Wiener Energies of Fuzzy Graphs with Application in Total Quality Management

In this paper, fuzzy Wiener matrix, Wiener Laplacian matrix and corresponding energies of fuzzy graph are defined. A bound on largest eigenvalue of fuzzy Wiener matrix is presented. Several results related to eigenvalues of fuzzy Wiener and fuzzy Wiener Laplacian matrices are proved. Several upper and lower bounds for energies of these matrices are also established in terms of parameters like, number of vertices, edges, minimum and maximum vertex and edge membership, etc. Finally, the idea of fuzzy Wiener energy is applied in multi criteria decision making of best organizations based on implementation of total quality management(TQM) attributes.