Related papers: p-Symmetric fuzzy measures
Porosity and dimension are two useful, but different, concepts that quantify the size of fractal sets and measures. An active area of research concerns understanding the relationship between these two concepts. In this article we will…
This paper is devoted to the relationships and properties of the endograph metric and the $\Gamma$-convergence. The main contents can be divided into three closely related parts. Firstly, on the class of upper semi-continuous fuzzy sets…
Interaction-free measurement is shown to arise from the forward-scattered wave accompanying absorption: a "quantum silhouette" of the absorber. Accordingly, the process is not free of interaction. For a perfect absorber the…
The concept of measure synchronization between two coupled quantum many-body systems is presented. In general terms we consider two quantum many-body systems whose dynamics gets coupled through the contact particle-particle interaction.…
In this article we investigate a way in which quantum computing can be used to extend the class of fuzzy sets. The core idea is to see states of a quantum register as characteristic functions of quantum fuzzy subsets of a given set. As the…
We present a generalized information-theoretic measure of synchronization in quantum systems. This measure is applicable to dynamics of anharmonic oscillators, few-level atoms, and coupled oscillator networks. Furthermore, the new measure…
The transitivity of fuzzy relations plays an important role in fuzzy set theory, artificial intelligence, clustering and decision-making. However, it is often difficult for fuzzy relations to satisfy the transitivity property in many…
Recently, Wang et al. discussed the properties of fuzzy information systems under homomorphisms in the paper [C. Wang, D. Chen, L. Zhu, Homomorphisms between fuzzy information systems, Applied Mathematics Letters 22 (2009) 1045-1050], where…
We explore the relationship between symmetrisation and entanglement through measurements on few-particle systems in a multi-well potential. In particular, considering two or three trapped atoms, we measure and distinguish correlations…
We study distributional similarity measures for the purpose of improving probability estimation for unseen cooccurrences. Our contributions are three-fold: an empirical comparison of a broad range of measures; a classification of similarity…
Statistical limits are defined relaxing conditions on conventional convergence. The main idea of the statistical convergence of a sequence l is that the majority of elements from l converge and we do not care what is going on with other…
In this paper, a similarity-driven cluster merging method is proposed for unsuper-vised fuzzy clustering. The cluster merging method is used to resolve the problem of cluster validation. Starting with an overspecified number of clusters in…
We investigate the notion of quantumness based on the non-commutativity of the algebra of observables and introduce a measure of quantumness based on the mutual incompatibility of quantum states. We show that such a quantity can be…
Based on recent progress in research on copula based dependence measures, we review the original Renyi's axioms on symmetric measures and propose a new set of axioms that applies to nonsymmetric measures. We show that nonsymmetric measures…
The recently defined concept of a statistical depth function for fuzzy sets provides a theoretical framework for ordering fuzzy sets with respect to the distribution of a fuzzy random variable. One of the most used and studied statistical…
The fundamental principles of complementarity and uncertainty are shown to be related to the possibility of joint unsharp measurements of pairs of noncommuting quantum observables. A new joint measurement scheme for complementary…
The concept of weighted $\beta\gamma$ - summability of order $\theta$ in case of fuzzy functions is introduced and classified into ordinary and absolute sense. Several inclusion relations among the sets are investigated. Also we have found…
The complete characterization of spatial coherence is difficult because the mutual coherence function is a complex-valued function of four independent variables. This difficulty limits the ability of controlling and optimizing spatial…
In decision analysis and especially in multiple criteria decision analysis, several non additive integrals have been introduced in the last sixty years. Among them, we remember the Choquet integral, the Shilkret integral and the Sugeno…
The purpose of the paper is to provide a new way of seeing the p-value in terms of a fuzzy membership function. According to the ASAs statement, we aim at removing the arbitrary choice of the significance level and at demonstrating that the…