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Traffic congestion is a major problem in the last few decades. Though the Government is taking various measures like installing more traffic signals, constructing fly-overs, one-ways, etc., the problem could not be addressed effectively on the heavily congested areas. The increasing number of vehicles, the dynamic population of traffic, the narrowness of roads and the absence of alternative roads or other routes are the major obstacles to reduce traffic congestion. Researchers of various streams have been working on predicting traffic volume to solve this problem. In this paper, a new method named Intuitionistic Fuzzy Grey-Markov Model(IFGMM) is introduced, which is an extension of Grey-Markov to Intuitionistic fuzzy set. The model is distinctive when compared with other models as it has a high level of accuracy performance. The forecasting result of this model is almost in proximity with the actual result of the traffic volume. In addition, the relative errors shown in this method are lesser than that of other models, due to its prediction accuracy is higher. Since the data collected in this method are taken from a heavily congested road from a metropolitan city, the proposed approach will be suitable for any congested area of the world. [ABSTRACT FROM AUTHOR]

Planar graph is a special type in crisp as well as in fuzzy graphs. In fuzzy planar graphs, the planarity value is the amount of planarity of the crossed fuzzy edges, so that the intersection of fuzzy edges are possible in fuzzy graphs as compared to the planar graphs in crisp. Generally, the fuzzy planar graphs are depicted in the plane surface. In this paper, the embedding of fuzzy graphs are discussed in the surfaces like sphere and m-torus. Moreover, definition of fuzzy planar triangulation, straight-line, and piecewise embedding are also stated for planar embedding. Some of the effective definitions and theorems are illustrated with examples. Theorems like Euler's formula for plane and sphere surfaces are proved and formulated for fuzzy planar graphs. [ABSTRACT FROM AUTHOR]