Bipolar fuzzy integrals

Salvatore Greco, Fabio Rindone

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In decision analysis, and especially in multiple-criteria decision analysis, several non-additive integrals have been introduced in the last 60 years. These include the Choquet integral, the Shilkret integral and the Sugeno integral, among others. Recently, a bipolar Choquet integral was proposed for cases in which the underlying scale is bipolar. In this paper we propose a bipolar Shilkret integral and a bipolar Sugeno integral. Moreover, we provide an axiomatic characterization of all three bipolar fuzzy integrals.
Original languageEnglish
Pages (from-to)21-33
JournalFuzzy Sets and Systems
Early online date20 Dec 2012
Publication statusPublished - 1 Jun 2013


  • Non-additive measures
  • Multiple criteria evaluation
  • Bi-capacity
  • Bipolar fuzzy integrals


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