A quasi-linear fuzzy measure of multi-attributes

Evaluations of multi-attributes using fuzzy measures and fuzzy integrals have been recently found to be useful in the classification processes of complex systems. However, one of the existing problems in using the aggregation operation of fuzzy integral is the identification of fuzzy measures or the "fuzzy densities" in terms of the gλ-measure. This paper presents a new methodology to assess the weights of each individual attribute and the combinatorial subsets of these attributes. The measures of multi-attributes are considered herein as the regionalized variables in space ℝⁿ, whose spatial values are characterized by the membership function of a fuzzy set. The present algorithm is based on the concept of the theory of regionalized variables which provides a mathematical framework for estimating the unknown values of the variables whose magnitudes are dependent on the spatial continuity expressed by a semi-variogram, and the optimal estimation of kriging method. This is a quasi-linear approach as the estimation is based on a linear-unbiased estimator, but the combined evidences do not hold additivity due to the basic assumption and formulation. © 1997 Elsevier Science B.V.