- Full text PDF available (5)
- This year (0)
- Last 5 years (5)
- Last 10 years (15)
Journals and Conferences
In this paper we introduce a general definition of an information measure for fuzzy sets and we study its main properties. Then we describe a procedure to c~end any information measure from a a-algebra of ordinary sets to the ~-algebra of fuzz~/ sets of the same space.
The natural properties of the aggregation operators and the most elementary ones are the idempotence, the monotonicity and the continuity from below. We assume only these properties for the aggregation operators with infinitely many inputs, defined by functionals on the family of measurabe functions. A family of fuzzy measures is associated with each… (More)
We consider the aggregation operators which are ⊕-additive for commonotone functions. The main result is that any operator is expressed by a kind of general fuzzy integral which uses a family of fuzzy measures connected by a ⊕-additive Cauchy’s equations. In particular, the family of fuzzy measures can be obtained by a ⊕-fitting pseudomultiplication. In… (More)
The superposition principle is a useful tool for constructing new solutions of ordinary and partial differential equations. Therefore, through this paper, we are considering the pseudo-linear superposition principle based on generated pseudo-operations of the following form: x oplus y = g<sup>-1</sup> (g(x) + g(y)) , x odot y = g<sup>-1</sup> (g(x)g(y)) ,… (More)
The aim of this paper is to study sustainability of the pseudo-linear superposition principle, that is, of the nonlinear superposition principle (NLSP) observed in the pseudo-analysis' framework and to discuss some possible extensions.
In this paper we present some applications of pseudo-analysis in the theory of fluid mechanics. There is proved the monotonicity of the components of the velocity for the solutions of Euler equations. This help to prove the pseudo-linear superposition principle for Euler equations. The superposition principle is proven also for the Navier-Stokes equations… (More)
The set-valued function in general is an important mathematical notion that plays a crucial role in several practical areas. Also, the Jensen integral inequality is a significant mathematical tool that has applications in many areas, such as statistics, statistical physics, information theory, etc. Since the pseudo-analysis is, as well, a theory of the vast… (More)