A New Technique to Solve Game Matrix with Neutrosophic  Payoffs

Jitendra Singh; Ritika Chopra; Ratnesh R. Saxena; Pankaj Kumar Garg

Authors

Jitendra Singh Department of Mathematics, University of Delhi, Delhi, India;
Ritika Chopra Department of Mathematics, Shaheed Rajguru College of Applied Sciences For Women, University of Delhi, Delhi, India;
Ratnesh R. Saxena Department of Mathematics, Deen Dayal Upadhyay College, University of Delhi, Delhi, India;
Pankaj Kumar Garg Department of Mathematics, Rajdhani College, University of Delhi, Delhi, India;

Keywords:

Neutrosophic Matrix Game ; Single Valued Trapezoidal Neutrosophic numbers; Zero Sum Two Person Game;( )-cut sets.

Abstract

Matrix games are extensively applied to con icting situations that frequently arise in real world
since it gives the ability to the decision maker to make more informed decisions. However, modeling of such
situations often cannot be done by conventional techniques as the payo s may not be concretely determined due
to uncertainty present in the system. This uncertainty can be handled in numerous ways but neutrosophic set
theory plays an important role in examining intricacy, inadequacy, enigma and self-contradictory parameters in
real life problems. This article develops a more structured technique to solve neutrosophic game matrix with
payo s as Single Valued Trapezoidal Neutrosophic (SVTrN) numbers. This method converts the considered
game matrix to interval valued game matrix problem by using (
)- cut on SVTrN numbers. This interval
valued game matrix problem is further converted to a crisp game matrix (pessimistic, optimistic and moderate
)problem by using a ranking function. Then, these problems are solved by maxmin theorem if saddle point exist.
In case of no saddle point or many saddle points, the problem is solved by converting it to linear programming
primal-dual problem. The proposed technique can be applied to a wider range of game theory problems existing
in practical, as the data encountered in practice is often imprecise with some level of hesitation, inconsistent or
incompleteness which can best be described using single valued neutrosophic number. Numerical illustrations
are provided to demonstrate the methodology and to prove the vitality of the proposed method.