EFFICIENT METHODS FOR COMPUTING LINGUISTIC CONSISTENCY

In decision making situations involving various sources of information it is necessary to be able to assess and measure the consistency of the information. The problem is further compounded when, due to the nature of the sources, the data is expressed by fuzzy statements. This paper reviews two existing methods for computing a consistency measure between fuzzy statements and proposes new methods that are computationally efficient and sensitive to changes in the data. The method proposed by Cayrol, Farreny and Prade uses the concepts of necessity and possibility to obtain a consistency measure graded on the interval [0, 1]. The method proposed by Yager is based on the concept of fuzzy variables and uses the extension principle to obtain a consistency measure in the format of a fuzzy subset. The new proposed methods for computing a consistency measure are based on the concept of the Bhattacharyya coefficient. The first method uses the Gaussian quadrature approximation technique to get a more practical and easy-to-compute consistency measure under some assumptions of the shape of the membership functions. The second method, not restricted by such assumptions, provides an approximate result based on nonuniform sampling of the membership distributions. Both proposed methods use approximation techniques that drastically decrease the computational complexity. The accuracy of the results is still more than adequate for making decisions about the consistency of the information.