24,465 research outputs found
On Fuzzy Concepts
In this paper we try to combine two approaches. One is the theory of knowledge graphs in which concepts are represented by graphs. The other is the axiomatic theory of fuzzy sets (AFS).
The discussion will focus on the idea of fuzzy concept. It will be argued that the fuzziness of a concept in natural language is mainly due to the difference in interpretation that people give to a certain word. As different interpretations lead to different knowledge graphs, the notion of fuzzy concept should be describable in terms of sets of graphs. This leads to a natural introduction of membership values for elements of graphs. Using these membership values we apply AFS theory as well as an alternative approach to calculate fuzzy decision trees, that can be used to determine the most relevant elements of a concept
FSL-BM: Fuzzy Supervised Learning with Binary Meta-Feature for Classification
This paper introduces a novel real-time Fuzzy Supervised Learning with Binary
Meta-Feature (FSL-BM) for big data classification task. The study of real-time
algorithms addresses several major concerns, which are namely: accuracy, memory
consumption, and ability to stretch assumptions and time complexity. Attaining
a fast computational model providing fuzzy logic and supervised learning is one
of the main challenges in the machine learning. In this research paper, we
present FSL-BM algorithm as an efficient solution of supervised learning with
fuzzy logic processing using binary meta-feature representation using Hamming
Distance and Hash function to relax assumptions. While many studies focused on
reducing time complexity and increasing accuracy during the last decade, the
novel contribution of this proposed solution comes through integration of
Hamming Distance, Hash function, binary meta-features, binary classification to
provide real time supervised method. Hash Tables (HT) component gives a fast
access to existing indices; and therefore, the generation of new indices in a
constant time complexity, which supersedes existing fuzzy supervised algorithms
with better or comparable results. To summarize, the main contribution of this
technique for real-time Fuzzy Supervised Learning is to represent hypothesis
through binary input as meta-feature space and creating the Fuzzy Supervised
Hash table to train and validate model.Comment: FICC201
Fuzziness and Funds Allocation in Portfolio Optimization
Each individual investor is different, with different financial goals,
different levels of risk tolerance and different personal preferences. From the
point of view of investment management, these characteristics are often defined
as objectives and constraints. Objectives can be the type of return being
sought, while constraints include factors such as time horizon, how liquid the
investor is, any personal tax situation and how risk is handled. It's really a
balancing act between risk and return with each investor having unique
requirements, as well as a unique financial outlook - essentially a constrained
utility maximization objective. To analyze how well a customer fits into a
particular investor class, one investment house has even designed a structured
questionnaire with about two-dozen questions that each has to be answered with
values from 1 to 5. The questions range from personal background (age, marital
state, number of children, job type, education type, etc.) to what the customer
expects from an investment (capital protection, tax shelter, liquid assets,
etc.). A fuzzy logic system has been designed for the evaluation of the answers
to the above questions. We have investigated the notion of fuzziness with
respect to funds allocation.Comment: 21 page
Quantum Gravity - Testing Time for Theories
The extreme smallness of both the Planck length, on the one side, and the
ratio of the gravitational to the electrical forces between, say, two
electrons, on the other side has led to a widespread belief that the realm of
quantum gravity is beyond terrestrial experiments. A series of classical and
quantum arguments are put forward to dispel this view. It is concluded that
whereas the smallness of the Planck length and the ratio of gravitational to
electrical forces, does play its own essential role in nature, it does not make
quantum gravity a science where humans cannot venture to probe her secrets. In
particular attention is drawn to the latest neutron and atomic interferometry
experiments, and to gravity wave interferometers. The latter, as Giovanni
Amelino-Camelia argues [Nature 398, 216 (1999)], can be treated as probes of
space-time fuzziness down to Planck length for certain quantum-gravity models
Micro-Macro Analysis of Complex Networks
Complex systems have attracted considerable interest because of their wide range of applications, and are often studied via a \u201cclassic\u201d approach: study a specific system, find a complex network behind it, and analyze the corresponding properties. This simple methodology has produced a great deal of interesting results, but relies on an often implicit underlying assumption: the level of detail on which the system is observed. However, in many situations, physical or abstract, the level of detail can be one out of many, and might also depend on intrinsic limitations in viewing the data with a different level of abstraction or precision. So, a fundamental question arises: do properties of a network depend on its level of observability, or are they invariant? If there is a dependence, then an apparently correct network modeling could in fact just be a bad approximation of the true behavior of a complex system. In order to answer this question, we propose a novel micro-macro analysis of complex systems that quantitatively describes how the structure of complex networks varies as a function of the detail level. To this extent, we have developed a new telescopic algorithm that abstracts from the local properties of a system and reconstructs the original structure according to a fuzziness level. This way we can study what happens when passing from a fine level of detail (\u201cmicro\u201d) to a different scale level (\u201cmacro\u201d), and analyze the corresponding behavior in this transition, obtaining a deeper spectrum analysis. The obtained results show that many important properties are not universally invariant with respect to the level of detail, but instead strongly depend on the specific level on which a network is observed. Therefore, caution should be taken in every situation where a complex network is considered, if its context allows for different levels of observability
Do quantum states evolve? Apropos of Marchildon's remarks
Marchildon's (favorable) assessment (quant-ph/0303170, to appear in Found.
Phys.) of the Pondicherry interpretation of quantum mechanics raises several
issues, which are addressed. Proceeding from the assumption that quantum
mechanics is fundamentally a probability algorithm, this interpretation
determines the nature of a world that is irreducibly described by this
probability algorithm. Such a world features an objective fuzziness, which
implies that its spatiotemporal differentiation does not "go all the way down".
This result is inconsistent with the existence of an evolving instantaneous
state, quantum or otherwise.Comment: To appear in Foundations of Physics; 22 pages, LaTe
This elusive objective existence
Zurek's existential interpretation of quantum mechanics suffers from three
classical prejudices, including the belief that space and time are
intrinsically and infinitely differentiated. They compel him to relativize the
concept of objective existence in two ways. The elimination of these prejudices
makes it possible to recognize the quantum formalism's ontological implications
- the relative and contingent reality of spatiotemporal distinctions and the
extrinsic and finite spatiotemporal differentiation of the physical world -
which in turn makes it possible to arrive at an unqualified objective
existence. Contrary to a widespread misconception, viewing the quantum
formalism as being fundamentally a probability algorithm does not imply that
quantum mechanics is concerned with states of knowledge rather than states of
Nature. On the contrary, it makes possible a complete and strongly objective
description of the physical world that requires no reference to observers. What
objectively exists, in a sense that requires no qualification, is the
trajectories of macroscopic objects, whose fuzziness is empirically irrelevant,
the properties and values of whose possession these trajectories provide
indelible records, and the fuzzy and temporally undifferentiated states of
affairs that obtain between measurements and are described by counterfactual
probability assignments.Comment: To appear in IJQI; 21 pages, LaTe
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