The Alternative Representation of the Bipolar Sugeno Integral

Abstract

In the context of decision support systems, bi-capacities were introduced as an extension of classical capacities. Many bipolar fuzzy integrals related to the bi-capacities have been presented in recent years. One of these integrals is the Sugeno integral concerning aggregation on bipolar scales. The paper aims to build an equivalent representation of the bipolar Sugeno integral. Therefore, we first employ in this paper the framework based on a ternary-criterion set for proposing an alternative formula of the bipolar Sugeno integral to be suitable for bipolar scales. Then, we discuss some basic properties and give an illustrative example of this representation. This representation is consistent as an extension of the representation concerning the classical capacities and aggregation on the Sugeno integral unipolar scales.

Keywords

• bi-capacities
• decision support systems
• fuzzy integrals
• bipolar sugeno integral