Integral with respect to fuzzy mesure in finite dimensional Banach spaces.
Integrales normadas y conormadas. (generalización de la integral de Sugeno).
En este trabajo se generaliza ampliamente la integral de Sugeno a partir de la definición de dos familias de integrales difusas, normadas y conormadas, de las que la integral de Sugeno es un caso particular.El propósito de este trabajo es el estudio de las propiedades de las mencionadas integrales y la relación existente entre ambas familias. También se extienden estas familias de integrales a dominio difuso.Finalmente se sugieren algunas posibles maneras de utilizar los resultados obtenidos.
Integration of real functions with respect to a -measure
Integration with respect to a -measure
Investigation of a Stolarsky type Inequality for Integrals in Pseudo-Analysis
MSC 2010: 03E72, 26E50, 28E10In this paper, we prove a Stolarsky type inequality for pseudo-integrals.
Less than many translates of a compact nullset may cover the real line
We answer a question of Darji and Keleti by proving that there exists a compact set C₀ ⊂ ℝ of measure zero such that for every perfect set P ⊂ ℝ there exists x ∈ ℝ such that (C₀+x) ∩ P is uncountable. Using this C₀ we answer a question of Gruenhage by showing that it is consistent with ZFC (as it follows e.g. from ) that less than many translates of a compact set of measure zero can cover ℝ.
Loeb completion of internal vector-valued measures.
Łukasiewicz tribes are absolutely sequentially closed bold algebras
We show that each sequentially continuous (with respect to the pointwise convergence) normed measure on a bold algebra of fuzzy sets (Archimedean -algebra) can be uniquely extended to a sequentially continuous measure on the generated Łukasiewicz tribe and, in a natural way, the extension is maximal. We prove that for normed measures on Łukasiewicz tribes monotone (sequential) continuity implies sequential continuity, hence the assumption of sequential continuity is not restrictive. This yields...
Maple tools for the Kurzweil integral
Riemann sums based on -fine partitions are illustrated with a Maple procedure.
Mathematical aspects of the theory of measures of fuzziness.
After recalling the axiomatic concept of fuzziness measure, we define some fuzziness measures through Sugeno's and Choquet's integral. In particular, for the so-called homogeneous fuzziness measures we prove two representation theorems by means of the above integrals.
Measurable envelopes, Hausdorff measures and Sierpiński sets
We show that the existence of measurable envelopes of all subsets of ℝⁿ with respect to the d-dimensional Hausdorff measure (0 < d < n) is independent of ZFC. We also investigate the consistency of the existence of -measurable Sierpiński sets.
Measure and measurable functions of
Measures on Corson compact spaces
We prove that the statement: "there is a Corson compact space with a non-separable Radon measure" is equivalent to a number of natural statements in set theory.
Mesures semi-classiques et mesures de défaut
Metrics on vector spaces with -localisation.
Misure su --semigruppi e su MV-algebre
Möbius fitting aggregation operators
Standard Möbius transform evaluation formula for the Choquet integral is associated with the -aggregation. However, several other aggregation operators replacing operator can be applied, which leads to a new construction method for aggregation operators. All binary operators applicable in this approach are characterized by the 1-Lipschitz property. Among ternary aggregation operators all 3-copulas are shown to be fitting and moreover, all fitting weighted means are characterized. This new method...
Moment estimation inequalities based on random variable on Sugeno measure space.
Multicriteria Decision Making by Fuzzy Integrals - Fuzzy Measures Determination
Multiplication, distributivity and fuzzy-integral. I
The main purpose is the introduction of an integral which covers most of the recent integrals which use fuzzy measures instead of measures. Before we give our framework for a fuzzy integral we motivate and present in a first part structure- and representation theorems for generalized additions and generalized multiplications which are connected by a strong and a weak distributivity law, respectively.