Recent Advances in the Field of Left-continuous t-norms

The recent advances in the research of left-continuous t-norms is summarized in this talk. The main focus is on construction methods, geometric description, and structural characterization. We point out further research directions and open problems. 1 Summary The structure of continuous t-norms has been known since ages [19]. In many mathematical theories leftcontinuous t-norms have been used for a few decades without having a single (non-continuous) example at hand. After this long period – when no left-continuous t-norm1 was known – the first example, the nilpotent minimum, was found by Fodor [2]. Even after finding this example many researchers believed that this is the only one, and a conjecture was published saying, roughly speaking, that the nilpotent minimum is the only left-continuous t-norm. Next, a series of papers have appeared [11, 14, 15, 8, 7, 3, 1, 16, 5, 20, 6, 22], in which new construction methods provided the interested community with a huge number of new left...

• Type: Conference
• Year: 2007
• Where: EUSFLAT
• Authors: Sándor Jenei
• Keywords: Construction Method, EUSFLAT 2007, Fuzzy Logic, Geometric Description, Left-continuous T-norms