Fuzzy Graph Associated to a Leontief’s I-O Matrix

Antonio Morillas, Luis Robles, Bárbara Díaz.

In inter-industry studies, the coefficients of the production function matrices have been analyzed with different techniques in order to recognize in some way those coefficients that can be considered to be important for an economy. Many criticisms have been posed to the procedures, the most remarkable one being their lack of connectivity with the values of the absolute flows behind the coefficients. In our approach, we define the importance of a coefficient as a fuzzy concept, and the grade of importance takes into account those absolute flows. This grade can be considered as a membership function, which is used to define a fuzzy graph associated to an I-O matrix. We apply this new procedure to the Spanish 2000 I-O matrix and compare our results to those reached by classical methods.

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