Authors: Stanojević, Bogdana 
Dzitac, Ioan
Dzitac, Simona
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
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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