Intuitionistic Quadri-Partitioned Neutrosophic Sets with  Extended Operators

Sai Anu P; Arulselvam A; Bobin A

Authors

Sai Anu P Department of Mathematics, Bharath Institute of Higher Education and Research, Chennai, Tamilnadu;
Arulselvam A Department of Mathematics, Bharath Institute of Higher Education and Research, Chennai, Tamilnadu;
Bobin A Department of Mathematics, IFET College of Engineering (An Autonomous Institution), Villupuram, Tamilnadu.

Keywords:

soft set; intuitionistic set; neutrosophic set; quadri-partitioned neutrosophic set.

Abstract

We present the concept of intuitionistic quadri-partitioned neutrosophic sets (IQ-PNSs) and extend
it to intuitionistic quadri-partitioned neutrosophic soft sets (IQ-PNSSs). These sets introduce a constraint
where the combined membership values for truth and falsity must not exceed one, while the indeterminacy and
contradiction membership values are restricted to the interval [01], ensuring the total sum of all membership
values remains below three. In addition, we de ne necessity and possibility operators, along with two novel
operators, ( and ), on IQ-PNSSs and explore their properties. Furthermore, we introduce and analyze the
operators
,
, and
, as well as the concentration (CO) and dilation (DO) operators on IQ-PNSSs. This
framework e ectively addresses complex uncertainties, particularly in situations where conventional approaches,
such as those used for modeling ambivalent psychological behaviors, are insu cient.

DOI: 10.5281/zenodo.14708891