Duality in Linear Fractional Programming Under Fuzzy Environment Using Hyperbolic Membership Functions

2020 ◽  
Vol 9 (3) ◽  
pp. 1-21
Author(s):  
Pratiksha Saxena
Keyword(s):  
Programming Problem ◽  
Fractional Programming ◽  
Dual Problem ◽  
Aspiration Level ◽  
Membership Functions ◽  
Linear Fractional Programming ◽  
Duality Results ◽  
Fuzzy Environment ◽  
Degree Of Satisfaction ◽  
Linear Fractional Programming Problem

A linear fractional programming problem and its dual problem is presented under fuzzy environment. Appropriate fuzzy version of duality results are established using an aspiration level approach. This study uses the hyperbolic membership functions to represent fulfillment of the decision maker's degree of satisfaction in contrast to available literature which relied on linear membership functions/exponential membership functions.

A New Ranking Approach for Interval Valued Intuitionistic Fuzzy Sets and its Application in Decision Making

2019 ◽  
Vol 8 (2) ◽  
pp. 89-104 ◽  
Author(s):  
Pranjal Talukdar ◽  
Palash Dutta
Keyword(s):  
Intuitionistic Fuzzy Sets ◽  
Aspiration Level ◽  
Membership Functions ◽  
Hyperbolic Tangent ◽  
Numerical Examples ◽  
Duality Results ◽  
Fuzzy Environment ◽  
Degree Of Satisfaction ◽  
Primal Dual ◽  
Interval Valued

In this article, a pair of primal-dual problems of linear programming are presented under a fuzzy environment. The appropriate duality results are established using aspiration level approach. This study uses the hyperbolic tangent membership functions to represent fulfilment of the decision maker's degree of satisfaction in contrast to available literature which relied on linear membership functions. The solutions obtained from the use of hyperbolic tangent membership functions are elicited through a comparison of solutions obtained by employing linear membership functions. The demonstration of approach and verification of results is presented through numerical examples.

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