A Dual Hesitant Fuzzy Multigranulation Rough Set over Two-Universe Model for Medical Diagnoses

In medical science, disease diagnosis is one of the difficult tasks for medical experts who are confronted with challenges in dealing with a lot of uncertain medical information. And different medical experts might express their own thought about the medical knowledge base which slightly differs from other medical experts. Thus, to solve the problems of uncertain data analysis and group decision making in disease diagnoses, we propose a new rough set model called dual hesitant fuzzy multigranulation rough set over two universes by combining the dual hesitant fuzzy set and multigranulation rough set theories. In the framework of our study, both the definition and some basic properties of the proposed model are presented. Finally, we give a general approach which is applied to a decision making problem in disease diagnoses, and the effectiveness of the approach is demonstrated by a numerical example

A comprehensive study of implicator-conjunctor based and noise-tolerant fuzzy rough sets: definitions, properties and robustness analysis

© 2014 Elsevier B.V. Both rough and fuzzy set theories offer interesting tools for dealing with imperfect data: while the former allows us to work with uncertain and incomplete information, the latter provides a formal setting for vague concepts. The two theories are highly compatible, and since the late 1980s many researchers have studied their hybridization. In this paper, we critically evaluate most relevant fuzzy rough set models proposed in the literature. To this end, we establish a formally correct and unified mathematical framework for them. Both implicator-conjunctor-based definitions and noise-tolerant models are studied. We evaluate these models on two different fronts: firstly, we discuss which properties of the original rough set model can be maintained and secondly, we examine how robust they are against both class and attribute noise. By highlighting the benefits and drawbacks of the different fuzzy rough set models, this study appears a necessary first step to propose and develop new models in future research.Lynn D’eer has been supported by the Ghent University Special Research Fund, Chris Cornelis was partially supported by the Spanish Ministry of Science and Technology under the project TIN2011-28488 and the Andalusian Research Plans P11-TIC-7765 and P10-TIC-6858, and by project PYR-2014-8 of the Genil Program of CEI BioTic GRANADA and Lluis Godo has been partially supported by the Spanish MINECO project EdeTRI TIN2012-39348-C02-01Peer Reviewe

Baby Universes in String Theory

We argue that the holographic description of four-dimensional BPS black holes naturally includes multi-center solutions. This suggests that the holographic dual to the gauge theory is not a single AdS_2 times S^2 but a coherent ensemble of them. We verify this in a particular class of examples, where the two-dimensional Yang-Mills theory gives a holographic description of the black holes obtained by branes wrapping Calabi-Yau cycles. Using the free fermionic formulation, we show that O(e^{-N}) non-perturbative effects entangle the two Fermi surfaces. In an Euclidean description, the wave-function of the multi-center black holes gets mapped to the Hartle-Hawking wave-function of baby universes. This provides a concrete realization, within string theory, of effects that can be interpreted as the creation of baby universes. We find that, at least in the case we study, the baby universes do not lead to a loss of quantum coherence, in accord with general arguments.Comment: 39 pages, 7 figure

Scaling Functions for Baby Universes in Two-Dimensional Quantum Gravity

We apply the recently proposed transfer matrix formalism to 2-dimensional quantum gravity coupled to $(2, 2k-1)$ minimal models. We find that the propagation of a parent universe in geodesic (Euclidean) time is accompanied by continual emission of baby universes and derive a distribution function describing their sizes. The $k\to \infty~ (c\to -\infty)$ limit is generally thought to correspond to classical geometry, and we indeed find a classical peak in the universe distribution function. However, we also observe dramatic quantum effects associated with baby universes at finite length scales.Comment: 20 pages, 6 figures (not included, available upon request), PUPT-142

A Novel Rough Set Model in Generalized Single Valued Neutrosophic Approximation Spaces and Its Application

In this paper, we extend the rough set model on two different universes in intuitionistic fuzzy approximation spaces to a single-valued neutrosophic environment

Locally Causal Dynamical Triangulations in Two Dimensions

We analyze the universal properties of a new two-dimensional quantum gravity model defined in terms of Locally Causal Dynamical Triangulations (LCDT). Measuring the Hausdorff and spectral dimensions of the dynamical geometrical ensemble, we find numerical evidence that the continuum limit of the model lies in a new universality class of two-dimensional quantum gravity theories, inequivalent to both Euclidean and Causal Dynamical Triangulations