|Affiliations:||Mathematical Institute of the Serbian Academy of Sciences and Arts||Title:||On the ratio of fuzzy numbers - exact membership function computation and applications to decision making||Journal:||Technological and Economic Development of Economy||Volume:||21||Issue:||5||First page:||815||Last page:||832||Issue Date:||3-Sep-2015||Rank:||M21a||ISSN:||2029-4913||DOI:||10.3846/20294913.2015.1093563||Abstract:||
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.
|Keywords:||decision making | error approximation | full fuzzy program | fuzzy aggregation | linear fractional programming | triangular fuzzy number||Publisher:||Vilnius Gediminas Technical University Press||Project:||Optimization of Distributive and Reverse Flows in Logistic Systems|
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