Application of Neutrosophic Set Theory in Generalized Assignment Problem

Abstract

This paper presents the application of
Neutrosophic Set Theory (NST) in solving
Generalized Assignment Problem (GAP). GAP has
been solved earlier under fuzzy environment. NST is
a generalization of the concept of classical set, fuzzy
set, interval-valued fuzzy set, intuitionistic fuzzy set.
Elements of Neutrosophic set are characterized by a
truth-membership function, falsity and also
indeterminacy which is a more realistic way of
expressing the parameters in real life problem. Here
the elements of the cost matrix for the GAP are
considered as neutrosophic elements which have not
been considered earlier by any other author. The
problem has been solved by evaluating score
function matrix and then solving it by Extremum
Difference Method (EDM) [1] to get the optimal
assignment. The method has been demonstrated by a
suitable numerical example.