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...

We show that the sup-t-norm and inf-residuum types of fuzzy relational equations, considered in the literature as two different types, are in fact two particular instances of a single, more general type of equations. We demonstrate that several pairs of corresponding results on the sup-t-norm and inf-residuum types of equations are simple consequences of single results regarding the more genera...

Finding strongly standard complete axiomatizations for t-norm based fuzzy logics (i.e. complete for deductions with infinite sets of premises w.r.t. semantics on the real unit interval [0, 1]) is still an open problem in general, even though results are already available for some particular cases like some infinitary logics based on a continuous t-norm or certain expansions of Monoidal t-norm b...

of the origin in C ' , and vice versa. But clearly, not every convex compact neighbourhood of the origin in C ~' belongs to a lub norm. The principal problem to be considered here is the geometric characterizat ion of those convex bodies in C ~' which are associated with lub norms. The question arises because of the fact tha t m a n y of the properties of vector norms fall quite easily and natu...

This paper establishes in two completely different ways that the abstract degenerate initial value problem —(Mu(t)) + Lu{t) = f(t),Q < t < r ,Mu(0) = Uh Muo, has always an integrated solution, provided that for ali complex numbers z in the half-plane Rez > a > 0 the operator pencil P(z) = zM + L has a bounded inverse from the Banach space X to T>(L), endowed with the graph-norm, and its norm ha...

We show that the weak solutions of parabolic equation ∂tu−∆u+ b(t, x) · ∇u = 0 with vector field b(t, x) satisfying form-boundedness condition constitute a Feller evolution family and, thus, determine a strong Markov process. Our proof uses a Moser-type iterative procedure and an a priori estimate on the L-norm of the gradient of solution in terms of the L-norm of the gradient of initial function.

The label semantics linguistic representation framework is introduced as an alternative approach to computing and modelling with words, based on the concept of appropriateness rather than graded truth. A possible worlds interpretation of label semantics is then proposed. In this model it is shown that certain assumptions about the underlying possible worlds can result in appropriateness measure...