The Generalized Pignistic Transformation

TL;DR

This paper introduces the generalized pignistic transformation within the Dezert-Smarandache Theory framework, enabling conversion of belief assignments into subjective probabilities, with detailed focus on the 3D case and validation against probability theory.

Contribution

It provides a detailed formulation of the GPT in DSmT, especially for the 3D case, and demonstrates its validation using probability theory principles.

Findings

GPT effectively converts belief assignments to probabilities

Validation confirms consistency with probability theory

Detailed 3D case analysis provided

Abstract

This paper presents in detail the generalized pignistic transformation (GPT) succinctly developed in the Dezert-Smarandache Theory (DSmT) framework as a tool for decision process. The GPT allows to provide a subjective probability measure from any generalized basic belief assignment given by any corpus of evidence. We mainly focus our presentation on the 3D case and provide the complete result obtained by the GPT and its validation drawn from the probability theory.