Penta and Hexa Valued Representation of Neutrosophic Information

TL;DR

This paper introduces a novel penta and hexa valued representation of neutrosophic information, expanding the traditional three-component model to include indices of ignorance, contradiction, hesitation, and ambiguity, along with associated logical operators.

Contribution

It develops a new multi-valued fuzzy framework for neutrosophic data, including the construction of a corresponding logic and operators, extending the representation to six components.

Findings

Defined penta and hexa valued neutrosophic representations

Constructed associated logical operators for the new framework

Extended the model to include ambiguity as a sixth component

Abstract

Starting from the primary representation of neutrosophic information, namely the degree of truth, degree of indeterminacy and degree of falsity, we define a nuanced representation in a penta valued fuzzy space, described by the index of truth, index of falsity, index of ignorance, index of contradiction and index of hesitation. Also, it was constructed an associated penta valued logic and then using this logic, it was defined for the proposed penta valued structure the following operators: union, intersection, negation, complement and dual. Then, the penta valued representation is extended to a hexa valued one, adding the sixth component, namely the index of ambiguity.