Bipolar semicopulas

Salvatore Greco, Radko Mesiar, Fabio Rindone

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The concept of semicopula plays a fundamental role in the aggregation theory on interval [0, 1]. Semicopulas are applied, for example, in the definition of universal integrals. We present an extension of the notion of semicopula to the case of symmetric bipolar interval [−1, 1]. We call this extension bipolar semicopula. The last definition can be used to obtain a simplified definition of the bipolar universal integral. Moreover, bipolar semicopulas allow for an extension of theory of quasi-copulas to the interval [−1, 1].
Original languageEnglish
Pages (from-to)141-148
JournalFuzzy Sets and Systems
Early online date18 Oct 2014
Publication statusPublished - 1 Jun 2015


  • Semicopula
  • Bipolar semicopula
  • Bipolar universal integrals


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