Extension principle based on neutrosophic multi-sets and algebraic operations

Abstract

The Smaradanche's neutrosophic set theory has become a popular topic of investigation in the fuzzyand intuitionistic community. However, there is less investigation on the cut sets and extension principlesfor neutrosophic sets and neutrosophic multi-sets, as well as algebraic operations. In this paper, we first proposed the extension principles of neutrosophic multi-sets and cut sets which is a bridge betweenneutrosophic multi-sets and crisp sets. Then the representation theorem of neutrosophic multi-setsbased on cut sets are studied. Finally, the addition, subtraction, multiplication and division operationsover neutrosophic multi-sets are defined based on the extension principle.