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Über dieses Buch

This book is a collection of several contributions which show the state of the art in specific areas of Computational Intelligence. This carefully edited book honors the 65th birthday of Rudolf Kruse. The main focus of these contributions lies on treating vague data as well as uncertain and imprecise information with automated procedures, which use techniques from statistics, control theory, clustering, neural networks etc. to extract useful and employable knowledge.



What a Fuzzy Set Is and What It Is not?

Although in the literature there appear ‘type-one’ fuzzy sets, ‘type-two’ fuzzy sets, ‘intuitionistic’ fuzzy sets, etc., this theoretically driven paper tries to argue that only one type of fuzzy sets actually exists. This is due to the difference between the concepts of a fuzzy set” and a “membership function”.
Enric Trillas, Rudolf Seising

Fuzzy Random Variables à la Kruse & Meyer and à la Puri & Ralescu: Key Differences and Coincidences

The concept of the so-called fuzzy random variables has been introduced in the literature aiming to model random mechanisms ‘producing’ fuzzy values. However, the best known approaches (namely, the one by Kwakernaak-Kruse and Meyer and the one by Féron-Puri and Ralescu) have been thought to deal with two different situations and, to a great extent, with two different probabilistic and statistical targets. This contribution highlights some of the most remarkable differences and coincidences between the two approaches.
María Ángeles Gil

Statistical Inference for Incomplete Ranking Data: A Comparison of Two Likelihood-Based Estimators

We consider the problem of statistical inference for ranking data, namely the problem of estimating a probability distribution on the permutation space. Since observed rankings could be incomplete in the sense of not comprising all choice alternatives, we propose to tackle the problem as one of learning from imprecise or coarse data. To this end, we associate an incomplete ranking with its set of consistent completions. We instantiate and compare two likelihood-based approaches that have been proposed in the literature for learning from set-valued data, the marginal and the so-called face-value likelihood. Concretely, we analyze a setting in which the underlying distribution is Plackett-Luce and observations are given in the form of pairwise comparisons.
Inés Couso, Eyke Hüllermeier

Interval Type–2 Defuzzification Using Uncertainty Weights

One of the most popular interval type–2 defuzzification methods is the Karnik–Mendel (KM) algorithm. Nie and Tan (NT) have proposed an approximation of the KM method that converts the interval type–2 membership functions to a single type–1 membership function by averaging the upper and lower memberships, and then applies a type–1 centroid defuzzification. In this paper we propose a modification of the NT algorithm which takes into account the uncertainty of the (interval type–2) memberships. We call this method the uncertainty weight (UW) method. Extensive numerical experiments motivated by typical fuzzy controller scenarios compare the KM, NT, and UW methods. The experiments show that (i) in many cases NT can be considered a good approximation of KM with much lower computational complexity, but not for highly unbalanced uncertainties, and (ii) UW yields more reasonable results than KM and NT if more certain decision alternatives should obtain a larger weight than more uncertain alternatives.
Thomas A. Runkler, Simon Coupland, Robert John, Chao Chen

Exploring Time-Resolved Data for Patterns and Validating Single Clusters

Cluster analysis is often described as the task to partition a data set into subset—called clusters—so that similar data objects belong to the same cluster and data objects from different clusters are not very similar. However, partitioning the whole data set into clusters is often not the aim when clustering algorithms are applied. Instead, the main goal is sometimes to find a few “good” clusters containing a limited amount of data objects, while even the majority of data objects might not be assigned to any cluster, contradicting the principle of partitioning the data set into clusters. In this paper, we revisit a method called dynamic data assigning assessment clustering to discover and validate single clusters in a data set and extend the dynamic data assigning assessment approach to the context of time-resolved data.
Frank Klawonn

Interpreting Cluster Structure in Waveform Data with Visual Assessment and Dunn’s Index

Dunn’s index was introduced in 1974 as a way to define and identify a “best” crisp partition on n objects represented by either unlabeled feature vectors or dissimilarity matrix data. This article examines the intimate relationship that exists between Dunn’s index, single linkage clustering, and a visual method called iVAT for estimating the number of clusters in the input data. The relationship of Dunn’s index to iVAT and single linkage in the labeled data case affords a means to better understand the utility of these three companion methods when data are crisply clustered in the unlabeled case (the real case). Numerical examples using simulated waveform data drawn from the field of neuroscience illustrate the natural compatibility of Dunn’s index with iVAT and single linkage. A second aim of this note is to study customizing the three methods by changing the distance measure from Euclidean distance to one that may be more appropriate for assessing the validity of crisp clusters of finite sets of waveform data. We present numerical examples that support our assertion that when used collectively, the three methods afford a useful approach to evaluation of crisp clusters in unlabeled waveform data.
Sara Mahallati, James C. Bezdek, Dheeraj Kumar, Milos R. Popovic, Taufik A. Valiante

A Shared Encoder DNN for Integrated Recognition and Segmentation of Traffic Scenes

Detection of traffic related objects in the vehicles surroundings is an important task for future automated cars. Visual object recognition and scene labeling from onboard cameras provides valuable information for the driving task. In computer vision, the task of generating meaningful image regions representing specific object categories such as cars or road area, is denoted as semantic segmentation. In contrast, scene recognition computes a global label that reflects the overall category of the scene. This contribution presents an efficient deep neural network (DNN) capable of solving both problems. The network topology avoids redundant computations, by employing a shared feature encoder stage combined with designated decoders for the two specific tasks. Additionally, element-wise weights in a novel Hadamard layer efficiently exploit spatial priors for the segmentation task. Traffic scene segmentation is examined in conjunction with road topology recognition based on the cityscapes dataset [2] augmented with manually labeled road topology data.
Malte Oeljeklaus, Frank Hoffmann, Torsten Bertram

Fuzzy Ontology Support for Knowledge Mobilisation

Classical management science is making the transition to analytics, which has the same agenda to support managerial planning, problem solving and decision making in industrial and business contexts but is combining the classical models and algorithms with modern, advanced technology for handling data, information and knowledge. We run a knowledge mobilisation project as a joint effort by Institute for Advanced Management Systems Research, and VTT Technical Research Centre of Finland. The goal was to mobilise knowledge stored in heterogeneous databases for users with various backgrounds, geographical locations and situations. The working hypothesis of the project was that fuzzy mathematics combined with domain-specific data models, in other words, fuzzy ontologies, would help manage the uncertainty in finding information that matches the users’ needs. In this paper, we describe an industrial application of fuzzy ontologies in information retrieval for a paper machine where problem-solving reports are annotated with keywords and then stored in a database for later use. One of the key insights turned out to be that using the Bellmann-Zadeh principles for fuzzy decision-making are useful for identifying keyword dependencies in a keyword taxonomic tree.
Christer Carlsson
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