Triangular norms, or t-norms for short, play an important role for the semantics of fuzzy logics. Although an enormous number of examples and a remarkable number of construction methods for this kind of operation has been established, a uniform approach is still outstanding. This paper is devoted to a specific algebraic-geometrical framework within which t-norms, up to isomorphism, can be descr...

Contour lines totally fix the structure of leftcontinuous t-norms. For each t-norm, these contour lines are determined by the corresponding residual implicator. Most properties involving residual implicators can now easily be translated into properties involving contour lines. As the portation law expresses associativity, we dispose of a powerful tool for constructing left-continuous t-norms. I...

Each t-norm can be identified with its Cayley tomonoid, which consists of pairwise commuting order-preserving functions from the real unit interval to itself. Cayley tomonoids provide an easily manageable, yet versatile tool for the construction of t-norms. To give evidence to this claim, we review and reformulate several construction methods that are known in the literature. We adopt, on the o...

We introduce nearly Frank t-norms as t-norms which are generated from Frank t-norms by means of a negation-preserving automorphism. We state basic properties of nearly Frank t-norms and we show their speci c role in the characterization of T -measures. 1 Basic facts about T -norms A t-norm (fuzzy conjunction) is a binary operation T : [0; 1]2 ! [0; 1] which is commutative, associative, nondecre...

In this paper we consider compound conditionals, Fr\'echet-Hoeffding bounds and the probabilistic interpretation of Frank t-norms. By studying solvability suitable linear systems, show under logical independence sharpness for prevision conjunctions disjunctions $n$ conditional events. We study set all coherent assessments on a family containing events their conjunction, by verifying that it is ...

A comparison of different T-norms and S-norms for interval type-2 fuzzy number weights is proposed in this work. The interval type-2 fuzzy number weights are used in a neural network with an interval backpropagation learning enhanced method for weight adjustment. Results of experiments and a comparative research between traditional neural networks and the neural network with interval type-2 fuz...

this researc h c enters on a c omparative study of various norms breakings among high-sc hool students in khwaf town and birjand c ity public sc hools. sample population is drawn from the high sc hool (3rd year level) students studying in 2005 2006 educ ational year. ac c ording to the population size of the c ities, the sample populations were dec ided at 250 and 300, based on the simple rando...