Fuzzy Sets and Systems 133 (2003) 175–180 www.elsevier.com/locate/fss Should fuzzy equality and similarity satisfy transitivity? Comments on the paper by M. De Cock and E. Kerre Frank Klawonn Department of Computer Science, University of Applied Sciences Braunschweig= Wolfenbuettel, Salzdahlumer Str. 46= 48, D-38302 Wolfenbuettel, Germany Accepted 18 February 2002 Abstract This brief paper addresses problems that were raised in the paper (Fuzzy Sets and Systems, this issue) in connection with modelling fuzzy equality and similarity. In addition to specic comments to the cited paper, we also point out the more fundamental questions underlying this discussion. c 2002 Elsevier Science B.V. All rights reserved. 1. Introduction If the reader expects a denite answer to the question stated in the title, I regret that he will be disappointed by nding none in this short note. Nevertheless, the least I can do is, to elucidate important issues that are connected with the question. In the following, starting from some general comments in connection with the concept of similarity modelling, specic aspects of De Cock’s and Kerre’s paper are discussed and questioned. 2. Poincar e paradox, equivalence relations and transitivity Poincar e’s observation that indistinguishability might behave non-transitive in real life can be elucidated by the following example. A microscope or a telescope has a certain resolution so that we can only distinguish between two points, if their distance exceeds a certain value, say . Therefore, it might be the case that points A and B are indistinguishable as well as B and C , since both distances are smaller than . However, the distance between A and C might be greater than so that they can be distinguished. The following example is more or less in the same line as the previous example, but does even better clarify what the underlying problems in handling such things are. Assume a person wants to E-mail address: f.klawonn@fh-wolfenbuettel.de (F. Klawonn). 0165-0114/02/$ - see front matter c 2002 Elsevier Science B.V. All rights reserved. PII:S0165-0114(02)00243-9