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In the present situation, the sustainable development goal on "Gender Equality" (SDG 5) is a challenging problem over the entire globe, also in India. In this paper, the fuzzy graph theory is used to analyse the overall performance of India for the SGD 5. To solve this problem, the new concept of pseudo-vertex-covering set of a fuzzy graph to make a well coverage of the entire fuzzy graph with the combined coverage of vertex-covering set and underlying edge-covering set of the fuzzy graph is defined. With this new covering concept of pseudo-vertex-covering set of fuzzy graphs, an analysis of the performance status of India for SDG 5 is made with the individual performance status of all the states/UTs of India. We show a nice covering of the whole country by some particular states/UTs which are actively helping to make the pseudo-vertex-covering of the transformed form of the graph of India as a fuzzy graph. At last, a comparison between the covering score and index score for SDG 5 is given. Here, covering score is a new term in fuzzy graph theory for coverage of a fuzzy graph by some vertices with underlying some edges. Also, an analysis is given which reflecting a clean idea of the methodology for the performance status of India and these help to find the self-governing states/UTs in India for a better performance. [ABSTRACT FROM AUTHOR]