Triangular fuzzy quadripartitioned neutrosophic set and its properties

The main objective of the paper is to hybridize the triangular fuzzy number and the quadripartitioned neutrosophic set and develop the triangular fuzzy quadripartitioned neutrosophic set. The triangular fuzzy numbers have great potential to express uncertainty systematically. So, the combination of the triangular fuzzy numbers and quadripartitioned neutrosophic sets is an intelligent mathematical tool that will be a helpful mathematical tool for decision-making. We define some operations on the triangular fuzzy quadripartitioned neutrosophic sets such as union, intersection, and complement. We establish some important theorems on operations like union, intersection in between three triangular fuzzy quadripartitioned neutrosophic sets in an elaborate way. We have defined unity and null triangular fuzzy quadripartitioned neutrosophic sets and established some mathematical operations on them. We establish some fundamental properties of the developed triangular fuzzy quadripartitioned neutrosophic sets.