Bipolar Fuzzy Integrals

TL;DR

This paper introduces bipolar versions of the Shilkret and Sugeno integrals for decision analysis, extending the bipolar Choquet integral, and provides axiomatic characterizations for these three integrals.

Contribution

It proposes new bipolar fuzzy integrals (Shilkret and Sugeno) and offers axiomatic foundations for all three bipolar integrals, expanding the theoretical framework.

Findings

Introduced bipolar Shilkret integral

Introduced bipolar Sugeno integral

Provided axiomatic characterizations

Abstract

In decision analysis and especially in multiple criteria decision analysis, several non additive integrals have been introduced in the last sixty years. Among them, we remember the Choquet integral, the Shilkret integral and the Sugeno integral. Recently, the bipolar Choquet integral has been proposed for the case in which the underlying scale is bipolar. In this paper we propose the bipolar Shilkret integral and the bipolar Sugeno integral. Moreover, we provide an axiomatic characterization of all these three bipolar fuzzy integrals.