Polar Representation of Bipolar Information: A Case Study to Compare Intuitionistic Entropies

Abstract

In this paper, a new approach to compare measures of entropy in the setting of the intuitionistic fuzzy sets introduced by Atanassov. A polar representation is introduced to represent such bipolar information and it is used to study the three main intuitionistic fuzzy sets entropies of the literature. A theoretical comparison and some experimental results highlight the interest of such a representation to gain knowledge on these entropies.

Interpretable Monotonicities for Entropies of Intuitionistic Fuzzy Sets or Interval-valued Fuzzy Sets

“…An IFS A = {(u, µ A (u), ν A (u)) | u ∈ U} can be represented in a cartesian space by the set of points 13,14,15].…”

“…In [15], this polar representation of IFS allows to study the variations of measures of entropy of IFS and it brings a better interpretation of these variations.…”

“…More generally, any definition of monotonicity could be used to define a particular entropy E [3,13,15].…”

“…In [15], three measures of entropy of IFS have been studied in the polar form and we present them in this section.…”

“…In order to enable a more interpretable study of entropies in the IFS/IVFS setting, we introduced a polar representation of these kinds of fuzzy sets [13,15]. Indeed, it is very promising to manipulate and to study such bipolar information represented as polar coordinates [13,15,20] and we can highlight the gain in interpretability it allows.…”