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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]

Fuzzy logic is one of the effective tools to handle uncertainty and vagueness in engineering and mathematics. One major part of fuzzy logic is ranking fuzzy numbers. In many fuzzy program systems, ranking fuzzy numbers has a remarkable role in decision making and data analysis. Despite the fact that a variety of methods exists for ranking fuzzy numbers, no one can rank fuzzy numbers perfectly in all cases and situations. In this paper, a new method for ranking fuzzy numbers based on the left and right using distance method and α-cut has been presented. To achieve this, a fuzzy distance measure between two generalized fuzzy numbers is proposed. The new measure is expanded with the help of the fuzzy ambiguity measure. The calculation of this method is derived from generalized trapezoidal fuzzy numbers and distance method concepts. Furthermore, a comparison of generalized fuzzy numbers between the proposed method and other resembled methods is provided. [ABSTRACT FROM AUTHOR]