Given a lattice (X,≤,∧,∨) we define a multi-valued operation ∧ which is analogous to a t-norm (i.e. it is commutative, associative, has one as a neutral element and is monotone). The operation is parametrized by the set Q, hence we actually obtain an entire family of such multi-valued t-norms. Similarly we define a family of multi-valued t-conorms ∨ . We show that, when P, Q are chosen appropri...

The definition of t-norms and t-conorms of the class of Hamacher with multilayer feedforward artificial neural networks is achieved in this work. This fact lets to insert fuzzy knowledge into neural network before its training.

Introduction: Medication adherence is regarded as one of the most important factors in caring for hypertension. This study aimed to investigate the effect of intervention based on the theory of planned behavior (TPB) on medication adherence and its influencing factors on the elderly with hypertension in a rural area, Kerman province, Iran.                  Methods: This quasi-experimental stud...

We consider the one-dimensional quantum harmonic oscillator perturbed by a linear operator which is polynomial of degree $2$ in $(x,-{\rm i}\partial_x)$, with coefficients quasi-periodically depending on time. By establishing reducibility results, we describe growth Sobolev norms. In particular, $t^{2s}-$polynomial ${\mathcal H}^s-$norm observed this model if original time quasi-periodic equati...

The application of conjunctive aggregation operators in fuzzy control systems with 2 inputs is discussed and the effect of the choice of a continuous t-norm operator in inference phase for TSK systems is computed. It is shown that the choice of a continuous t-norm modelling AND connective in antecedent part of fuzzy rules can be reduced just to strict or nilpotent t-norm. Moreover, it is shown ...

The morphological gradient is a widely used edge detector for grey-level images in many applications. In this paper, we generalize the definition of the morphological gradient of the fuzzy mathematical morphology based on t-norms. Concretely, instead of defining the morphological gradient from the usual definitions of fuzzy dilation and erosion, where the minimum and the maximum are used, we de...

Residuated fuzzy logic calculi are related to continuous t-norms, which are used as truth functions for conjunction, and their residua as truth functions for implication. In these logics, a negation is also definable from the implication and the truth constant 0, namely ¬φ isφ → 0. However, this negation behaves quite differently depending on the t-norm. For a nilpotent t-norm (a t-norm which i...

In [7], J. J. Kohn proved C∞ hypoellipticity with loss of k − 1 derivatives in Sobolev norms (and at least that loss in L∞) for the highly non-subelliptic singular sum of squares Pk = LL + L|z| L = −L ∗ L − (zL)zL with L = ∂ ∂z + iz ∂ ∂t . In this paper, we prove hypoellipticity with loss of k−1 m derivatives in Sobolev norms for the operator (0.1) P F m,k = L F mL F m + L F m |z| Lm with L F m...