Solution of Fuzzy Multi-Objective Fractional Linear Programming Problem Using Fuzzy Programming Technique based on Exponential Membership Function

2018 ◽  
Vol 37e (1) ◽  
pp. 109
Author(s):  
Priyadarsini Rath ◽  
Rajani B. Dash ◽  
Swapan Kumar Ghosh
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Membership Function ◽  
Linear Programming Problem ◽  
Fuzzy Programming ◽  
Programming Technique ◽  
Multi Objective ◽  
Fractional Linear Programming

scholarly journals A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem

2017 ◽  
Vol 27 (3) ◽  
pp. 563-573 ◽  
Author(s):  
Rajendran Vidhya ◽  
Rajkumar Irene Hepzibah
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Method ◽  
Arithmetic Operations ◽  
Intuitionistic Fuzzy Numbers ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

AbstractIn a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers (IVIFNs) are often used in order to represent a range of IFNs unstable from the most pessimistic evaluation to the most optimistic one. IVIFNs are a construction which helps us to avoid such a prohibitive complexity. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers (IVIFNs) to solve the interval valued intuitionistic fuzzy multi-objective linear programming problem with pentagonal intuitionistic fuzzy numbers (PIFNs) by assuming differentαandβcut values in a comparative manner. The objective functions involved in the problem are ranked by the ratio ranking method and the problem is solved by the preemptive optimization method. An illustrative example with MATLAB outputs is presented in order to clarify the potential approach.

scholarly journals Generalized Transformation Techniques for Multi-Choice Linear Programming Problems

2012 ◽  
Vol 3 (1) ◽  
pp. 45-54 ◽  
Author(s):  
Srikumar ACHARYA ◽  
Mitali Madhumita ACHARYA
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Decision Maker ◽  
Linear Programming Problem ◽  
Programming Model ◽  
Mixed Integer ◽  
Transformation Techniques ◽  
Programming Technique ◽  
Binary Variables ◽  
Non Linear

The multi-choice programming allows the decision maker to consider multiple number of resources for each constraint or goal. Multi-choice linear programming problem can not be solved directly using the traditional linear programming technique. However, to deal with the multi-choice parameters, multiplicative terms of binary variables may be used in the transformed mathematical model. Recently, Biswal and Acharya (2009) have proposed a methodology to transform the multi-choice linear programming problem to an equivalent mathematical programming model, which can accommodate a maximum of eight goals in righthand side of any constraint. In this paper we present two models as generalized transformation of the multi-choice linear programming problem. Using any one of the transformation techniques a decision maker can handle a parameter with nite number of choices. Binary variables are introduced to formulate a non-linear mixed integer programming model. Using a non-linear programming software optimal solution of the proposed model can be obtained. Finally, a numerical example is presented to illustrate the transformation technique and the solution procedure.

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