Frank Klawonn

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In this paper we propose a natural approach to handle imprecise numbers as they arise for example from measurements. Fuzzy sets turn out to be a canonical representation for such imprecise numbers that are induced by taking diierent tolerance or error bounds into account. Fuzzy sets are induced by scaling factors that describe the magnitude of the(More)
Fuzzy set theory is based on a `fuzziication' of the predicate 2 (element of), the concept of membership degrees is considered as fundamental. In this paper we elucidate the connection between indis-tinguishability modelled by fuzzy equivalence relations and fuzzy sets. We show that the indistinguishability inherent to fuzzy sets can be computed and that(More)
This book is an essential tool for second-year undergraduate students and above, providing clear and concise explanations of the basic concepts of computer graphics, and Features provides an essential tool for surface problems are expected. Thoroughly revised and program examples at work via. You can be found on its server with extensive usage. Various(More)
We introduce an objective function based fuzzy clustering technique that assigns one in uence parameter to each single data vari able for each cluster Our method is not only suited to detect structures or groups in unevenly over the structure s single domains distributed data but gives also information about the in uence of individual variables on the(More)
This paper proposes a new clustering algorithm in the fuzzy-c-means family, which is designed to cluster time series and is particularly suited for short time series and those with unevenly spaced sampling points. Short time series, which do not allow a conventional statistical model, and unevenly sampled time series appear in many practical situations. The(More)
The fundamental updating process in the tmnsfemble belief model is related to Lhe concept of specialization and can be described by a specialization matrix. The degree of belief in the truth of a proposition is a degree of justified support. The Principle of Minimal Commitment implies that one should never give more support to the truth of a proposition(More)