Abstract
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.
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Notes
- 1.
In set theory the natural number 0 is defined to be the empty set, that is, \(0{\mathop {=}\limits ^{\mathrm {def}}}\emptyset \). If x is a natural number, then \(x^{+}\) is its successor and is defined as follows:
$$\begin{aligned} x^{+}{\mathop {=}\limits ^{\mathrm {def}}}x\cup \{x\}. \end{aligned}$$Thus, numbers are identified with sets and so
$$\begin{aligned} 1&= 0^{+} = \{0\}=\{\emptyset \}\\ 2&= 1^{+} = \{0,1\}\\ 3&= 2^{+} = \{0,1,2,\}\\ \vdots&\qquad \vdots \\ m&= (m-1)^{+} = \{0,1,2,\ldots ,m-1\} \end{aligned}$$The reader should consult any basic introduction to set theory for more details (e.g., see [7]).
- 2.
A partially ordered set P is a frame if and only if
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every subset has a least upper bound;
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every finite subset has a greatest lower bound; and
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the operator \(\wedge \) distributes over \(\vee \):
$$\begin{aligned} x\wedge \bigvee Y=\bigvee \left\{ x\wedge y\mathrel {\bigm |}y\in Y \right\} . \end{aligned}$$
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1.
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I would like to thank the editors of this volume for inviting me to present my work and I would like to thank the anonymous reviewer for her comments and suggestions that helped me to substantially improve the presentation of my work.
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Syropoulos, A. (2020). Fuzzy Bigraphs. In: Nguyen, H., Kreinovich, V. (eds) Algebraic Techniques and Their Use in Describing and Processing Uncertainty. Studies in Computational Intelligence, vol 878. Springer, Cham. https://doi.org/10.1007/978-3-030-38565-1_13
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