## APPLICATIONS OF BIPOLAR FUZZY SETS IN INTERVAL GRAPHS

## *G. GHORAI1, M. PAL1*

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## Abstract

Currently, bipolar fuzzy graph is a growing research topic as it is the gener-alization of fuzzy graphs. In this paper, normal and convex bipolar fuzzy sets are dened and the notion of bipolar fuzzy interval is introduced as a generalization of fuzzy interval and described various methods of their construction. It is shown that intersection of two bipolar fuzzy intervals may not be a bipolar fuzzy interval. Finally, bipolar fuzzy interval graphs is introduced as the intersection graph of a nite family of bipolar fuzzy intervals. The relationship between the intersection graph of a f; g-level family of bipolar fuzzy intervals and f; g-cut of the intersection graph for that family have been established. It is proved that for every bipolar fuzzy interval graph G, the (; )-cut level graph G is an interval graph for each (; ) 2 (0; 1] [