New Dimensions in MCDM with Multi Phase Hyper Neutrosophic Sets

Abstract

This work introduces a new mathematical model of the human brain, the Multi-Phase Neutrosophic set, which is an extension of the Neutrosophic set: which deal with human mind uncertainties on a level-by-level basis, encountering sentimental and emotional activity in the human mind as well as presenting the mathematical expression of Neutrality - a distinct state of human psychology. Firstly, we have built a Neutrality degree for a Neutrosophic set and defined a new modified neutrosophic set called Neutro-intelligent set (NIS) which consist of membership, indeterminacy, neutrality and non-membership. We have built Neutro-Intelligent constructive and mathematical operators such as union, intersection, complement, cross product, and special product as well as two families of cardinality measure called Weighted Possible Cardinality and Weighted Neutral Cardinality. Using these measures we have defined relative sigma count and a Ranking Relation between Neutro-Intelligent Sets. Later, by utilizing the new introduced Neutrality Degree we have built a State/Phase Function –a function giving level wise classifications of human thought which then is employed in defining the initially mentioned Multi-Phase Neutrosophic set. A Neutro-Intelligent version of Multi- Phase Neutrosophic Set namely Final Phase Neutrosophic Set is also introduced in order to incorporate the basic building operations and measures in Multi-Phase Neutrosophic Set Theory and Logic. Moreover, we have worked on implementing a Multi-Phase Neutrosophic set in the MCDM environment, with a specific focus on developing an effective COVID -19 Medical Diagnosis approach.