Generalized bipolar product and sum

Salvatore Greco, Radko Mesiar, Fabio Rindone

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Aggregation functions on [0, 1] with annihilator 0 can be seen as a generalized product on [0, 1]. We study the generalized product on the bipolar scale [−1, 1], stressing the axiomatic point of view ( compare also [9]). Based on newly introduced bipolar properties, such as the bipolar increasingness, bipolar unit element, bipolar idempotent element, several kinds of generalized bipolar product are introduced and studied. A special stress is put on bipolar semicopulas, bipolar quasi-copulas and bipolar copulas. Inspired by the truncated sum on [−1, 1] we introduce also the class of generalized bipolar sums, which differ from uninorms due to the non-associativity.
Original languageEnglish
Pages (from-to)21-31
JournalFuzzy Optimization and Decision Making
Issue number1
Early online date23 Apr 2015
Publication statusPublished - 1 Mar 2016


  • Aggregation function
  • bipolar copula
  • bipolar scale
  • bipolar semicopula
  • symmetric minimum


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