6,403 research outputs found
A study on irregularity in vague graphs with application in social relations
Considering all physical, biological and social systems, fuzzy graph models serves the elemental processes of all natural and artificial structures. As the indeterminate information is an essential real-life problems, which are mostly uncertain, modelling those problems based on fuzzy graph is highly demanding for an expert. Vague graph can manage the uncertainty relevant to the inconsistent and indeterminate information of all real-world problems, in which fuzzy graphs possibly will not succeed into bringing about satisfactory results. Also, vague graphs are so useful tool to examine many issues such as networking, social systems, geometry, biology, clustering, and traffic plan. Hence, in this paper, we introduce strongly edge irregular vague graphs and strongly edge totally irregular vague graphs. A comparative study between strongly edge irregular vague graphs and strongly edge totally irregular vague graphs is done. Finally, we represent an applicationof irregular vague influence graph to show the importance of irregularity in vague graphs.Publisher's Versio
Computing Crisp Bisimulations for Fuzzy Structures
Fuzzy structures such as fuzzy automata, fuzzy transition systems, weighted
social networks and fuzzy interpretations in fuzzy description logics have been
widely studied. For such structures, bisimulation is a natural notion for
characterizing indiscernibility between states or individuals. There are two
kinds of bisimulations for fuzzy structures: crisp bisimulations and fuzzy
bisimulations. While the latter fits to the fuzzy paradigm, the former has also
attracted attention due to the application of crisp equivalence relations, for
example, in minimizing structures. Bisimulations can be formulated for fuzzy
labeled graphs and then adapted to other fuzzy structures. In this article, we
present an efficient algorithm for computing the partition corresponding to the
largest crisp bisimulation of a given finite fuzzy labeled graph. Its
complexity is of order , where , and are
the number of vertices, the number of nonzero edges and the number of different
fuzzy degrees of edges of the input graph, respectively. We also study a
similar problem for the setting with counting successors, which corresponds to
the case with qualified number restrictions in description logics and graded
modalities in modal logics. In particular, we provide an efficient algorithm
with the complexity for the considered problem in
that setting
A Fuzzy Petri Nets Model for Computing With Words
Motivated by Zadeh's paradigm of computing with words rather than numbers,
several formal models of computing with words have recently been proposed.
These models are based on automata and thus are not well-suited for concurrent
computing. In this paper, we incorporate the well-known model of concurrent
computing, Petri nets, together with fuzzy set theory and thereby establish a
concurrency model of computing with words--fuzzy Petri nets for computing with
words (FPNCWs). The new feature of such fuzzy Petri nets is that the labels of
transitions are some special words modeled by fuzzy sets. By employing the
methodology of fuzzy reasoning, we give a faithful extension of an FPNCW which
makes it possible for computing with more words. The language expressiveness of
the two formal models of computing with words, fuzzy automata for computing
with words and FPNCWs, is compared as well. A few small examples are provided
to illustrate the theoretical development.Comment: double columns 14 pages, 8 figure
Cactus Graphs with Cycle Blocks and Square Product Labeling
A graph G is known to be square product labeling, if there exists a bijection f from V (G) to {1, 2, 3,..., p} which induces f* from E(G) to N, defined by f*(uv) = f(u)^2 f(v)^2 is injective for each uv in E(G), for which the labeling pattern of edges are distinct. G is considered to be square product graph, if it admits a square product labeling. In this article, the results are obtained on square product labeling for some cactus graphs with cycle blocks
A STUDY ON DISTANCE OF FUZZY GRAPH THEORY
Graph theory is one of the parts of current Mathshaving encountered a most noteworthy advancement lately. The theory of fuzzy graphs was created by in the year 1975. During a similarand have additionally presented different connectedness ideas in fuzzy graphs. Fuzzy set theory gives us not just an important and ground-breaking portrayal of measurement of vulnerabilities, yet an increasingly reasonable portrayal of dubious ideas communicated in natural languages. A few properties of unusual hubs, fringe hubs and focal hubs are gotten. The scientific implanting of ordinary set theory into fuzzy has become a natural marvel. Therefore the possibility of fluffiness is an improving one. This Research study analyzes the distancetotal conceptthat is a measurement, in a fuzzy graph is presented
Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs
Laplacian mixture models identify overlapping regions of influence in
unlabeled graph and network data in a scalable and computationally efficient
way, yielding useful low-dimensional representations. By combining Laplacian
eigenspace and finite mixture modeling methods, they provide probabilistic or
fuzzy dimensionality reductions or domain decompositions for a variety of input
data types, including mixture distributions, feature vectors, and graphs or
networks. Provable optimal recovery using the algorithm is analytically shown
for a nontrivial class of cluster graphs. Heuristic approximations for scalable
high-performance implementations are described and empirically tested.
Connections to PageRank and community detection in network analysis demonstrate
the wide applicability of this approach. The origins of fuzzy spectral methods,
beginning with generalized heat or diffusion equations in physics, are reviewed
and summarized. Comparisons to other dimensionality reduction and clustering
methods for challenging unsupervised machine learning problems are also
discussed.Comment: 13 figures, 35 reference
MOD Graphs
Zadeh introduced the degree of membership/truth (t) in 1965 and defined the fuzzy set. Atanassov introduced the degree of nonmembership/ falsehood (f) in 1986 and defined the intuitionistic fuzzy set. Smarandache introduced the degree of indeterminacy/ neutrality (i) as independent component in 1995 (published in 1998) and defined the neutrosophic set on three components (t, i, f) = (truth, indeterminacy, falsehood): http://fs.gallup.unm.edu/FlorentinSmarandache.htm Etymology. The words “neutrosophy” and “neutrosophic” were coined/ invented by F. Smarandache in his 1998 book. Neutrosophy: A branch of philosophy, introduced by F. Smarandache in 1980, which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophy considers a proposition, theory, event, concept, or entity, A in relation to its opposite, Anti-A and that which is not A, Non-A , and that which is neither A nor Anti-A , denoted by Neut-A . Neutrosophy is the basis of neutrosophic logic, neutrosophic probability, neutrosophic set, and neutrosophic statistics. {From: The Free Online Dictionary of Computing, edited by Denis Howe from England. Neutrosophy is an extension of the Dialectics.} Neutrosophic Logic is a general framework for unification of many existing logics, such as fuzzy logic (especially intuitionistic fuzzy logic), paraconsistent logic, intuitionistic logic, etc
A graph theoretic approach to scene matching
The ability to match two scenes is a fundamental requirement in a variety of computer vision tasks. A graph theoretic approach to inexact scene matching is presented which is useful in dealing with problems due to imperfect image segmentation. A scene is described by a set of graphs, with nodes representing objects and arcs representing relationships between objects. Each node has a set of values representing the relations between pairs of objects, such as angle, adjacency, or distance. With this method of scene representation, the task in scene matching is to match two sets of graphs. Because of segmentation errors, variations in camera angle, illumination, and other conditions, an exact match between the sets of observed and stored graphs is usually not possible. In the developed approach, the problem is represented as an association graph, in which each node represents a possible mapping of an observed region to a stored object, and each arc represents the compatibility of two mappings. Nodes and arcs have weights indicating the merit or a region-object mapping and the degree of compatibility between two mappings. A match between the two graphs corresponds to a clique, or fully connected subgraph, in the association graph. The task is to find the clique that represents the best match. Fuzzy relaxation is used to update the node weights using the contextual information contained in the arcs and neighboring nodes. This simplifies the evaluation of cliques. A method of handling oversegmentation and undersegmentation problems is also presented. The approach is tested with a set of realistic images which exhibit many types of sementation errors
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