An Application of the Modified Subgradient Method for Solving Fuzzy Linear Fractional Programming Problem

2011 ◽  
pp. 115-131
Author(s):  
Pankaj Gupta ◽  
Mukesh Kumar Mehlawat
Keyword(s):  
Programming Problem ◽  
Fractional Programming ◽  
Subgradient Method ◽  
Linear Fractional Programming ◽  
Fractional Programming Problem ◽  
Fuzzy Linear Fractional Programming ◽  
Linear Fractional Programming Problem

scholarly journals ON THE RATIO OF FUZZY NUMBERS – EXACT MEMBERSHIP FUNCTION COMPUTATION AND APPLICATIONS TO DECISION MAKING

2015 ◽  
Vol 21 (5) ◽  
pp. 815-832 ◽  
Author(s):  
Bogdana STANOJEVIĆ ◽  
Ioan DZIŢAC ◽  
Simona DZIŢAC
Keyword(s):  
Decision Making ◽  
Programming Problem ◽  
Membership Function ◽  
Fractional Programming ◽  
Fuzzy Numbers ◽  
Linear Constraints ◽  
Linear Fractional Programming ◽  
Fractional Programming Problem ◽  
Fuzzy Linear Fractional Programming ◽  
Linear Fractional Programming Problem

In the present paper, we propose a new approach to solving the full fuzzy linear fractional programming problem. By this approach, we provide a tool for making good decisions in certain problems in which the goals may be modelled by linear fractional functions under linear constraints; and when only vague data are available. In order to evaluate the membership function of the fractional objective, we use the α-cut interval of a special class of fuzzy numbers, namely the fuzzy numbers obtained as sums of products of triangular fuzzy numbers with positive support. We derive the α-cut interval of the ratio of such fuzzy numbers, compute the exact membership function of the ratio, and introduce a way to evaluate the error that arises when the result is approximated by a triangular fuzzy number. We analyse the effect of this approximation on solving a full fuzzy linear fractional programming problem. We illustrate our approach by solving a special example – a decision-making problem in production planning.

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