On the ratio of fuzzy numbers – exact membership function computation and applications to decision making

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:

• full fuzzy program
• triangular fuzzy number
• fuzzy aggregation
• linear fractional programming
• error approximation
• decision making

JEL Classification:

• C61

Additional information

Bogdana STANOJEVIĆ, obtained her doctoral degree in Mathematics in 2003 from the Romanian Academy. Currently she is researcher at Mathematical Institute of the Serbian Academy of Sciences and Arts. She authored and co-authored more than 40 scientific papers in the field of Operations Research. Her research interests include different aspects of fuzzy optimization, multiple objective optimization, and fractional programming.

Ioan DZIŢAC, obtained his doctoral degree in Information Sciences in 2002 from the Babes-Bolyai University of Cluj-Napoca, Romania. Currently he is professor at Aurel Vlaicu University of Arad, and rector of Agora University of Oradea. He authored and co-authored more than 60 scientific papers in journals and conference proceedings. His research interests include different aspects of Distributed Systems, Fuzzy Logic Applications and Artificial Intelligence.

Simona DZIŢAC, obtained her doctoral degree in Energetic Engineering in 2007 from the University of Oradea. Currently she is an associate professor at University of Oradea. She authored and co-authored more than 40 scientific papers in journals and conference proceedings. Her research interests include different aspects of Fuzzy Methods and Monte Carlo Methods in Reliability.