Weighted aggregation systems and an expectation level-based weighting and scoring procedure

This paper presents a novel approach to the weighted aggregation and to determination of weights in an aggregation procedure. In our study, we introduce the concept of a weighted aggregation system that consists of two components: (1) a weighting transformation and (2) an aggregation operator, both induced by a common generator function. We provide the necessary and sufficient condition for the form of a generator function-based weighted aggregation system. We show that the weighted quasi-arithmetic means on the non-negative extended real line are none other than the aggregation functions induced by weighted aggregation systems, i.e., these means are compositions of an n-ary aggregation operator and n weighting transformations (n∈N, n≥1). Next, using weighted quasi-arithmetic means on the unit interval, we introduce a new, expectation level-based weight determination method and a scoring procedure. In this method, the decision-maker’s expectation levels for the input variables are directly transformed into weights by making use of the generator function of a weighted quasi-arithmetic mean. We utilize this mean as a scoring function to evaluate the decision alternatives. Lastly, by the means of illustrative numerical examples, we present a novel decision model, in which the expectation levels can be even intervals, i.e., the weights are also intervals. Finally, we get an interval-valued score for each alternative.