In decision making, in order to avoid misleading solutions, the study of consistency when the decision makers express their opinions by means of preference relations becomes a very important aspect. In decision making problems based on fuzzy preference relations the study of consistency is associated with the study of the transitivity property. In this paper, a new characterization of the consistency property defined by the additive transitivity property of the fuzzy preference relations is presented. Using this new characterization a method for constructing consistent fuzzy preference relations from a set of n-1 preference data is proposed. Applying this method it is possible to assure better consistency of the fuzzy preference relations provided by the decision makers, and in such a way, to avoid the inconsistent solutions in the decision making processes. Additionally, a similar study of consistency is developed for the case of multiplicative preference relations.

No abstract

The dichromatic color appearance of a chromatic stimulus T can be described if a stimulus S is found that verifies that a normal observer experiences the same sensation viewing S as a dichromat viewing T. If dichromatic and normal versions of the same color vision model are available, S can be computed by applying the inverse of the normal model to the descriptors of T obtained with the dichromatic model. We give analytical form to this algorithm, which we call the corresponding-pair procedure. The analytical form highlights the requisites that a color vision model must verify for this procedure to be used. To show the capabilities of the method, we apply the algorithm to different color vision models that verify such requisites. This algorithm avoids the need to introduce empirical information alien to the color model used, as was the case with previous methods. The relative simplicity of the procedure and its generality makes the prediction of dichromatic color appearance an additional test of the validity of color vision models.

iii) Results. The results show that the green, brown and blue filters, do not cause significant changes in contrast sensitivity when compared with a grey filter of equal luminance, although chromatic discrimination is disturbed. Yellow and orange filters improve achromatic contrast at certain spatial frequencies, but impair chromatic discrimination. iv) Conclusions. Compared to grey filters of the same luminance, yellow filters may be useful when enhancement of low achromatic contrasts is desirable, although overall brightness decrements may occur. Nevertheless, these lenses cause tritanlike defects with discrimination losses increasing with the cut-off wavelength.