The negation of permutation mass function

TL;DR

This paper introduces a novel negation method for permutation mass functions within evidence theory, analyzing its convergence and effects on uncertainty and dissimilarity, supported by numerical examples.

Contribution

It proposes the first negation approach for permutation mass functions, extending evidence theory and analyzing its properties and implications.

Findings

The negation method converges reliably.

Uncertainty increases after negation.

Dissimilarity trends are systematically analyzed.

Abstract

Negation is an important perspective of knowledge representation. Existing negation methods are mainly applied in probability theory, evidence theory and complex evidence theory. As a generalization of evidence theory, random permutation sets theory may represent information more precisely. However, how to apply the concept of negation to random permutation sets theory has not been studied. In this paper, the negation of permutation mass function is proposed. Moreover, in the negation process, the convergence of proposed negation method is verified. The trends of uncertainty and dissimilarity after each negation operation are investigated. Numerical examples are used to demonstrate the rationality of the proposed method.