751 research outputs found
Discrete Mathematics and Symmetry
Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group
The legacy of 50 years of fuzzy sets: A discussion
International audienceThis note provides a brief overview of the main ideas and notions underlying fifty years of research in fuzzy set and possibility theory, two important settings introduced by L.A. Zadeh for representing sets with unsharp boundaries and uncertainty induced by granules of information expressed with words. The discussion is organized on the basis of three potential understanding of the grades of membership to a fuzzy set, depending on what the fuzzy set intends to represent: a group of elements with borderline members, a plausibility distribution, or a preference profile. It also questions the motivations for some existing generalized fuzzy sets. This note clearly reflects the shared personal views of its authors
Algebraic Models for Qualified Aggregation in General Rough Sets, and Reasoning Bias Discovery
In the context of general rough sets, the act of combining two things to form
another is not straightforward. The situation is similar for other theories
that concern uncertainty and vagueness. Such acts can be endowed with
additional meaning that go beyond structural conjunction and disjunction as in
the theory of -norms and associated implications over -fuzzy sets. In the
present research, algebraic models of acts of combining things in generalized
rough sets over lattices with approximation operators (called rough convenience
lattices) is invented. The investigation is strongly motivated by the desire to
model skeptical or pessimistic, and optimistic or possibilistic aggregation in
human reasoning, and the choice of operations is constrained by the
perspective. Fundamental results on the weak negations and implications
afforded by the minimal models are proved. In addition, the model is suitable
for the study of discriminatory/toxic behavior in human reasoning, and of ML
algorithms learning such behavior.Comment: 15 Pages. Accepted. IJCRS-202
Weighted logics for artificial intelligence : an introductory discussion
International audienceBefore presenting the contents of the special issue, we propose a structured introductory overview of a landscape of the weighted logics (in a general sense) that can be found in the Artificial Intelligence literature, highlighting their fundamental differences and their application areas
Uncertainty Measures in Ordered Information System Based on Approximation Operators
This paper focuses on constructing uncertainty measures by the pure rough set approach in ordered information system. Four types of definitions of lower and upper approximations and corresponding uncertainty measurement concepts including accuracy, roughness, approximation quality, approximation accuracy, dependency degree, and importance degree are investigated. Theoretical analysis indicates that all the four types can be used to evaluate the uncertainty in ordered information system, especially that we find that the essence of the first type and the third type is the same. To interpret and help understand the approach, experiments about real-life data sets have been conducted to test the four types of uncertainty measures. From the results obtained, it can be shown that these uncertainty measures can surely measure the uncertainty in ordered information system
Comparison of solar photospheric bright points between SUNRISE observations and MHD simulations
Bright points (BPs) in the solar photosphere are radiative signatures of
magnetic elements described by slender flux tubes located in the darker
intergranular lanes. They contribute to the ultraviolet (UV) flux variations
over the solar cycle and hence may influence the Earth's climate. Here we
combine high-resolution UV and spectro-polarimetric observations of BPs by the
SUNRISE observatory with 3D radiation MHD simulations. Full spectral line
syntheses are performed with the MHD data and a careful degradation is applied
to take into account all relevant instrumental effects of the observations. It
is demonstrated that the MHD simulations reproduce the measured distributions
of intensity at multiple wavelengths, line-of-sight velocity, spectral line
width, and polarization degree rather well. Furthermore, the properties of
observed BPs are compared with synthetic ones. These match also relatively
well, except that the observations display a tail of large and strongly
polarized BPs not found in the simulations. The higher spatial resolution of
the simulations has a significant effect, leading to smaller and more numerous
BPs. The observation that most BPs are weakly polarized is explained mainly by
the spatial degradation, the stray light contamination, and the temperature
sensitivity of the Fe I line at 5250.2 \AA{}. The Stokes asymmetries of the
BPs increase with the distance to their center in both observations and
simulations, consistent with the classical picture of a production of the
asymmetry in the canopy. This is the first time that this has been found also
in the internetwork. Almost vertical kilo-Gauss fields are found for 98 % of
the synthetic BPs. At the continuum formation height, the simulated BPs are on
average 190 K hotter than the mean quiet Sun, their mean BP field strength is
1750 G, supporting the flux-tube paradigm to describe BPs.Comment: Accepted for publication in Astronomy & Astrophysics on May 30 201
Fuzzy Techniques for Decision Making 2018
Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches
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Hierarchical wireless framework for real-time collaborative generation and distribution of telemetry data
This project introduces a novel multidisciplinary approach combining Vehicular Ad Hoc Networks and Granular Computing, to the data processing and information generation problem in large urban traffic systems. It addresses the challenge of realtime information generation and dissemination in such systems by designing and investigating a hierarchical real-time information framework. The research work is complemented by designing and developing a simulator for such a system, which provides a simulation environment for the model developed. The proposed multidisciplinary hierarchical real-time information processing and dissemination system framework utilises results from two different areas of study, which are Vehicular Ad Hoc Networks (VANETS) and Granular Computing concepts. Furthermore, a new geographically constrained VANET topology for information generation is proposed, simulated and investigated
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