The aim of this paper is to discuss the uncertainty in soft graphs and a new type of graphs, called Z-soft rough fuzzy graphs is introduced. The notions of Z-soft rough vertex graphs, Z-soft rough edge graphs and Z-soft rough fuzzy graphs are given, and their related properties are explored. The theory of graph approximation space is developed. To validate the applicability of Z-soft rough fuzzy graphs, we put forward an innovative approach to multicriteria group decision making problems.
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