Related papers: p-Symmetric fuzzy measures
For a multi-attribute decision making (MADM) problem, the information of alternatives under different attributes is given in the form of intuitionistic fuzzy number(IFN). Intuitionistic fuzzy set (IFS) plays an important role in dealing…
We introduce a type of measurements that generalize the so-called "partial measurements" performed in recent years with phase qubits. While in the case of partial measurements it has been demonstrated that one could undo the effect of the…
How to distribute a set of points uniformly on a spherical surface is a very old problem that still lacks a definite answer. In this work, we introduce a physical measure of uniformity based on the distribution of distances between points,…
Our purpose is to offer a logical analysis of the system of units and to explore possible paths towards a consistent and unified system with an original perspective. The path taken here builds on the fact that, thanks to optical or…
Fourier analysis and representation of circular distributions in terms of their Fourier coefficients, is quite commonly discussed and used for model-free inference such as testing uniformity and symmetry etc. in dealing with 2-dimensional…
Intuitionistic fuzzy Banach algebra is introduced and a few properties of it is studied. The properties of invertible elements and relation among invertible elements, open set, closed set are emphasized. Topological divisors of zero is…
This paper shows that the endograph metric and the $\Gamma$-convergence are compatible on a large class of fuzzy set in $\mathbb{R}^m$.
In this paper, we investigate the Fourier transform of self-similar measures on R. We provide quantitative decay rates of Fourier transform of some self-similar measures. Our method is based on random walks on lattices and Diophantine…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
In a close form without referring the time-dependent Hamiltonian to the total system, a consistent approach for quantum measurement is proposed based on Zurek's triple model of quantum decoherence [W.Zurek, Phys. Rev. D 24, 1516 (1981)]. An…
A mathematically correct approach to study theories with infinite-dimensional groups of symmetries is presented. It is based on quasi-invariant measures on the groups. In this paper, the properties of the measure on the group of…
Topological measures and deficient topological measures generalize Borel measures and correspond to certain non-linear functionals. We study integration with respect to deficient topological measures on locally compact spaces. Such an…
We introduce and investigate in this short report the new notion of uniform measure (distribution) on the arbitrary compact metric space. We consider also some possible applications of these measures in the theory of imbedding theorems and…
We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particular, the new integral emerges as a generalization of the…
The problem of replacing an integral norm with respect to a given probability measure by the corresponding integral norm with respect to a discrete measure is discussed in the paper. The above problem is studied for elements of finite…
Real-world phenomena often exhibit vagueness, partial truth, and incomplete information. To model such uncertainty in a mathematically rigorous way, many generalized set-theoretic frameworks have been introduced, including Fuzzy Sets [1],…
The real world is inherently uncertain, imprecise and vague. Soft set theory was firstly introduced by Molodtsov in 1999 as a general mathematical tool for dealing with uncertainties, not clearly defined objects. A soft set consists of two…
I propose a superoscillation measurement method for subdiffraction incoherent optical sources, with potential applications in astronomy, remote sensing, fluorescence microscopy, and spectroscopy. The proposal, based on coherent optical…
This article is meant to give a lucid and widely accessible, self-contained account of a novel way of performing arithmetic operations on fuzzy intervals. Based on two formulae of generalized inversion (the first in close analogy to the…
The paper is to prove the Gaussian correlation conjecture stating that, under the standard Gaussian measure, the measure of the intersection of any two symmetric convex sets is greater than or equal to the product of their measures.…