Cycles and cocycles of fuzzy graphs

Fuzzy pogroupoids

“…Using this approach several theorems about conditions on fuzzy pogroupoids being equivalent to conditions on these fuzzy posets and their underlying crisp posets are obtained. These conditions also lead to some polynomial invariants of finite pogroupoids, finite posets and accordingly finite Hasse diagrams in terms of their fuzzy substructures which thus provide additional perspectives on objects studied in a number of papers which have appeared in Information Sciences, e.g., [4,5,11].…”

Types of arcs in a fuzzy graph

“…; n and the degree of membership of a weakest arc is defined as its strength. If u 0 ¼ u n and n P 3, then P is called a cycle and a cycle P is called a fuzzy cycle (f-cycle) if it contains more than one weakest arc [10]. The strength of connectedness between two nodes x and y is defined as the maximum of the strengths of all paths between x and y and is denoted by CONN G ðx; yÞ.…”

Connections between interval valued fuzzy graphs and fuzzy groups with (S,T)-norms

“…Many studies on fuzzy graphs are performed by Bhutani, Rosenfeld, Blue, Bush, Puckett, Mordeson, Nair, Peng, Jun, etc. (see [4][5][6], [12] and [14][15][16][17]). …”