Fuzzy Sets and Systems 145 (2004) 471–479 www.elsevier.com/locate/fss Problems on triangular norms and related operators Erich Peter Klement a ; ∗ , Radko Mesiar b; c , Endre Pap d a Fuzzy Logic Laboratory, Department of Algebra, Stochastics and Knowledge-Based Mathematical Systems, Johannes Kepler University, Linz-Hagenberg, 4040 Linz, Austria b Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Bratislava 81 368, Slovakia c Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czech Republic d Department of Mathematics and Informatics, University of Novi Sad, Novi Sad 21000, Yugoslavia Received 17 June 2003; accepted 7 July 2003 Abstract A number of open problems on triangular norms and related operators was posed during the 24th Linz seminar on fuzzy set theory “Triangular norms and related operators in many-valued logics” held in February 2003. They are collected here, together with some other open problems in this context and with some problems which were posed earlier and have been solved in the meantime. c  2003 Elsevier B.V. All rights reserved. Keywords: Triangular norm; Triangular conorm; Uninorm; Aggregation operator 1. Introduction Triangular norms are, on the one hand, special semigroups and, on the other hand, solutions of some functional equations [1,23,34,35]. This mixture quite often requires new approaches to answer questions about the nature of triangular norms. A triangular norm (t-norm for short) T : [0; 1] 2 → [0; 1] is an associative, commutative, non-decrea- sing function such that 1 acts as a neutral element [34]. Most important t-norms are the minimum T M ; the product T P and the Lukasiewicz t-norm T L given by T L (x;y) = max(x + y - 1; 0). Observe that each continuous Archimedean t-norm T can be represented by means of a continuous additive gen- erator [23,27], i.e., a strictly decreasing continuous function t : [0; 1] → [0; ∞] with t (1) = 0 such that T (x;y)= t (-1) (t (x)+ t (y)); * Corresponding author. Tel. +43-732-2468-9151; fax: +43-732-2468-1351. E-mail addresses: ep.klement@jku.at (E.P. Klement), mesiar@math.sk (R. Mesiar), pap@im.ns.ac.yu, pape@eunet.yu (E. Pap). 0165-0114/$ - see front matter c  2003 Elsevier B.V. All rights reserved. doi:10.1016/S0165-0114(03)00303-8