A t-tautology (triangular tautology) is a propositional formula which is a tautology in all fuzzy logics deened by continuous triangular norms. In this paper we show that the problem of recognizing t-tautologies is coNP complete, and thus decidable.

In this paper we propose computationally simple, pointwise formulas for extended t-norms and t-conorms on fuzzy truth values. The complex convolutions of the extended operations are shown to be equivalent to simple pointwise expressions for several special cases. Linear fuzzy truth values are defined and it is shown that the extended Łukasiewicz operations preserve linearity. Since linear fuzzy...

In fuzzy logic in wider sense, i.e. in the field of fuzzy sets applications, t-norms got a prominent rôle in recent times. In many-valued logic, the Lukasiewicz systems, the Gödel sytems, and also the product logic all are t-norm based systems. The present paper discusses the more general problem of the adequate axiomatizability for such t-norm based logical systems in general, surveying result...

The extension principle defines the arithmetic operations on fuzzy numbers. In the extension principle one can use any t-norm for modeling the conjunction operator. It is therefore important to know, which t-norms are consistent with a particular type of fuzzy number. We call a t-norm consistent, if the arithmetic operation is closed. In this paper we investigate the addition of sigmoid and two...

Triangular norms (t-norms for short) play a crucial role in several fields of mathematics and AI. For an exhaustive overview on t-norms we refer to [20]. Recently an increasing interest of left-continuous t-norm based theories can be observed (see e.g. [3, 5, 6, 7, 18]). In this paper we discuss in detail the presently existing construction methods which result in left-continuous triangular nor...

Fuzzy relations are able to model vagueness, in the sense that they provide the degree to which two objects are related to each other. However, they cannot model uncertainty: there is no means to attribute reliability information to the membership degrees. Intuitionistic fuzzy sets, as de1ned by Atanassov (Instuitionistic Fuzzy Sets, Physica-Verlag, Heidelberg, New York, 1999), give us a way to...

Prioritized fuzzy constraint satisfaction problems (pFCSP’s) are used to model the concept of priority in real time systems. Schur-concave t-norms are a key factor in the implementation of pFCSP. In this paper there are presented some results on the characterization of Schur-concave t-norms. There are tested two different pFCSP’s on a candidate evaluation scenario. Using pFCSP’s, different cand...

Using generalized modus ponens reasoning, we examine the values of the inferred conclusion using the Fodor’s implication in order to interpret a fuzzy if-then rule with a single input single output and the T-norms t1(x, y) = min(x, y), t2(x, y) = xy and t3(x, y) = max(0, x + y − 1) for composition operation. These are the very used T-norms in generalized modus ponens reasoning.

We present the basic analytical and algebraic properties of triangular norms. We discuss continuity as well as the important classes of Archimedean, strict and nilpotent t-norms. Triangular conorms and De Morgan triples are also mentioned. Finally, a brief historical survey on triangular norms is given. Submitted for publication Johannes Kepler Universität Linz Fuzzy Logic Laboratorium Linz-Hag...