Abstract
In bipolar aggregation the total score depends not just on previous score and the value of additional argument but on distribution of all other arguments as well. In addition the process of bipolar aggregation is not Markovian, i.e. aggregation is not associative. To model bipolar aggregation was introduced general \({R_{G}^\ast}\) aggregation based on uninorms. By discarding associativity we built a variation of the uninorm using generating functions that can be applied as an intuitively appealing bipolar aggregation operator. This modified uninorm operator will allow us to control the aggregation depending on distribution of the arguments above and below the neutral element: the closer proportion of arguments below the neutral value to 1 or to 0 the closer bipolar aggregation is to some t-norm or t-conorm with desirable properties.
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Yager, R.R., Rybalov, A. Bipolar aggregation using the Uninorms. Fuzzy Optim Decis Making 10, 59–70 (2011). https://doi.org/10.1007/s10700-010-9096-8
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DOI: https://doi.org/10.1007/s10700-010-9096-8