Abstract
Interval-valued fuzzy graphs (IVFGs) belonging to the fuzzy graphs (FGs) family, have good capabilities when faced with problems that cannot be expressed by FGs. The notion of an IVFG is a new mathematical attitude to model the ambiguity and uncertainty in decision-making issues. IVFGs are well-articulated, useful and practical tools to manage the uncertainty preoccupied in all real-life difficulties where not sure facts, figures and explorations are explained. In this paper, the concepts of neighbourly irregular intervalvalued fuzzy graphs, neighbourly totally irregular interval-valued fuzzy graphs, and highly irregular interval-valued fuzzy graphs are introduced and several examples are presented.
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