Among various approaches to fuzzy logics, we have chosen two of them, which are built up in a similar way. Although starting from diierent basic logical connectives, they both use interpretations based on Frank t-norms. Diierent interpretations of the implication lead to diierent axiomatizations, but most logics studied here are complete. We compare the properties, advantages and disadvantages ...

Many algebraic preconditioners rely on incomplete factorization, where nonzero entries are dropped, based on some rule, during the factorization process. In a series of papers by Bollhöfer and Saad [2, 3, 4] it was shown that robust rules for both dropping and pivoting can be obtained from information about the inverses of the submatrices that are consecutively constructed. In particular, monit...

This paper deals with Zadeh’s compositional rule of inference [12] under triangular norms: IF X is P AND X and Y have relation R, THEN Y is Q, where P and Q are fuzzy sets of the real line IR, R is a fuzzy relation on IR and the conclusion Q is defined via sup-T composition of P and R: μQ(y) = sup x∈IR T (μP (x), μR(x, y)), y ∈ IR. It is shown that (i) when the triangular norm T and the members...

Suppose U is an upper-triangular matrix, and D a nonsingular diagonal matrix whose diagonal entries appear in nondescending order of magnitude down the diagonal. It is proved that kD UDk kUk for any matrix norm that is reduced by a pinching. In addition to known examples { weakly unitarily invariant norms { we show that any matrix norm de ned by kAk def = max x 6=0; y 6=0 Re (x Ay) (x) (y) ; wh...

In the literature on social choice with fuzzy preferences, a central question is how to represent the transitivity of a fuzzy binary relation. Arguably the most general way of doing this is to assume a form of transitivity called max-star transitivity. The star operator in this formulation is commonly taken to be a triangular norm. The familiar max-min transitivity condition is a member of this...

Abstract A prominent problem in knowledge representation is how to answer queries taking into account also the implicit consequences of an ontology representing domain knowledge. While this has been widely studied within realm description logic ontologies, it surprisingly neglected context vague or imprecise knowledge, particularly from point view mathematical fuzzy logic. In paper, we study an...

In this paper, we introduce a class of lowest-order nonconforming immersed finite element (IFE) methods for solving two-dimensional Stokes interface problems. The proposed do not require the solution mesh to align with fluid and can use either triangular or rectangular meshes. On meshes, Crouzeix–Raviart is used velocity approximation, piecewise constant pressure. Rannacher–Turek rotated Q1-Q0 ...

The ordinal sum construction provides a very effective way to generate new triangular norm on the real unit interval from existing ones. One of most prominent theorems concerning norms states that is continuous if and only it uniquely representable as an Archimedean norms. However, subintervals bounded lattice not always (even one summand involved), just extends in naïve way. In present paper, ...

Mesh reduction techniques are used for accelerating the visualization process for large datasets. Typical examples are scalar or vector valued functions deened on complex 2 or 3 dimensional meshes. Grosso et al. presented a method for mesh optimization based on nite elements approximations with the L2 norm and adaptive local mesh reenement. Starting with a very coarse triangulation of the funct...

For gasless combustion in a one-dimensional solid, we show a type of nonlinear stability of the physical combustion front: if a perturbation of the front is small in both a spatially uniform norm and an exponentially weighted norm, then the perturbation stays small in the spatially uniform norm and decays in the exponentially weighted norm, provided the linearized operator has no eigenvalues in...