Exponential membership function and duality gaps for I-fuzzy linear programming problems

Abstract

<span class="fontstyle0">Fuzziness is ever presented in real life decision making problems. In this paper, we adapt the pessimistic approach to<br />study a pair of linear primal-dual problem under intuitionistic fuzzy (I-fuzzy) environment and prove certain duality<br />results. We generate the duality results using exponential membership and non-membership functions to represent the<br />decision maker's satisfaction and dissatisfaction level. Further, two numerical examples have been given. In each of<br />these illustrations, varying the values of the shape variables in the exponential membership functions, various nonlinear<br />optimization problems have been constructed, analyzed and solved. The duality gaps for all these optimization problems<br />have been computed and compared with the duality gap under the linear membership function. We found that these<br />gaps for the I-fuzzy linear primal-dual pair under the exponential membership functions are smaller as compared with<br />the linear membership functions. The main advantage of using the exponential membership function is that it has the<br />flexibility of altering the values of the shape parameters (as per the decision-maker's satisfaction). Finally, with the<br />help of a suitable ranking defuzzification function, we have extended our approach to the I-fuzzy linear problem with<br />fuzzy parameters and fuzzy constraints.</span> <br /><br />