A Modified Fuzzy Labeling Graph using Geometric Mean and Harmonic mean and its Application
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Abstract
The Modified Fuzzy Labeling Graph (MFLG) has gained popularity in the field of image processing due to its ability to accurately represent complex images. However, there are limitations to the MFLG approach that can be addressed through the use of geometric mean and harmonic measures. In this paper, the authors propose a new idea on a modified fuzzy labeling graph. A Modified fuzzy (M ) graph σ is a function from V to [0,1] and µ is a function from E to [0,1] where ∀ . The modified fuzzy labeling has an edge value, which is less than or equal to the maximum of two endpoints that is To obtain the result, the edge weight is assigned as Geometric labeling mean, where W(e) is equal to the square root of two end points. The edge weight is assigned as Harmonic mean labeling, which is . The study examines the modified fuzzy labeling for the different graphs including Alternate Pentagon snake graph, Alternate Double Pentagon snake graph, and Alternate Triple Pentagon snake graphs using Geometric mean; and the discussed , D and Quadrilateral snake graph using Harmonic mean. Graph that permits modified fuzzy (MFL) labeling is called a . Some of the properties and results thereof have been explained. The authors also discuss an application of critical path method in Operation Research for students Higher studies problem.
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