Table 1 Meanings of the symbols used in this article.
From: Bipolar fuzzy outerplanar graphs approach in image shrinking
Notations | Meanings |
|---|---|
\(G\) | Crisp graph |
\(\psi\) | an arbitrary graph |
\({\mathbb{V}}\) | vertices in the set of \(\psi\) |
\({\mathbb{E}}\) | edges in the set of \(\psi\) |
\({\mathbb{X}}\) | universal set |
\({\mathbb{A}}\) | a fuzzy set |
\({\mathring{\rm A}}\) | Bipolar fuzzy set |
\(\mathcal{B}\) | Bipolar fuzzy graph |
\({\mu }_{\mathcal{B}}^{\mathcal{P}}(\mathcalligra{x})\) | Positive membership degree |
\({\mu }_{\mathcal{B}}^{\mathcal{N}}(\mathcalligra{x})\) | Negative membership degree |
\({O}^{+}\left(\psi \right)\) | Positive order |
\({O}^{-}\left(\psi \right)\) | Negative order |
\({S}^{+}\left(\psi \right)\) | Positive size |
\({S}^{-}\left(\psi \right)\) | Negative size |
\(\mathfrak{a}\mathfrak{b}\) | Bipolar fuzzy edge |
\({I}_{\mathfrak{a}\mathfrak{b}}\) | Strength of the bipolar fuzzy edge (\(\mathfrak{a},\mathfrak{b})\) |
\(\tau\) | The function defining the degree of membership for each vertex |
\(\delta\) | The function defining the degree of membership for each edge |
\(\wedge\) | Minimum |
\(\vee\) | Maximum |
