Fuzzy Mason graphs (Q1311789)

The extension of a well-known class of Mason graphs (linear flow graphs) deals with their generalization through fuzzy variables. The \(k\)th node of the graph is described in the form, \(\widetilde\Sigma_ j X_ j\otimes T_{jk}= X_ k\), \(k=12,\dots,N\). Here \(\widetilde\Sigma\) and \(\otimes\) are viewed as extended operations of addition and multiplication applied to fuzzy numbers \(X_ j\) and \(T_{jk}\) describing the corresponding nodes \((X_ j)\) and branches \((T_{jk})\) of the graph. The analysis carried out in the paper is confined to these fuzzy numbers described by triangular membership functions (that means that each object is completely described by a single modal value and the two boundary points determining the support of the corresponding fuzzy number). Some equivalent structures of the graphs are derived; the relevance of the resulting operations is also quantified with respect to the fuzziness of the nodes and branches involved in the computations.