assumption of avalanche triggering without the loading of new snow. The knowledge base of the model is created by using investigations on the system behaviour of wet snow avalanches in the Italian Ortles Alps, and is represented by a fuzzy logic rule-base. Input parameters of the expert system are numerical and linguistic variables, measurable meteorological and topographical factors and observable characteristics of the snow cover. Output of the inference method is the quantified release disposition for wet snow avalanches. Combining topographical parameters and the spatial interpolation of the calculated release disposition a hazard index map is dynamically generated. Furthermore, the spatial and temporal variability of damage potential on roads exposed to wet snow avalanches can be quantified, expressed by the number of persons at risk. The application of the rule base to the available data in the study area generated plausible results. The study demonstrates the potential for the application of expert systems and fuzzy logic in the field of natural hazard monitoring and risk management.

Enhanced Knowledge Management by Synchronizing Mind Maps and Fuzzy Cognitive Maps

This paper presents a conceptual approach to enhance knowledge management by synchronizing mind maps and fuzzy cognitive maps. The use of mind maps allows taking advantage of human creativity, while the application of fuzzy cognitive maps enables to store information expressed in natural language. By applying cognitive computing, it makes possible to gather and extract relevant information out of a data pool. Therefore, this approach is supposed to give a framework that enhances knowledge management. To demonstrate the potential of this framework, a use case concerning the development of a smart city app is presented.

Classification of Satellite Images by means of Fuzzy Rules generated by a Genetic Algorithm

The data acquired by Remote Sensing systems allow obtaining thematic maps of the earth's surface, by means of the registered image classification. This implies the identification and categorization of all pixels into land cover classes. Traditionally, methods based on statistical parameters have been widely used, although they show some disadvantages. Nevertheless, some authors indicate that those methods based on artificial intelligence, may be a good alternative. Thus, fuzzy classifiers, which are based on Fuzzy Logic, include additional information in the classification process through based-rule systems. In this work, we propose the use of a genetic algorithm (GA) to select the optimal and minimum set of fuzzy rules to classify remotely sensed images. Input information of GA has been obtained through the training space determined by two uncorrelated spectral bands (2D scatter diagrams), which has been irregularly divided by five linguistic terms defined in each band. The proposed methodology has been applied to Landsat-TM images and it has showed that this set of rules provides a higher accuracy level in the classification process

Fuzzy min-max neural networks for categorical data: application to missing data imputation

The fuzzy min–max neural network classifier is a supervised learning method. This classifier takes the hybrid neural networks and fuzzy systems approach. All input variables in the network are required to correspond to continuously valued variables, and this can be a significant constraint in many real-world situations where there are not only quantitative but also categorical data. The usual way of dealing with this type of variables is to replace the categorical by numerical values and treat them as if they were continuously valued. But this method, implicitly defines a possibly unsuitable metric for the categories. A number of different procedures have been proposed to tackle the problem. In this article, we present a new method. The procedure extends the fuzzy min–max neural network input to categorical variables by introducing new fuzzy sets, a new operation, and a new architecture. This provides for greater flexibility and wider application. The proposed method is then applied to missing data imputation in voting intention polls. The micro data—the set of the respondents’ individual answers to the questions—of this type of poll are especially suited for evaluating the method since they include a large number of numerical and categorical attributes.

Some geometrical methods for constructing contradiction measures on Atanassov's intuitionistic fuzzy sets

Trillas et al. (1999, Soft computing, 3 (4), 197–199) and Trillas and Cubillo (1999, On non-contradictory input/output couples in Zadeh's CRI proceeding, 28–32) introduced the study of contradiction in the framework of fuzzy logic because of the significance of avoiding contradictory outputs in inference processes. Later, the study of contradiction in the framework of Atanassov's intuitionistic fuzzy sets (A-IFSs) was initiated by Cubillo and Castiñeira (2004, Contradiction in intuitionistic fuzzy sets proceeding, 2180–2186). The axiomatic definition of contradiction measure was stated in Castiñeira and Cubillo (2009, International journal of intelligent systems, 24, 863–888). Likewise, the concept of continuity of these measures was formalized through several axioms. To be precise, they defined continuity when the sets ‘are increasing’, denominated continuity from below, and continuity when the sets ‘are decreasing’, or continuity from above. The aim of this paper is to provide some geometrical construction methods for obtaining contradiction measures in the framework of A-IFSs and to study what continuity properties these measures satisfy. Furthermore, we show the geometrical interpretations motivating the measures.

Supplementarity measures on fuzzy sets.

In this paper, we commence the study of the so called supplementarity measures. They are introduced axiomatically and are then related to incompatibility measures by antonyms. To do this, we have to establish what we mean by antonymous measure. We then prove that, under certain conditions, supplementarity and incompatibility measuresare antonymous. Besides, with the aim of constructing antonymous measures, we introduce the concept of involution on the set made up of all the ordered pairs of fuzzy sets. Finally, we obtain some antonymous supplementarity measures from incompatibility measures by means of involutions.

Solving Incidents in Telecommunications Using a Multiagent System

This article presents the model and implementation of a multiagent fuzzy system (MAFS), to automate the search of solutions of incidents in telecommunications, expressed by the users in an imprecise way and, later, registered in a a knowledge base keeping their original vaguenesses and the relationships between the incidents considered as ancestors and descendants. The process of the fuzzy incidents, no matter their causes, is based on the application of a formula which transforms the intervals of the fuzzy incidents to a computational language and in the interaction between the different kinds of software agents and the humans. To search and suggest solutions of the incident originally stated, a search algorithm is used and illustrated with an example. The preliminary results obtained show the users' satisfaction, in a great percentage of the presented cases. The system is adaptive and allows to record new solutions for future users.