In this paper further development of Chebyshev type inequalities for Sugeno integrals based on an aggregation function and a scale transformation is given. Consequences for T-(S-)evaluators are established.
We introduce a fuzzy equality for -observables on an -quantum space which enables us to characterize different kinds of convergences, and to represent them by pointwise functions on an appropriate measurable space.
We have modified the axiomatic system of orness measures, originally introduced by Kishor in 2014, keeping altogether four axioms. By proposing a fuzzy orness measure based on the inner product of lattice operations, we compare our orness measure with Yager's one which is based on the inner product of arithmetic operations. We prove that fuzzy orness measure satisfies the newly proposed four axioms and propose a method to determine OWA operator with given fuzzy orness degree.
The procedures for constructing a fuzzy number and a fuzzy-valued function from a family of closed intervals and two families of real-valued functions, respectively, are proposed in this paper. The constructive methodology follows from the form of the well-known “Resolution Identity” (decomposition theorem) in fuzzy sets theory. The fuzzy-valued measure is also proposed by introducing the notion of convergence for a sequence of fuzzy numbers. Under this setting, we develop the fuzzy-valued integral...
This note contains a simple example which does clearly indicate the differences in the Henstock-Kurzweil, McShane and strong McShane integrals for Banach space valued functions.
Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.
We address the problem of the multifractal analysis of local entropies for arbitrary invariant measures. We obtain an upper estimate on the multifractal spectrum of local entropies, which is similar to the estimate for local dimensions. We show that in the case of Gibbs measures the above estimate becomes an exact equality. In this case the multifractal spectrum of local entropies is a smooth concave function. We discuss possible singularities in the multifractal spectrum and their relation to phase...
By means of two general operations + and x, called pan-operations'', we build a new kind of integral. This formulation contains, as particular cases, both Choquet's and Sugeno's integrals.