"A Quadratic Programming Approach In Estimating Similarity Relations"

IEEE Transactions on Fuzzy Systems, 1993, Vol. 1, No. 2, pp. 138-145.

Evangelos Triantaphyllou

This paper examines the problem of estimating how similar N objects are when they are compared with each other. The proposed approach uses as data comparative judgments of all possible pairs of the N objects. Pairwise comparisons have long been used with success in determining the relative importance of individual members in a group of objects. In the proposed approach the pairwise comparisons focus on the similarity relations instead of the relative importance of each object. A quadratic programming model is also proposed. This model processes the similarity based pairwise comparisons and determines the similarity relations among the N objects. The proposed quadratic programming model has linear constraints and therefore it can be solved easily by transferring it into a system of linear equations.

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