822 research outputs found
Fuzzy graphs: Algebraic structure and syntactic recognition
© Springer Science+Business Media Dordrecht 2013. Directed fuzzy hypergraphs are introduced as a generalization of both crisp directed hypergraphs and directed fuzzy graphs. It is proved that the set of all directed fuzzy hypergraphs can be structured into a magmoid with operations graph composition and disjoint union. In this framework a notion of syntactic recognition inside magmoids is defined. The corresponding class is proved to be closed under boolean operations and inverse mor-phisms of magmoids. Moreover, the language of all strongly connected fuzzy graphs and the language that consists of all fuzzy graphs that have at least one directed path from the begin node to the end node through edges with membership grade 1 are recognizable. Additionally, a useful characterization of recognizability through left derivatives is also achieved
Fuzzy Hypergraphs
Graph theory has found many application area in science, engineering, and mathematics. In order to expand the application base, the notion of a graph was generalized to that of a hypergraph, that is, a set X of vertices together with a collection of subsets of X. In this chapter, we fuzzify the notation of a hypergraph and state some possible applications. In this article, we apply the concept of bipolar fuzzy sets to hypergraphs and investigate some basic theorems and some properties of bipolar fuzzy hypergraphs. Some basic concepts of bipolar fuzzy set are defined. It is shown that any bipolar fuzzy graph can be expressed as the bipolar fuzzy intersection graphs of some bipolar fuzzy sets
Properties of Bipolar Fuzzy Hypergraphs
In this article, we apply the concept of bipolar fuzzy sets to hypergraphs
and investigate some properties of bipolar fuzzy hypergraphs. We introduce the
notion of tempered bipolar fuzzy hypergraphs and present some of their
properties. We also present application examples of bipolar fuzzy hypergraphs
On the relation between the base of an EI algebra and word graphs
This paper is an attempt to investigate the possibilities to link algebraic fuzzy set theory with the theory of word graphs. In both theories concepts are studied and concepts can be set in correspondence. This enables to use algebraic results in the context of word graph theory
Higher-dimensional models of networks
Networks are often studied as graphs, where the vertices stand for entities
in the world and the edges stand for connections between them. While relatively
easy to study, graphs are often inadequate for modeling real-world situations,
especially those that include contexts of more than two entities. For these
situations, one typically uses hypergraphs or simplicial complexes.
In this paper, we provide a precise framework in which graphs, hypergraphs,
simplicial complexes, and many other categories, all of which model higher
graphs, can be studied side-by-side. We show how to transform a hypergraph into
its nearest simplicial analogue, for example. Our framework includes many new
categories as well, such as one that models broadcasting networks. We give
several examples and applications of these ideas
Fuzzy Bigraphs: An Exercise in Fuzzy Communicating Agents
Bigraphs and their algebra is a model of concurrency. Fuzzy bigraphs are a
generalization of birgraphs intended to be a model of concurrency that
incorporates vagueness. More specifically, this model assumes that agents are
similar, communication is not perfect, and, in general, everything is or
happens to some degree.Comment: 11 pages, 3 figure
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Matrix formulation of fuzzy rule-based systems
In this paper, a matrix formulation of fuzzy rule based systems is introduced. A gradient descent training algorithm for the determination of the unknown parameters can also be expressed in a matrix form for various adaptive fuzzy networks. When converting a rule-based system to the proposed matrix formulation, only three sets of linear/nonlinear equations are required instead of set of rules and an inference mechanism. There are a number of advantages which the matrix formulation has compared with the linguistic approach. Firstly, it obviates the differences among the various architectures; and secondly, it is much easier to organize data in the implementation or simulation of the fuzzy system. The formulation will be illustrated by a number of examples
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