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.
Multiplication, distributivity and fuzzy-integral. II
Based on results of generalized additions and generalized multiplications, proven in Part I, we first show a structure theorem on two generalized additions which do not coincide. Then we prove structure and representation theorems for generalized multiplications which are connected by a strong and weak distributivity law, respectively. Finally – as a last preparation for the introduction of a framework for a fuzzy integral – we introduce generalized differences with respect to t-conorms (which are...
Multiplication, distributivity and fuzzy-integral. III
Based on the results of generalized additions, multiplications and differences proven in Part I and II of this paper a framework for a general integral is presented. Moreover it is shown that many results of the literature are contained as special cases in our results.