Possibility of Quadripartitioned Neutrosophic Cubic Sets and Their Application of Multi-Criteria Decision Making

J. Sharmila^1,*, F. Nirmala Irudayam²

Research Scholar, Nirmala College for women, Coimbatore, India

Assistant Professor, Department of Mathematics, Nirmala College for women, Coimbatore, India

Emails: evan.sylin@gmail.com; nirmalairudayam78@gmail.com

Abstract

This study introduces the innovative idea of associating a possibility measure with the membership of an element in a set, and further proposes the structure of quadripartitioned neutrosophic cubic sets (PQNCS). Within this framework, the authors define four distinct components—truth, contradiction, ignorance, and falsity—each in two modes: internal and external. They explore the corresponding sets (truth-internal, contradiction-internal, ignorance-internal, falsity-internal and truth-external, contradiction-external, ignorance-external, falsity-external) and uncover their interrelated properties. Moreover, the work emphasizes the role of a score function as a central instrument for multi-attribute decision-making, and examines how measures of PQNCS—through score, accuracy and certainty functions grounded in the possibility concept—can be employed to support and guide decision-making in the quadripartitioned neutrosophic cubic setting.

Keywords:  Possibility; Internal and external possibility; Multi-attribute decision-making; Score’s comparative function; Accuracy and certainty