Multiset Estimates and Combinatorial Synthesis
  The paper addresses an approach to ordinal assessment of alternatives based on assignment of elements into an ordinal scale. Basic versions of the assessment problems are formulated while taking into account the number of levels at a basic ordinal scale [1,2,...,l] and the number of assigned elements (e.g., 1,2,3). The obtained estimates are multisets (or bags) (cardinality of the multiset equals a constant). Scale-posets for the examined assessment problems are presented. 'Interval multiset estimates' are suggested. Further, operations over multiset estimates are examined: (a) integration of multiset estimates, (b) proximity for multiset estimates, (c) comparison of multiset estimates, (d) aggregation of multiset estimates, and (e) alignment of multiset estimates. Combinatorial synthesis based on morphological approach is examined including the modified version of the approach with multiset estimates of design alternatives. Knapsack-like problems with multiset estimates are briefly described as well. The assessment approach, multiset-estimates, and corresponding combinatorial problems are illustrated by numerical examples. 
Mark Sh. Levin
cs.SY cs.AI math.OC