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

Document Type : Original Manuscript


1 Indian Institute of Technology Roorkee

2 Indian Institute of Technology, Roorkee


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


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