A goal programming approach for fuzzy multiobjective fractional programming problems

Fuzzy multiple objective fractional programming (FMOFP) is an important technique for solving many real-world problems involving the nature of vagueness, imprecision and/or random. Following the idea of binary behaviour of fuzzy programming (Chang 2007), there may exist a situation where a decision-maker would like to make a decision on FMOFP involving the achievement of fuzzy goals, in which some of them may meet the behaviour of fuzzy programming (i.e. level achieved) or the behaviour of binary programming (i.e. completely not achieved). This is turned into a fuzzy multiple objective mixed binary fractional programming (FMOMBFP) problem. However, to the best of our knowledge, this problem is not well formulated by mathematical programming. Therefore, this article proposes a linearisation strategy to formulate the FMOMBFP problem in which extra binary variable is not required. In addition, achieving the highest membership value of each fuzzy goal defined for the fractional objective function, the proposed method can alleviate the computational difficulties when solving the FMOMBFP problem. To demonstrate the usefulness of the proposed method, a real-world case is also included.