We consider problems of rating alternatives based on their pairwisecomparison under various assumptions, including constraints on the final scoresof alternatives. The problems are formulated in the framework of tropicalmathematics to approximate pairwise comparison matrices by reciprocal matricesof unit rank, and written in a common form for both multiplicative and additivecomparison scales. To solve the unconstrained and constrained approximationproblems, we apply recent results in tropical optimization, which provide newcomplete direct solutions given in a compact vector form. These solutionsextend known results and involve less computational effort. As an illustration,numerical examples of rating alternatives are presented.
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