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...

In this paper, the connection between Menger probabilistic norms and H"{o}hle probabilistic norms is discussed. In addition, the correspondence between probabilistic norms and Wu-Fang fuzzy (semi-) norms is established. It is shown that a probabilistic norm (with triangular norm $min$) can generate a Wu-Fang fuzzy semi-norm and conversely, a Wu-Fang fuzzy norm can generate a probabilistic norm.

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...

Abstract In this paper, I outline and defend the view that variations in compliance levels with one same norm represent different norms about following . support of claim, first argue classic game-theoretic accounts, which define as Nash equilibria noncooperative games, typically consider separate norms. After that, suggest a more fine-grained, distinction accounts for degrees show how to incor...

In this paper, we introduce the notion of an action $Y_X$as a generalization of the notion of a module,and the notion of a norm $vt: Y_Xto F$, where $F$ is a field and $vartriangle(xy)vartriangle(y') =$ $ vartriangle(y)vartriangle(xy')$ as well as the notion of fuzzy norm, where $vt: Y_Xto [0, 1]subseteq {bf R}$, with $bf R$  the set of all real numbers. A great many standard mappings on algebr...

Abstract The paper defends an account of the context-sensitivity norms that draws on resources counterfactual conditionals. combines two assumptions: assumption permission is rule-abiding performance in some contextually relevant situations; and situations are picked out by mechanism selects possible worlds for evaluation explains non-monotonicity permissions solves a puzzle, raised Timothy Wil...