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In this study, the authors envisage the neutrosophic number from various distinct rational perspectives and viewpoints to give it a look of a conundrum. They focused and analysed neutrosophic fuzzy numbers when indeterminacy and falsity functions are dependent on each other, which serves an indispensable role for the uncertainty concept. Additionally, the idea of cylindrical neutrosophic single-valued number is focused here, when the indeterminacy and falsity functions are dependent to each other using an influx of different logical and innovative graphical representation. They also developed the score and accuracy function for this particular cylindrical neutrosophic single-valued number and analysed some real-life problems like networking critical path model problem and minimal spanning tree problem of operation research field when the numbers are in cylindrical neutrosophic ambiance. They also introduced a multi-criterion group decision-making problem in this cylindrical neutrosophic domain. This noble thought will help us to solve a plethora of daily life problems in the neutrosophic arena.